{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "c47ebc4d-d172-4e70-9e16-cf6a0ba7153a",
   "metadata": {},
   "source": [
    "# GLM for Between Subjects Data - R"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4ecefac5-3aac-4309-a413-d1e62eb0fc81",
   "metadata": {},
   "source": [
    "## GLM for Normal Distribution Data\n",
    "\n",
    "* **Distribution:** Normal\n",
    "* **Link:** identity\n",
    "* **Typical Uses:** Linear Regression: equivalent to linear (mixed) model (`lm` / `lmm`)\n",
    "* **Reporting:** \"Figure 12a shows an interaction plot with ±1 standard deviation error bars for X1 and X2. An analysis of variance based on linear regression indicated a statistically significant effect on Y of X1 (F(1, 56) = 7.06, p < .05), but not of X2 (F(1, 56) = 1.02, n.s.). Also, the X1×X2 interaction was not statistically significant (F(1, 56) = 2.74, n.s.).\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "c7fa707e-af25-4dab-a4f6-cddd99a5ca4e",
   "metadata": {
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   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 20 × 4</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>S</th><th scope=col>X1</th><th scope=col>X2</th><th scope=col>Y</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td> 1</td><td>a</td><td>a</td><td> 9.587838</td></tr>\n",
       "\t<tr><th scope=row>2</th><td> 2</td><td>a</td><td>b</td><td> 9.217284</td></tr>\n",
       "\t<tr><th scope=row>3</th><td> 3</td><td>b</td><td>a</td><td>10.663489</td></tr>\n",
       "\t<tr><th scope=row>4</th><td> 4</td><td>b</td><td>b</td><td>14.932123</td></tr>\n",
       "\t<tr><th scope=row>5</th><td> 5</td><td>a</td><td>a</td><td> 5.157908</td></tr>\n",
       "\t<tr><th scope=row>6</th><td> 6</td><td>a</td><td>b</td><td>11.025094</td></tr>\n",
       "\t<tr><th scope=row>7</th><td> 7</td><td>b</td><td>a</td><td>10.741292</td></tr>\n",
       "\t<tr><th scope=row>8</th><td> 8</td><td>b</td><td>b</td><td> 3.169121</td></tr>\n",
       "\t<tr><th scope=row>9</th><td> 9</td><td>a</td><td>a</td><td>10.863238</td></tr>\n",
       "\t<tr><th scope=row>10</th><td>10</td><td>a</td><td>b</td><td> 6.244845</td></tr>\n",
       "\t<tr><th scope=row>11</th><td>11</td><td>b</td><td>a</td><td>14.949621</td></tr>\n",
       "\t<tr><th scope=row>12</th><td>12</td><td>b</td><td>b</td><td>10.081778</td></tr>\n",
       "\t<tr><th scope=row>13</th><td>13</td><td>a</td><td>a</td><td> 6.167002</td></tr>\n",
       "\t<tr><th scope=row>14</th><td>14</td><td>a</td><td>b</td><td> 7.761871</td></tr>\n",
       "\t<tr><th scope=row>15</th><td>15</td><td>b</td><td>a</td><td>12.335185</td></tr>\n",
       "\t<tr><th scope=row>16</th><td>16</td><td>b</td><td>b</td><td> 8.212590</td></tr>\n",
       "\t<tr><th scope=row>17</th><td>17</td><td>a</td><td>a</td><td> 6.552768</td></tr>\n",
       "\t<tr><th scope=row>18</th><td>18</td><td>a</td><td>b</td><td>10.075766</td></tr>\n",
       "\t<tr><th scope=row>19</th><td>19</td><td>b</td><td>a</td><td>13.765247</td></tr>\n",
       "\t<tr><th scope=row>20</th><td>20</td><td>b</td><td>b</td><td> 9.038398</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 20 × 4\n",
       "\\begin{tabular}{r|llll}\n",
       "  & S & X1 & X2 & Y\\\\\n",
       "  & <int> & <chr> & <chr> & <dbl>\\\\\n",
       "\\hline\n",
       "\t1 &  1 & a & a &  9.587838\\\\\n",
       "\t2 &  2 & a & b &  9.217284\\\\\n",
       "\t3 &  3 & b & a & 10.663489\\\\\n",
       "\t4 &  4 & b & b & 14.932123\\\\\n",
       "\t5 &  5 & a & a &  5.157908\\\\\n",
       "\t6 &  6 & a & b & 11.025094\\\\\n",
       "\t7 &  7 & b & a & 10.741292\\\\\n",
       "\t8 &  8 & b & b &  3.169121\\\\\n",
       "\t9 &  9 & a & a & 10.863238\\\\\n",
       "\t10 & 10 & a & b &  6.244845\\\\\n",
       "\t11 & 11 & b & a & 14.949621\\\\\n",
       "\t12 & 12 & b & b & 10.081778\\\\\n",
       "\t13 & 13 & a & a &  6.167002\\\\\n",
       "\t14 & 14 & a & b &  7.761871\\\\\n",
       "\t15 & 15 & b & a & 12.335185\\\\\n",
       "\t16 & 16 & b & b &  8.212590\\\\\n",
       "\t17 & 17 & a & a &  6.552768\\\\\n",
       "\t18 & 18 & a & b & 10.075766\\\\\n",
       "\t19 & 19 & b & a & 13.765247\\\\\n",
       "\t20 & 20 & b & b &  9.038398\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 20 × 4\n",
       "\n",
       "| <!--/--> | S &lt;int&gt; | X1 &lt;chr&gt; | X2 &lt;chr&gt; | Y &lt;dbl&gt; |\n",
       "|---|---|---|---|---|\n",
       "| 1 |  1 | a | a |  9.587838 |\n",
       "| 2 |  2 | a | b |  9.217284 |\n",
       "| 3 |  3 | b | a | 10.663489 |\n",
       "| 4 |  4 | b | b | 14.932123 |\n",
       "| 5 |  5 | a | a |  5.157908 |\n",
       "| 6 |  6 | a | b | 11.025094 |\n",
       "| 7 |  7 | b | a | 10.741292 |\n",
       "| 8 |  8 | b | b |  3.169121 |\n",
       "| 9 |  9 | a | a | 10.863238 |\n",
       "| 10 | 10 | a | b |  6.244845 |\n",
       "| 11 | 11 | b | a | 14.949621 |\n",
       "| 12 | 12 | b | b | 10.081778 |\n",
       "| 13 | 13 | a | a |  6.167002 |\n",
       "| 14 | 14 | a | b |  7.761871 |\n",
       "| 15 | 15 | b | a | 12.335185 |\n",
       "| 16 | 16 | b | b |  8.212590 |\n",
       "| 17 | 17 | a | a |  6.552768 |\n",
       "| 18 | 18 | a | b | 10.075766 |\n",
       "| 19 | 19 | b | a | 13.765247 |\n",
       "| 20 | 20 | b | b |  9.038398 |\n",
       "\n"
      ],
      "text/plain": [
       "   S  X1 X2 Y        \n",
       "1   1 a  a   9.587838\n",
       "2   2 a  b   9.217284\n",
       "3   3 b  a  10.663489\n",
       "4   4 b  b  14.932123\n",
       "5   5 a  a   5.157908\n",
       "6   6 a  b  11.025094\n",
       "7   7 b  a  10.741292\n",
       "8   8 b  b   3.169121\n",
       "9   9 a  a  10.863238\n",
       "10 10 a  b   6.244845\n",
       "11 11 b  a  14.949621\n",
       "12 12 b  b  10.081778\n",
       "13 13 a  a   6.167002\n",
       "14 14 a  b   7.761871\n",
       "15 15 b  a  12.335185\n",
       "16 16 b  b   8.212590\n",
       "17 17 a  a   6.552768\n",
       "18 18 a  b  10.075766\n",
       "19 19 b  a  13.765247\n",
       "20 20 b  b   9.038398"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Example data\n",
    "# df has subjects (S), two between-Ss factors (X1,X2) each w/levels (a,b), and continuous response (Y)\n",
    "df <- read.csv(\"data/2F2LBs_normal.csv\")\n",
    "head(df, 20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "16232a79-412b-4f96-9665-843bb01774b7",
   "metadata": {
    "vscode": {
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   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Loading required package: carData\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A anova: 4 × 4</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>Sum Sq</th><th scope=col>Df</th><th scope=col>F values</th><th scope=col>Pr(&gt;F)</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>X1</th><td> 61.014582</td><td> 1</td><td>7.061331</td><td>0.01024486</td></tr>\n",
       "\t<tr><th scope=row>X2</th><td>  8.787594</td><td> 1</td><td>1.017005</td><td>0.31756830</td></tr>\n",
       "\t<tr><th scope=row>X1:X2</th><td> 23.639063</td><td> 1</td><td>2.735793</td><td>0.10371815</td></tr>\n",
       "\t<tr><th scope=row>Residuals</th><td>483.877154</td><td>56</td><td>      NA</td><td>        NA</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A anova: 4 × 4\n",
       "\\begin{tabular}{r|llll}\n",
       "  & Sum Sq & Df & F values & Pr(>F)\\\\\n",
       "  & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\tX1 &  61.014582 &  1 & 7.061331 & 0.01024486\\\\\n",
       "\tX2 &   8.787594 &  1 & 1.017005 & 0.31756830\\\\\n",
       "\tX1:X2 &  23.639063 &  1 & 2.735793 & 0.10371815\\\\\n",
       "\tResiduals & 483.877154 & 56 &       NA &         NA\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A anova: 4 × 4\n",
       "\n",
       "| <!--/--> | Sum Sq &lt;dbl&gt; | Df &lt;dbl&gt; | F values &lt;dbl&gt; | Pr(&gt;F) &lt;dbl&gt; |\n",
       "|---|---|---|---|---|\n",
       "| X1 |  61.014582 |  1 | 7.061331 | 0.01024486 |\n",
       "| X2 |   8.787594 |  1 | 1.017005 | 0.31756830 |\n",
       "| X1:X2 |  23.639063 |  1 | 2.735793 | 0.10371815 |\n",
       "| Residuals | 483.877154 | 56 |       NA |         NA |\n",
       "\n"
      ],
      "text/plain": [
       "          Sum Sq     Df F values Pr(>F)    \n",
       "X1         61.014582  1 7.061331 0.01024486\n",
       "X2          8.787594  1 1.017005 0.31756830\n",
       "X1:X2      23.639063  1 2.735793 0.10371815\n",
       "Residuals 483.877154 56       NA         NA"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(car) # for Anova\n",
    "df$S = factor(df$S)\n",
    "df$X1 = factor(df$X1)\n",
    "df$X2 = factor(df$X2)\n",
    "contrasts(df$X1) <- \"contr.sum\"\n",
    "contrasts(df$X2) <- \"contr.sum\"\n",
    "m = glm(Y ~ X1*X2, data=df, family=gaussian)\n",
    "Anova(m, type=3, test.statistic=\"F\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "a5b211d2-4b30-4357-b80c-6c814c9302fa",
   "metadata": {
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    }
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   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(ggplot2)\n",
    "library(ggthemes)\n",
    "library(scales)\n",
    "library(plyr)\n",
    "\n",
    "# Interaction plot\n",
    "# http://www.sthda.com/english/wiki/ggplot2-line-plot-quick-start-guide-r-software-and-data-visualization\n",
    "# http://www.sthda.com/english/wiki/ggplot2-error-bars-quick-start-guide-r-software-and-data-visualization\n",
    "# http://www.sthda.com/english/wiki/ggplot2-point-shapes\n",
    "# http://www.sthda.com/english/wiki/ggplot2-line-types-how-to-change-line-types-of-a-graph-in-r-software\n",
    "df2 <- ddply(df, ~ X1*X2, function(d) # make a summary data table\n",
    "  c(NROW(d$Y),\n",
    "    sum(is.na(d$Y)),\n",
    "    sum(!is.na(d$Y)),\n",
    "    mean(d$Y, na.rm=TRUE),\n",
    "    sd(d$Y, na.rm=TRUE),\n",
    "    median(d$Y, na.rm=TRUE),\n",
    "    IQR(d$Y, na.rm=TRUE)))\n",
    "colnames(df2) <- c(\"X1\",\"X2\",\"Rows\",\"NAs\",\"NotNAs\",\"Mean\",\"SD\",\"Median\",\"IQR\")\n",
    "ggplot(data=df2, aes(x=X1, y=Mean, color=X2, group=X2)) + theme_minimal() + \n",
    "  # set the font styles for the plot title and axis titles\n",
    "  theme(plot.title   = element_text(face=\"bold\",  color=\"black\", size=18, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.title.x = element_text(face=\"bold\",  color=\"black\", size=16, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.title.y = element_text(face=\"bold\",  color=\"black\", size=16, hjust=0.5, vjust=0.0, angle=90)) + \n",
    "  # set the font styles for the value labels that show on each axis\n",
    "  theme(axis.text.x  = element_text(face=\"plain\", color=\"black\", size=14, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.text.y  = element_text(face=\"plain\", color=\"black\", size=12, hjust=0.0, vjust=0.5, angle=0)) + \n",
    "  # set the font styles for the legend\n",
    "  theme(legend.title = element_text(face=\"bold\", color=\"black\", size=14, hjust=0.5, vjust=0.0, angle=0)) +\n",
    "  theme(legend.text  = element_text(face=\"plain\", color=\"black\", size=14, hjust=0.5, vjust=0.0, angle=0)) +\n",
    "  # create the plot lines, points, and error bars\n",
    "  geom_line(aes(linetype=X2), position=position_dodge(0.05)) + \n",
    "  geom_point(aes(shape=X2, size=X2), position=position_dodge(0.05)) + \n",
    "  geom_errorbar(aes(ymin=Mean-SD, ymax=Mean+SD), position=position_dodge(0.05), width=0.1) + \n",
    "  # place text labels on each bar\n",
    "  geom_text(aes(label=sprintf(\"%.2f (±%.2f)\", Mean, SD)), position=position_dodge(0.05), hjust=0.0, vjust=-1.0, color=\"black\", size=3.5) +\n",
    "  # set the labels for the title and each axis\n",
    "  labs(title=\"Y by X1, X2\", x=\"X1\", y=\"Y\") + \n",
    "  # set the ranges and value labels for each axis\n",
    "  scale_x_discrete(labels=c(\"a\",\"b\")) + \n",
    "  scale_y_continuous(breaks=seq(0,14,by=2), labels=seq(0,14,by=2), limits=c(0,14), oob=rescale_none) + \n",
    "  # set the name, labels, and colors for the traces\n",
    "  scale_color_manual(name=\"X2\", labels=c(\"a\",\"b\"), values=c(\"red\", \"blue\")) +\n",
    "  # set the size and shape of the points\n",
    "  scale_size_manual(values=c(4,4)) +\n",
    "  scale_shape_manual(values=c(16,10)) +\n",
    "  # set the linetype of the lines\n",
    "  scale_linetype_manual(values=c(\"solid\", \"longdash\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d84b1373-ff55-4fb7-9396-a2a0cbe42a07",
   "metadata": {},
   "source": [
    "## GLM for Binomial Distribution Data\n",
    "\n",
    "* **Distribution:** Binomial\n",
    "* **Link:** logit\n",
    "* **Typical Uses:** Logistic Regression: dichotomous responses (i.e. nominal responses with two categories)\n",
    "* **Reporting:** \"Figure 13a shows the number of ‘x’ and ‘y’ outcomes for each level of X1 and X2. An analysis of variance based on logistic regression indicated a statistically significant effect on Y of X1 (χ2(1, N=60) = 6.05, p < .05) and of the X1×X2 interaction (χ2(1, N=60) = 8.63, p < .01), but not of X2 (χ2(1, N=60) = 2.27, n.s.)\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "e82bf306-c599-462c-8f9c-34e7ce353aa5",
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 20 × 4</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>S</th><th scope=col>X1</th><th scope=col>X2</th><th scope=col>Y</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td> 1</td><td>a</td><td>a</td><td>x</td></tr>\n",
       "\t<tr><th scope=row>2</th><td> 2</td><td>a</td><td>b</td><td>y</td></tr>\n",
       "\t<tr><th scope=row>3</th><td> 3</td><td>b</td><td>a</td><td>y</td></tr>\n",
       "\t<tr><th scope=row>4</th><td> 4</td><td>b</td><td>b</td><td>y</td></tr>\n",
       "\t<tr><th scope=row>5</th><td> 5</td><td>a</td><td>a</td><td>x</td></tr>\n",
       "\t<tr><th scope=row>6</th><td> 6</td><td>a</td><td>b</td><td>y</td></tr>\n",
       "\t<tr><th scope=row>7</th><td> 7</td><td>b</td><td>a</td><td>y</td></tr>\n",
       "\t<tr><th scope=row>8</th><td> 8</td><td>b</td><td>b</td><td>x</td></tr>\n",
       "\t<tr><th scope=row>9</th><td> 9</td><td>a</td><td>a</td><td>x</td></tr>\n",
       "\t<tr><th scope=row>10</th><td>10</td><td>a</td><td>b</td><td>y</td></tr>\n",
       "\t<tr><th scope=row>11</th><td>11</td><td>b</td><td>a</td><td>x</td></tr>\n",
       "\t<tr><th scope=row>12</th><td>12</td><td>b</td><td>b</td><td>x</td></tr>\n",
       "\t<tr><th scope=row>13</th><td>13</td><td>a</td><td>a</td><td>x</td></tr>\n",
       "\t<tr><th scope=row>14</th><td>14</td><td>a</td><td>b</td><td>x</td></tr>\n",
       "\t<tr><th scope=row>15</th><td>15</td><td>b</td><td>a</td><td>x</td></tr>\n",
       "\t<tr><th scope=row>16</th><td>16</td><td>b</td><td>b</td><td>x</td></tr>\n",
       "\t<tr><th scope=row>17</th><td>17</td><td>a</td><td>a</td><td>y</td></tr>\n",
       "\t<tr><th scope=row>18</th><td>18</td><td>a</td><td>b</td><td>x</td></tr>\n",
       "\t<tr><th scope=row>19</th><td>19</td><td>b</td><td>a</td><td>y</td></tr>\n",
       "\t<tr><th scope=row>20</th><td>20</td><td>b</td><td>b</td><td>x</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 20 × 4\n",
       "\\begin{tabular}{r|llll}\n",
       "  & S & X1 & X2 & Y\\\\\n",
       "  & <int> & <chr> & <chr> & <chr>\\\\\n",
       "\\hline\n",
       "\t1 &  1 & a & a & x\\\\\n",
       "\t2 &  2 & a & b & y\\\\\n",
       "\t3 &  3 & b & a & y\\\\\n",
       "\t4 &  4 & b & b & y\\\\\n",
       "\t5 &  5 & a & a & x\\\\\n",
       "\t6 &  6 & a & b & y\\\\\n",
       "\t7 &  7 & b & a & y\\\\\n",
       "\t8 &  8 & b & b & x\\\\\n",
       "\t9 &  9 & a & a & x\\\\\n",
       "\t10 & 10 & a & b & y\\\\\n",
       "\t11 & 11 & b & a & x\\\\\n",
       "\t12 & 12 & b & b & x\\\\\n",
       "\t13 & 13 & a & a & x\\\\\n",
       "\t14 & 14 & a & b & x\\\\\n",
       "\t15 & 15 & b & a & x\\\\\n",
       "\t16 & 16 & b & b & x\\\\\n",
       "\t17 & 17 & a & a & y\\\\\n",
       "\t18 & 18 & a & b & x\\\\\n",
       "\t19 & 19 & b & a & y\\\\\n",
       "\t20 & 20 & b & b & x\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 20 × 4\n",
       "\n",
       "| <!--/--> | S &lt;int&gt; | X1 &lt;chr&gt; | X2 &lt;chr&gt; | Y &lt;chr&gt; |\n",
       "|---|---|---|---|---|\n",
       "| 1 |  1 | a | a | x |\n",
       "| 2 |  2 | a | b | y |\n",
       "| 3 |  3 | b | a | y |\n",
       "| 4 |  4 | b | b | y |\n",
       "| 5 |  5 | a | a | x |\n",
       "| 6 |  6 | a | b | y |\n",
       "| 7 |  7 | b | a | y |\n",
       "| 8 |  8 | b | b | x |\n",
       "| 9 |  9 | a | a | x |\n",
       "| 10 | 10 | a | b | y |\n",
       "| 11 | 11 | b | a | x |\n",
       "| 12 | 12 | b | b | x |\n",
       "| 13 | 13 | a | a | x |\n",
       "| 14 | 14 | a | b | x |\n",
       "| 15 | 15 | b | a | x |\n",
       "| 16 | 16 | b | b | x |\n",
       "| 17 | 17 | a | a | y |\n",
       "| 18 | 18 | a | b | x |\n",
       "| 19 | 19 | b | a | y |\n",
       "| 20 | 20 | b | b | x |\n",
       "\n"
      ],
      "text/plain": [
       "   S  X1 X2 Y\n",
       "1   1 a  a  x\n",
       "2   2 a  b  y\n",
       "3   3 b  a  y\n",
       "4   4 b  b  y\n",
       "5   5 a  a  x\n",
       "6   6 a  b  y\n",
       "7   7 b  a  y\n",
       "8   8 b  b  x\n",
       "9   9 a  a  x\n",
       "10 10 a  b  y\n",
       "11 11 b  a  x\n",
       "12 12 b  b  x\n",
       "13 13 a  a  x\n",
       "14 14 a  b  x\n",
       "15 15 b  a  x\n",
       "16 16 b  b  x\n",
       "17 17 a  a  y\n",
       "18 18 a  b  x\n",
       "19 19 b  a  y\n",
       "20 20 b  b  x"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Example data\n",
    "# df has subjects (S), two factors (X1,X2) each w/levels (a,b), and dichotomous response (Y)\n",
    "df <- read.csv(\"data/2F2LBs_binomial.csv\")\n",
    "head(df, 20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "20cf307a-8418-47c8-9a9e-847609d18bb3",
   "metadata": {
    "tags": [],
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A anova: 3 × 3</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>LR Chisq</th><th scope=col>Df</th><th scope=col>Pr(&gt;Chisq)</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>X1</th><td>6.045796</td><td>1</td><td>0.013939447</td></tr>\n",
       "\t<tr><th scope=row>X2</th><td>2.268063</td><td>1</td><td>0.132064859</td></tr>\n",
       "\t<tr><th scope=row>X1:X2</th><td>8.631018</td><td>1</td><td>0.003304868</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A anova: 3 × 3\n",
       "\\begin{tabular}{r|lll}\n",
       "  & LR Chisq & Df & Pr(>Chisq)\\\\\n",
       "  & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\tX1 & 6.045796 & 1 & 0.013939447\\\\\n",
       "\tX2 & 2.268063 & 1 & 0.132064859\\\\\n",
       "\tX1:X2 & 8.631018 & 1 & 0.003304868\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A anova: 3 × 3\n",
       "\n",
       "| <!--/--> | LR Chisq &lt;dbl&gt; | Df &lt;dbl&gt; | Pr(&gt;Chisq) &lt;dbl&gt; |\n",
       "|---|---|---|---|\n",
       "| X1 | 6.045796 | 1 | 0.013939447 |\n",
       "| X2 | 2.268063 | 1 | 0.132064859 |\n",
       "| X1:X2 | 8.631018 | 1 | 0.003304868 |\n",
       "\n"
      ],
      "text/plain": [
       "      LR Chisq Df Pr(>Chisq) \n",
       "X1    6.045796 1  0.013939447\n",
       "X2    2.268063 1  0.132064859\n",
       "X1:X2 8.631018 1  0.003304868"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(car) # for Anova\n",
    "df$S = factor(df$S)\n",
    "df$X1 = factor(df$X1)\n",
    "df$X2 = factor(df$X2)\n",
    "df$Y = factor(df$Y) # nominal response\n",
    "contrasts(df$X1) <- \"contr.sum\"\n",
    "contrasts(df$X2) <- \"contr.sum\"\n",
    "m = glm(Y ~ X1*X2, data=df, family=binomial)\n",
    "Anova(m, type=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "0cb032fc-ec12-4dcd-b960-9e8a3dc29f8c",
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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QCWEHABAJYQcAEAlhBwAQCWEHABAJYQcAEAlhBwAQCWEHABAJYQcAEAlhBwAQCWEHABAJYQcAEAlhBwAQCWEHABAJYQcAEAlhBwAQCWEHABAJYQcAEAlhBwAQCWEHABAJYQcAEAlhBwAQCWEHABAJYQcAEAlhBwAQCWEHABAJYQcAEAlhBwAQCWEHABAJYQcAEAlhBwAQCWEHABAJYQcAEAlhBwAQCWEHABAJYQcAEAlhBwAQCWEHABAJYQcAEAlhBwAQCWEHABAJYQcAEAlhBwAQCWEHABAJYQcAEAlhBwAQCWEHABAJYQcAEAlhBwAQifSFXdmYF8/dqmN2IrHBVT/Nf8v0B3ZL1KTXZd+nZVIAgIyQk5ZXLf7usdMPPv7OH0NhTbcWFRWF0Kz3ASdv32W+6zv3aZeS6QAAMlI6wm7q4APWP+jdtY5/6vOtn+u5z6ML3V5UVBRCh+1Pv+qqDdIwHQBAhkrHptjynJ7HPzf8g1v7rVpQ4+1FRUUhtG7dOsVjAQBktnSssWu7z+XXLu72oqKiEFZt3TqEUDFj3O9FiTYdl22Rnm3GAACZown2UsWUKTNCmPHxjf1uvf35ryeVhZDVapWtBlxy81UHr9Vs0Q8rKytL3YyZpqKiIoRQXl6eSCTSPQuNIplMhhDKysqyshzqHq1kMumDLlZVb+HKykqLeDFycnL8FftLTTDsioqKQgifPfFYm0NPGnTqyq2m/O/NB28ZfPMhfb6bMey/x3SrcZFWVlZOmTIlxYNmnOLi4nSPQOOaNm1aukegcfmgi1tZWZlFvBiFhYW5ubnpnqKpa4Jh13z7C5966sQ2a++47Rotq6458qSDevVd/+zXzr3klcMe2iW/hsckEokWLVqkdMyMUlpaWlZWVlBQkJ2dne5ZaBSzZs2qqKho3ry5f87Gqri4OJFINGu2mO0WZLBkMllcXJyTk5OfX9MfOUIIIfgTtiSaYNg1W32bfqvPf1Vuj1NP3eX8A//9zjsjwi4b1vAYn3eLV7UFJy8vLy8vL92z0CjKysoqKioKCgpsio3VzJkzfdBFrLKysri4ODs72yKmnjLlb0Behw6tQ5g+fXq6BwEAaKqaXthN/+a526+97NHP5999dPy3304IoWvXrmmaCgCgyWt6m2KbT3nzijP/NalPQa83/rFW1a4GleNfOufad0NWr733XCXN0wEANFlpCLuJ79xyzSu/hhBCGDm8PISxQwadU1QYQgiddz7z5C3bbXbOzf2f3+ehMzfp+cZ+e264fNb4b9985t+fjW+54cC7Tl99sc8MALA0S1SdOyeV/u+qDVY7d1hNt6x75Y/Dz1k1hFD+2/v3XnPNvS8N+79fxhXnte/We9t9TrnwrD1Xb57iUaNRXFxcXFy8zDLLOHgiVlOnTi0tLW3btq2DJ2I1adKkRCLRpk2bdA9Co6isrJw0aVJ+fn6rVq3SPQuZLQ1hR+oJu+gJu+gJu7gJOxqKvwEAAJEQdgAAkRB2AACREHYAAJEQdgAAkRB2AACREHYAAJEQdgAAkRB2AACREHYAAJEQdgAAkRB2AACREHYAAJEQdgAAkRB2AACREHYAAJEQdgAAkRB2AACREHYAAJEQdgAAkRB2AACREHYAAJEQdgAAkRB2AACREHYAAJEQdgAAkRB2AACREHYAAJEQdgAAkchJ9wAZ6bERH6V7hNopLy/fpcua6Z4CAGhc1tgBAERC2AEARELYpdH0UYMvOH2jTQ87791F3GHCW8dvf9C6/Z8fk9KxAIAMZR+79EgWffXShRc9832rDs0WeZ/JLwx67ONZ2SmcCgDIaNbYpcf01+4dUva3c568dKN2i7jHxNfuv2Z4z322bZnSuQCADCbs0qNgi3OvuO3wNdokFnF70YdXXP/dOqf037F1SscCADKZsEuP3I4dl1n0737a69c/9OHqB1+wW5sUjgQAZDr72DU9U9976Ir3u5z26JbLhfB7uocBADKHNXZNzfQvrr562MrHHdmvU7onAQAyjDV2TcvMD/5175tdDnyy37KL2vsOAGARhF3T8v2Q1yYXlzz4t74Pzr4iWRmST+7R56kNTr/97r0dIQsALIawa1q6n3jfoP6Vcy9///DA87/t+68rt165ffP0TQUAZARhlxYVk3/48o9pIYQ/x88MlRNHfvdZyxBC8y5rd+2w0god5rnjtMLskF/YZZUVlk/TpABA5hB2aTHz8+tOuO/jOZd+u+uyj0IIofs5L15wwKJOWAwA8BeEXVq03PauD7ddkjuud+ptXzb2MABAJJzuBAAgEsIOACASwg4AIBLCDgAgEsIOACASwg4AIBLCDgAgEsIOACASwg4AIBLCDgAgEsIOACASwg4AIBLCDgAgEsIOACASwg4AIBLCDgAgEsIOACASwg4AIBLCDgAgEsIOACASwg4AIBLCDgAgEsIOACASwg4AIBLCDgAgEsIOACASwg4AIBLCDgAgEsIOACASwg4AIBLCDgAgEsIOACASwg4AIBLCDgAgEsIOACASwg4AIBLCDgAgEsIOACASwg4AIBLCDgAgEjnpHqDBlJWVpey1KisrU/ZaDSKZTIYQysvLE4lEumehUVQt4rKysqws/1qLVjKZTOUHHalU9RaurKy0iBcjJyfHX7G/FEnYJZPJkpKSlL1cRUVFyl6rQVT/1c+4JGUJVf0/WVpa6lMvVlXv4lR+0JFK1WFnES9GVlZWdnZ2uqdo6iIJu0Qi0bJly5S9XG5ubspeq0GUl5eHEJo1a5aXl5fuWWgUU6dOLS0tbdGihTV2saqq9lR+0JFKVUmXk5NjEVNP/gYAAERC2AEARELYAQBEQtgBAERC2AEARELYAQBEQtgBAERC2AEARELYAQBEQtgBAERC2AEARELYAQBEQtgBAERC2AEARELYAQBEQtgBAERC2AEARELYAQBEQtgBAERC2AEARELYAQBEQtgBAERC2AEARELYAQBEQtgBAERC2AEARELYAQBEQtgBAERC2AEARELYAQBEQtgBAERC2AEARELYAQBEQtgBAERC2AEARELYAQBEQtgBAERC2AEARELYAQBEQtgBAERC2AEARELYAQBEQtgBAERC2AEARELYAQBEQtgBAERC2AEARELYAQBEQtgBAERC2AEARELYAQBEQtgBAERC2AEARELYAQBEQtgBAERC2AEARELYAQBEQtgBAERC2AEARELYAQBEQtgBAERC2AEARELYAQBEQtgBAERC2AEARELYAQBEQtgBAERC2AEARELYAQBEQtgBAERC2AEARELYAQBEQtgBAERC2AEARELYAQBEQtgBAERC2AEARELYAQBEQtgBAERC2AEARELYAQBEQtgBAERC2AEARELYAQBEQtgBAERC2AEARCJ9YVc25sVzt+qYnUhscNVPC9865cv7T99zg5XatcgvKOy81nZHXvf2HxUpHxEAIJPkpOVVi7977PSDj7/zx1BY482zhl20zeYDP89fZ+9Dzlyvw8yRrz7y4D+2e/ObFz69b+d2KZ4UACBjpGON3dTBB6x/0BNZBz31+T275dZw++jbT77y8+Rmg4Z+9vTNF59/waD73hn2cL82o+8/4YoPrbUDAFiUdIRdeU7P458b/sGt/VYtqOnmn5549IPyVnudfXKPOdWXWG7/8w7vFkY/+vDQZArnBADIKOkIu7b7XH7tHl1rWlcXQgglH330RQgb9O07X/X12rxvq/DnRx+NTsF8AAAZKT372C3Oz6NGVYaWXbu2ne/aRNeuK4YwatSoEFap+XHl5eUpmK5KZWVlyl6rQSSTyRBCRUVFKn9LpFLVIi4vL8/Kcqh7tJLJpLdwrKr+rFjEi5ednZ1IJNI9RVPX9MJu2rRpIbRs2XKBq1u1ahXCtKlTa35QZWVlUVFRo882R2lpacpeqwHNmDEj3SPQuKYu6h1CLFL5QUfqlZaWZujfl9QoLCzMzV3U9j5ma3phtwjJZDKERZZ6IpEoKKhxj71GkZ2dnbLXahBVq3Nyc3MzbnKWUGlpaWVlZX5+vn/OxqqkpOSOO97KuLfwiSdun+4RMkMymSwpKcnOzhYui2GLxJJoemFXWFgYwriFVjxMnTo1hGUKaz4/SkgkEguv5Gs8GffGq1q336xZs7y8vHTPQqOYOnVqaWlpixYtfPDFqrS0NJFIZNyHTyo/mTNaZWVlSUlJTk6O3xj11PTCrmu3bjnhy9Gjx4XQYe61FaNGjQlhrVVXTd9gADGY8cvQWx594f2idc6/6sBN5rl+1m+fPPjCO+//PGFGVssVV93wwD132Li1fyZApml679rczfpsmAjD3nln3v3BKj584+3i0HXzzbukbS6ATJec8d1b951825tjc/IXvGnqsGtvf+r9xDpHHn78FYfs2GPK+1fc8eI3duOHjNP0wi4sv/9h2xUUv3DVoGGzZl9TMfLOSx/8LWudwwdsmNbJADJa8YjH3yvf/ujTzlyn1QK3jH7/tY8TvY4/bMctV+265hobHXPojmtOGvr45w64gkyThk2xE9+55ZpXfg0hhDByeHkIY4cMOqeoMIQQOu985slbtgudB9w48OFNzxy49XrDD957/WVnfP/Sw08MK1/37DvP6Jn6aQGikd/jpNM3ad8y8euPC9ww6YsfJuSstvMG1Tvhtu65yfL/eeiH/yvbaN0M26sPlnJpCLvJHz4waNCwuZf/eOeOQe+EEEJYt/WRJ2/ZLoTcHv8Y8lHnS8+/4YnHr//vzLwOa/Q96a5LLzmqd4vUDwsQj5zC9jXvmT9+7ITQfs328zRc687tssv/HPdHCCumaDjIHEXPHbzaXo9OCCEk1rhg2DcD11vgcPWZrx292g53jw0hhJVOev/7m/sstPND40nDpthVz/ksWbPh51QfG9Gi+4GD/v3pT5OKS2YW/TL8xZuO6t069ZMCLBUqZ84oCc3nO2dUonmz/DBz5vS0zQRNWOs9r7pkm+YhhJD84YZz7/9j/luT39941n1jQwghtNn36otTWXWhSe5jB0DaJZMhBKdFhJqtcMz1Z66VFUIIM/578cC3Zs5z08RHzxk0vCKEEAo2/+fV+7St8fGNp25hN+q1O+644447Xvx21qLu8ePTF5x66qlnP/ZtnScDIDWymrfMDzNmzvuJniyeVRKaN1vwIAugSva6Z113+PIhhBDG3n3Ov0bOub5k6GUX/mdKCCEk1jj9hhO6pnywuoXd53ced9xxxx1347uLXEtf+s1/brrppquvf/6nuk4GQIp0WLFjmDB+3DxfZjXp13EVuR07dkzfTNDENd/xsit3aRVCCGWfXHXBM5NDCCH8dOtZt/0UQgih06HXnbt+Go5kaJxNsZW/Df3wpxBCGD16dKO8AAANp/X6ay5X8eNXH1evs5sw4oPfc3v3WK3pncQemo6OB1933oY5IYQw+YnzB31eEaY8e/7lH5SGEELLHS6/Yte0fItIrd6071263SXvhhDCuK9CCCF8cdPe2z290JHwlSUT/2/48F+mh+Br5wGajoqpv307fmYIYfyk0pCc9vPIkS1CCM3ad+9cuEKfnbb68ME7H3ilcru1OpaPff2l10Z32vqEdVP3FdyQiRJrnnbjcXf1+dfokPzh5nPv6rveTYMnhRBCdu9zrj+0U3pmqlXY/TnijTfemOfypO/ffeP7xT6iSxdfFQHQNMz65oXznqk+hd2kR27/MYQQuu310HF92rToedKxBz70/Ov33Pv2jOxlVuq+3SW7b93N4XXwF/I3u3jQvo/s++TkMPPVk/d6szwZQghdj7nxjLXS9fapVdittNEWK73y3k/FySW8f96mRx+6dh2GAqDhtdj0mBc2XeSteR3XO/Ko9Y5M4TwQg7b7XP3PzZ8/9b1Zoby8PIQQWvcbdMnm6VvbXaug3OCsd0b98eMbd5+/U9V6uPzWnZavyQpd1+i9xR4n3/HeC6ev4Vh5ACBeXY+/4bTq3Mnvc9HV+7VP4zS13TE20arbNkdeNmnI5UPGhND3yhGvH1ssk8sAACAASURBVJvO6QEA0it3/d136nzlD2NDCKHnbn9bOa3D1O2IpxU23XvvEMI63VJ7NmUAABatbmG3yRlPP93AgwAAUD/1OUdRcvrIt599/u0vfhw7adqs8pqPqNjolEdO3rAerwEAwBKqc9hNfOP8Pfe/6v0JlYu/26w9hR0AQErUMex+v7//nle8v8gvFAMAIOXqdv68nx+67WVVBwDQpNRtjd0333wz+6eOW5x66fmH7bBO147tWubWcM66rOy6zwYA0PRtcuOvyRvTPUSVuoVdbm5eCDND6HTEI6/csF3zBp4JAIA6qNum2B49q74Drddmm6k6AICmoW5ht3z/k/YqDCF8//XXFQ07DwAAdVS3sAvt9r/3Pxds0vqnWw8/bvAP02o+hR0AAKlUt33sxn/5yofjexz9j4Ouu/LuA3s8fdm2O2y8RpdOhXkLHz3R84DL9l+rvkMCAPDX6hZ27wzcZZ9nqi9N/va1J759reZ77t1L2AEApEQdN8UCANDUCDsAgEjUbVPs1ld+/PlFLZsV5OZk1XBS4nm17FSnFwAAoLbqFnbtVtuoXQMPAgBA/dgUCwAQibqtsfu/l2588cfF36Wyory8dOaMlf9+iaNiAQBSoW5hN/z+00575q/vFkLYu7uwAwCaqsdGfNSAz3bgOps04LPVgU2xAACRaNywS2TnZjfqCwAAMEcdT3dy2XvvnbrQtcnSKb///MNHz9x590u/rXTIoHuuPnyD5QqEHQBAatTxdCdr9u27iJt23XfAKac91X+zfU/YfmTRu6+f16tZ3YcDAGDJNcam2OwV97nmtE3DtA8uOOy67xrh+QEAqEEj7WPXsmXLEELyy8cGf9s4LwAAwAIaJezK//fgYx+GEEL46aefGuMFAABYSN32sfvt0+c+GVvD9eUzJv455qvXH3vo+a+nhxBCaNbMLnYAAKlRt7D7YNBe+yzJCYrzN9ts/Tq9AAAAtdWY57HL63HGBfsv04gvAADAXI0UdlmFa+458OXXB26c3zjPDwDAguq2KXaT0wYP7lfjLYns/BZtOq+6bq81l9V0AACpVLewW6HP/vs38CAAANRP3cJuAaUTfxr5y7jJxYkW7Tqt1G2FwgZ5UgAAaqVe+9hVjv/knjN2X7dj4bIr91hv4z59Nuq15opt23bt0/+K5/+vuKEmBACIyqyPz+mek0i03vXhP+a9Ovl/1/ctSCTye1/6dXkdn7nuYVf69Z1/693nqOtfGDFuVnLu1ZXTxnzw8Pl79O5z0it/LPrBAABLq4KNL7nv9O5ZU14+84xni6qv/f3Bky4eWpLb68IHzu1Z162fdQ27me+fuecJL/+6yJ6cNvyWfftd/7/KOj49AEC88je99L5T18j687FTL3iraitn0b/POHvItNzeFzxwzjq5dX7eOobdbw9efPvIiqqf85btvsXf9j/syGOPPfLQfXfdbNXW2VXXTx966UX/nlLnyQAAolWwyWX3nbZa1pjbT7h0WFkofvuC0waPy+113v3nrlufYxXq9tgpLz37VlkIIbTf7vKnHzlry47zPk3Jzy/988ADB30wNUx5bvDLs/odUFCP+QAAotRss4H3nvz8ljdef/ygdbZ+/I4xuete+sD59VhbF0Jd19h99eWXlSGE/J2uevy8+asuhJDfddernr58y5wQQsmnn46o13gAALFqtvnl9524asUnFx406Jus9c5/4Nx165d1dQ27yZMnhxBC975929V8h07bb98zhBDGjx9fx8EAAGLXfNMD91g5hBDCGnvtu079TxhXt7DLzc0NIYSpU6cu6h6lpaUhhJCdnV2nFwAAiF7Ft9eedMvI0KZN6/D1Vcf+a1Tyrx+yeHULu86dO4cQwqinHnivxvPVzfrk/ie+neeOAADMr/KHa4+4+LOS5QY8/Onte7crfve8I24ZWc+0q1vY9dx88zYhhDD6tj22POb2176dUDJ7jGTJhG9fvf3YLXa64YcQQmi9+eY96zcfAECMkv+78YiLP5q17L43X7Nrt/1vumaHVsVvn3vE7aPrlXZ1C7us7Y8+fKUQQgiTP7vr+B3WWrZFi7YdO3Xq0KZFi2XX2vH4Oz+dHEIIYeWjjt6+Xl9tAQAQo+TIfx1x4dBZhbtcd+M+7UIIyx9222VbFMx45+wjbv2pHmlXx730cja+4I6jn9vlrpGzz0BcMXPyuJnz3yV7tePuPG9jXxsLADRdB66zSRpeNfnTLUee935xi21vv+2QTlVXJbqdeMcFD/W64K1zjrxj19ePW7luT1znFWqtd7zl9SeO69Wy5ltb9T7hqddv3r51XZ8dACBWP9151HlvzyjY9OI7juk699qs7mfeeWaP7BlvnHXknT/Xca1dPdao5a7U77bPtjziiTvueea1oV+O+n1ScaJ52+VWWbfvDv2OPHbf3u0dDwsAsLCVjn1t2rE1XJ+3/mXflF9Wn2eu56bS7GXXP/DC9Q+8sH7PAgCQFtdd92IDPtsZZ+zWgM9WB3XcFDvjl18n13jDxE9efPuX0noMBABA3dQ+7CZ/esuh662wUr8Hf63hxt+fOGfPrVdbq98Nn9TcfQAANJZaht2EV0/ou8VJDw0vqvzszTcX/tqJsY8/+k5FKPm/Z07fepuz3l/k11IAANDwahV2fz58xAG3fTsrhBBCxbtvvlux4O3/efbD2ec/KR5+zX4nPl/UECMCALAkahF2lR9fe+Hzk6p+brn2IQOP2GDBe3Q85qn3bj1gzfyqS789cs5NX9X7O88AAFgytQi7oY8N/jmEEEJipUOffOOhkzZfbqETmmR37HP8o28+eVDVOVmS3z340CcNMiUAAH9pycPu5w8+GBtCCCF3u3Ov2nnZRd4v0Wn3a8/foWqt3eh33/2lfvMBALCEljzsRo4cWfXDJnvuudzi77rcHntsVPXTjz/+WMfBAAConSUPu2nTpoUQQsjv0qXDX923Q5cuBfM9CACAxrbk3zyRn58fQnkI5aWlyRASi71veXFxSQghhJYtF/FlskADu/POt/Pz8xOJxb85m5a0n6KdWD024qN0j1A7yWSypKRkn+7rp3sQMt6Sr7Fr27ZtCCGEihEjvvmr+34xbFjV4bDt27ev42AAANTOkofdmj16VN35h4fueb9scfec8dJtD40JIYTQrHfv7vUYDgCAJbfkm2KX2XKr9cJ/h4UQRt/S/+jN37577y41Pbj4m9sPOPyBP6qefPPttsxrmDmBlKsY//07D7/+6Yg/iqZntei0Qo+dd9pply7N0z0VpEX5n18+eMdz/xn26x/Tstouv/IWf9/n+L93a53uqWAhtTiP3WqHHr11VaZVjH6g3zobHHDR/f8d9tOkmRUhhMqyaX98P/TZf5228zobHP/CuKoHtDvglIP+8jgLoGkqHfXiBfe+8WuXHc8+5cxbjt9v12Y/3HHnff+ZkO6xIB1Kvr/+pGvu+bnbCZdf+uwjF17Sr8UH111xyuN/pHssMtYft2yVm0hkb3HzwieFK7p357xEIqvvjWPq9tS1+UqxTodecdpac9bSTfny8YGH77TByu2a52Tn5uTkLdOpe9+/n3zjkJGzZt+hzS5XX7qLf9xDpvr+82G/tdrg8L/16r5s2+WWW22nftv2Lvnp7a8npXsuSIOvh774S+EeJx2049qdll9+hY33POKIjWYN/++w39I9F5lquQMH7JQfKt9/8JFRC9wy+bmn3igLOVv1P7BL3Z66Vt8Vm7/J5f++ZZdOCz6msrxiwW8Oa9nrjCcfOXylus0ENAXJZEhkZVcfZJudlZ0IlUlfE8jSKJlMhqzsed4OOTmJUJmsTOdMZLS2/Qbs3iokP3/o4fkPSJ303FNvloX8HfvvW9dNnrUKuxCyVz/m+WEvXbjLKoteFZe73CbH3v/h0Gu3a1PHkYCmoMdGm644fdjgd36eXJFMlhUN/+/Q4fmr77xeu3TPBWnQa8t+K0158b6XR0wsT1aW/v7p04M/Kdh0r01XSPdcZK4WfxuwT/sQvn/4oU/nubbouadeLwvNd++/d5134FzygyfmyO6006Uv/e/k4c8/8dxr73zwxf/9NmHSlJLslm3adei61iZbbrvrPv22mH12YiCD5XTd+bL+JZc+9q/+L2Zlh8rKlqsedGT/newszlIpZ7WT/3XqzH/ceshuj2Vnh4pk4YZHnnXtnv6ZQz3k7jDgoM733TTy0YeGXrlhn6r1bEX/eer10lC4T//dW9X5eWsfdiGEELLb99rrhF57nVDn1wWauNIxb1wx+PPsjfa9tPeKrSsnfz30pQcfeLDF8Ufv1iGTToEMDaL0/+4+97aXsre6+MY+a7Wt+P2L1268/YbTW114R7/OtdzuBdWy+w7ov9pNV/04+MHXr++zQ24IYdKzT75RFjrs23+neqwg878kUJOpr7/46g+ddjh3j43WW7HTyl17/O2AA/co+PHB179Z7FksIUoTXhx8x9ddjr3ykL02XmX11Vbbct/jrtyv+ce3Pfe2twP1se6Aw9YLYeJTD700K4Q522E7H9B/uzqudQshCDugZuPH/FHZvGPHud8dk+iwwrJh1oQJDotl6fPT6F8rWiy/yty92RMrd10uzPxjzPg0DkUEVu8/YLOsUPSfwa/MnLMddpWD+vetV5sJO6AmLVu3CsV/jpubcclxv44P2W3a2K2IpU/bNoVhxtjRc0/jmBz98+8he9nOy6ZxKGKwwoEDts8L01988uXiqu2wax3Sv3f9nlLYATXpuE3f1ZqPfu2aIV9+P27SH3+Mfuu5p1+Y2G7nvt3rs4kAMtMqu+y4cYsf7rzwqVe//m3s2F8/H/LgpU+NW3GvHTbPTfdkZLp2+w3YvXkofunpRx99/LWy0PvQ/j3r+Yw+o4Eaddj0sGubv/XoO0Ouen/ytKyWHZfrtu9RO++xsm8JZGm03LY33tPivrtfueW8V/+YmtW20wrrH3r2iQes0Szdc5H5Wu05YO82Tz/84lkXzSrL6tv/oFXq+4TCDliE/BXX3emcdXdK9xjQFDRfaZMTL9/kxHSPQXzydxxwQKeHb/u9KOTs0P+AzvV+PmEHACy9zjhjt7S+fvZWhx3S9barfy7Yqe5fNzEP+9gBAKRN8W+/TQmhcK8Bfy9sgGeLZ41dRUVFyl4rmWnfl1k1cGVlZSp/S6RS1SLOuP8z/Q9ZWxbxEsq4X1T1W9ibYjGysrISiejOkJ4cddtVjxeFFU49YfcG2WkzkrBLJpPTp09P2cuVlWXYSSmrPjJmzpxZUlKS7lloFFV/DMrLy9M9SO2k8m2b6ZLJZDKZzLgPn3Qt4oz7RVUpLy/3pliMFi1a5ORE0i2zJSe9e97+F31U3nyb8//Rp2H+0yL5BSUSicLChliDuWTy8jLsyMCqv/ctWrTIuMlZQlOnTg0h5ObmZtY/Z1P5ts10kyZNSiQSGfcWTtcizrhfVDKZLCkpyc3NbdWq7l8SSib55q5DL3hhzPcfvvf9xIp2O91379HLN9AT28cOACC1isd8NGTI0F9yuu9yxpMfPjdgpQbrsUjW2AEAZIwNL/th5mWN8cTW2AEARELYAQBEQtgBAERC2AEARELYAQBEQtgBAERC2AEARELYAQBEQtgBAERC2AEARELYAQBEQtgBAERC2AEARELYAQBEQtgBAEQiJ90DQFP02IiP0j1C7ZSWlqZ7BKC+br319dzc3HRPUTtnnLFbukdgPtbYAQBEQtgBAETCplhofKPvP3vPu35d6Op1/vna2X9vmYZ5gOiNe+Laqx/5Y6Gr19jn8aM2bpGGeUgVYQeNr9POx9y7bsk8V5R//8Qt1/20SvfmaRsJiFubrfc7rse8+95W/Pb8I8//suIKzdI2Eikh7KDxFSy3ygbLzb1YOeb56z/M//u1e3S3LwTQOHI7rNitw9yLybFvvjgsb5OLtl3ex07kLGBItaLnb3zu5032P2mjvHRPAiwlpn569+vje++6U68MO+aW2rPGDlKr5LOnb/m40+GPbto63ZMAS4nyEf8d8sWy29zSy851SwFr7CClJv773ndnbbPX/isl0j0JsJQo+mjwZ2V9tu+zoo+dpYGwgxRK/u/Vx4YX7rZ3b/9uBlIjOWro+1+3XH+XHvnpnoSUEHaQQiOGDB3TcbPdennjASky5q3PJyy7Xu+ePnaWEhY0pM4vQz+a3HrTdXukew5gqfH798OmtFh/zRXTPQepIuwgZSZ8/fHoRI/uq3jbASky6ccff0mssJrd65Ye/sJAyvw27tdQ2LVLQbrnAJYaf06cGFot29n+dUsPYQepUjmhaFJo3spxE0CqJCdNmxEKCnzsLEWcxw5SJWubU774MN1DAEuTRJ/+V7+Q7iFIKWvsAAAiIewAACIh7AAAIiHsAAAiIewAACIh7AAAIiHsAAAiIewAACIh7AAAIiHsAAAiIewAACIh7AAAIiHsAAAiIewAACIh7AAAIiHsAAAiIewAACIh7AAAIiHsAAAiIewAACIh7AAAIiHsAAAiIewAACIh7AAAIiHsAAAiIewAACIh7AAAIiHsAAAiIewAACIh7AAAIiHsAAAiIewAACIh7AAAIiHsAAAiIewAACIh7AAAIiHsAAAiIewAACIh7AAAIiHsAAAiIewAACIh7AAAIiHsAAAiIewAACIh7AAAIiHsAAAiIewAACIh7AAAIiHsAAAiIewAACIh7AAAIiHsAAAiIewAACKRhrCb/sBuiZr0uuz71A8DABCNnNS/ZFFRUQjNeh9w8vZd5ru+c592qR8GACAa6Qq7DtufftVVG6T+xQEAopWGTbFFRUUhtG7dOvWvDAAQs/SGXcWMcb+OHT+jPPVDAABEJ/WbYiumTJkRwoyPb+x36+3Pfz2pLISsVqtsNeCSm686eK1m9XjeZDLZYDNGKplM+i3RpPgfMnoWcfRSuYgTiUTKXitzpT7sioqKQgifPfFYm0NPGnTqyq2m/O/NB28ZfPMhfb6bMey/x3Sr20KrrKycNGlSww66GLNmzUrZazWgadOmpXuEjJGhi7ikpCTdI9TOxIkT0z1CJkkmkxn3f2a6FnHG/aKqVFRUVFRUpHuK2knlIi4sLMzNzU3Zy2Wo1Idd8+0vfOqpE9usveO2a7SsuubIkw7q1Xf9s18795JXDntol/y6PGkikUjlws7KyrDz/1X9iyo7OzvjJk+XjPtFVS3ijBs7jZ/Rz/74Zbpeum4qKyuDRbzEMu4XFUKorKysOvlXugepnVQu4oz75aRF6sOu2erb9Ft9/qtye5x66i7nH/jvd94ZEXbZsC5PmkgkCgsLG2K8JZKXl5ey12oQ5eXlIYQWLVpk3OTpknG/qNLS0hBCbm5uZn3wpfJtu4CMW8QlJSWJRCLjxk7XIs64X1QymSwpKcnKysq4NVJpfBdTozSc7qQmeR06tA5h+vTp6R4EoPY+ObvvTUPm34LW6cCBQ05aJU3zAEutlIfd9G+ee/iVr5fZ5uyDes/zr5Lx3347IYT1unZN9TgA9VYyc0ZFWO+w807ccO72v7yOndM4EbC0SnnYNZ/y5hVn/mtSn4Jeb/xjrar96SrHv3TOte+GrF577+mft0DmmTFzesjt3H2tDXqnexJgaZfysMva7Jyb+z+/z0NnbtLzjf323HD5rPHfvvnMvz8b33LDgXedvvpfPx6gqZkxc0YoaN483WMApGMfu8573fvB25tdc829Lw259+1xxXntu/U+8J+nXHjWnqvX5zR2AOkyY+b0UNDcJxiQfmk5eCKnc99jbuh7zA3peG2AhjZj5oxQOXrIXUdc+uV3f5Y077jiBjv//ZSD1u6UYYc3AhHIvDP9ADQx5SG3sGLsH212O+nE22466eTtmg2/Z9Dh138zI91zAUufJnK6E4DMtfERbww5ovpSr3V7rlzyj4Mfe+WNk9fa3fZZIKWssQNoYNmrr7p8SI4f+3u6BwGWOsIOoH7GvvnwmRe+OLys+orSL7/6KeR07NIxjUMBSyebYgHqp9PyBaPeeeKss0pO2X/tFfOLR3348i3PTV1pv922a5HuyYCljrADqJ+sNfrddXPLW+97+6aLXiwqa95xxZW2P/uSY3dbOT/dgwFLH2EHUF+Jdr12vujmndM9BoB97AAAIiHsAAAiIewAACIh7AAAIiHsAAAiIewAACIh7AAAIiHsAAAiIewAACIh7AAAIiHsAAAiIewAACIh7AAAIiHsAAAiIewAACIh7AAAIiHsAAAiIewAACIh7AAAIiHsAAAiIewAACIh7AAAIiHsAAAiIewAACIh7AAAIiHsAAAiIewAACIh7AAAIiHsAAAiIewAACIh7AAAIiHsAAAiIewAACIh7AAAIiHsAAAiIewAACIh7AAAIiHsAAAiIewAACIh7AAAIiHsAAAiIewAACIh7AAAIiHsAAAiIewAACIh7AAAIiHsAAAiIewAACIh7AAAIiHsAAAiIewAACIh7AAAIiHsAAAiIewAACIh7AAAIiHsAAAiIewAACIh7AAAIiHsAAAiIewAACIh7AAAIiHsAAAiIewAACIh7AAAIiHsAAAiIewAACIh7AAAIiHsAAAiIewAACIh7AAAIiHsAAAiIewAACIh7AAAIiHsAAAiIewAACIh7AAAIiHsAAAiIewAACIh7AAAIpGT7gEaRjKZLCoqStnLlZSUpOy1GkQymQwhTJ8+PZFIpHuWzJChi7i0tDTdg9TO5MmT0/XSmbiIk8lkxo2drkWccb+oKhUVFZWVlemeonZSuYhbtWqVkxNJtzSeSH5BiUSiTZs2KXu5/Pz8lL1WgygvLw8htGzZMi8vL92zZIaMW8RVSZeXl5dZ7Z7Kt+0CMm4Rl5SUJBKJjBs7XYs4435RVdWenZ2dm5ub7llqJ43vYmpkUywAQCSEHQBAJIQdAEAkhB0AQCSEHQBAJIQdAEAkhB0AQCSEHQBAJIQdAEAkhB0AQCSEHQBAJIQdAEAkhB0AQCSEHQBAJIQdAEAkhB0AQCSEHQBAJIQdAEAkhB0AQCSEHQBAJIQdAEAkhB0AQCSEHQBAJIQdAEAkhB0AQCSEHQBAJIQdAEAkhB0AQCSEHQBAJIQdAEAkhB0AQCSEHQBAJIQdAEAkhB0AQCSEHQBAJIQdAEAkhB0AQCSEHQBAJIQdAEAkhB0AQCSEHQBAJIQdAEAkhB0AQCSEHQBAJIQdAEAkhB0AQCSEHQBAJIQdAEAkhB0AQCSEHQBAJIQdAEAkhB0AQCSEHQBAJIQdAEAkhB0AQCRy0j0AKXLnnW/n5eVlZWVYyp9xxm7pHgEAMkaG/ZkHAGBRhB0AQCSEHfUx45ehg64652/nPPZRuicBAOxjR10lZ3z39hPXvjq2Rbv8dI8CAIQQrLGjzopHPP5e+fZHn3bmOq3SPQoAEEKwxo46y+9x0umbtG+Z+PXHdE8CAFQRdtRRTmH7lumeAQCYl02xAACREHYAAJEQdgAAkRB2AACREHYAAJFwVCx1UzH1t2/HzwwhjJ9UGpLTfh45skUIoVn77p0L/U8FAOnhbzB1M+ubF857pvoUdpMeuf3HEELottdDx/Vpk76pAGCpJuyomxabHvPCpukeAgCYl33sAAAiIewAACIh7AAAIiHsAAAiIewAACIh7AAAIiHsAAAiIewAACIh7AAAIiHsAAAiIewAACIh7AAAIiHsAAAiIewAACIh7AAAIpGmsJvy5f2n77nBSu1a5BcUdl5ruyOve/uPivRMAgAQi5w0vOasYRdts/nAz/PX2fuQM9frMHPkq488+I/t3vzmhU/v27ldGsYBAIhDGsJu9O0nX/l5crNBQ98+q0duCCGcf9oO+659wP0nXHHUj9dtmp36gQAAopD6TbE/PfHoB+Wt9jr75KqqCyEkltv/vMO7hdGPPjw0mfJxAABikfKwK/nooy9C2KBv34J5r+21ed9W4c+PPhqd6nEAAKKR8rD7edSoytCya9e2812b6Np1xRBGjRqV6nEAAKKR8n3spk2bFkLLli0XuLpVq1YhTJs6tY7PWllZOXny5PrOtsRmzZqVstdqQKWlpekeodYmTpyYltfN0EVcUlKS7hFqJ13LN2TmIk4mkxk3trdwrVRUVFRUZNg5IlK5iJdZZpnc3Ny/vt/SLR1HxdYkmUyGkEgk6vjwRCKRlZW6tY97rbZuyl6rQVRWViZXSWZlZdX9V7yUsYijl3GLuKKiInFsSj/oMlrGLd9gES8Bn29LIuVhV1hYGMK4hVbNTZ06NYRlCgvr+KyJRKJNmzb1nS1excXFxcXFLVu2zMvLS/csNIqpU6eWlpa2bt3aX4VYTZo0yQddxCorKydNmpSXl9eqVat0z0JmS/nfgK7duuWE4tGjx813bcWoUWNCWHXVVVM9DgBANFIedrmb9dkwEYa9886Mea6s+PCNt4tD180375LqcQAAopH6rTbL73/YdgXFL1w1aNicXVsrRt556YO/Za1z+IANUz4NAEA00nDwROcBNw58eNMzB2693vCD915/2Rnfv/TwE8PK1z37zjN6pn4YAIBopOOo2Nwe/xjyUedLz7/hicev/+/MvA5r9D3prksvOap3izTMAgAQjUQy6Wu84ld1VOwyyyzjqNhYVR0V27ZtW0fFxspRsXGrOio2Pz/fUbHUk78BAACREHYAAJEQdgAAkRB2AACREHYAAJEQdgAAkRB2AACREHYAAJEQdgDA/7d352FV1Xkcx7+X5bIp5IJIYKJmaJMkCY7bCGNmIS2W1eOSNlKJC2ouaDa5kFNaLmPiMoxb4TwujeWkPtqmRmmSpuUYqI3mgIooiqKxSF3O/HEvBuoU99x77uWc5/366/I75/f8fvDle/hwVxgEwQ4AAMAgCHYAAAAGQbADAAAwCIIdAACAQRDsAAAADIJgBwAAYBAEOwAAAIMg2AEAABgEwQ4AAMAgCHYAAAAGQbADAAAwCIIdAA+IRAAACj9JREFUAACAQRDsAAAADIJgBwAAYBAEOwAAAIMg2AEAABiESVEUd+8BmrNW2WQyuXsj0AolNjxKbHiUGE5BsAMAADAIHooFAAAwCIIdAACAQRDsAAAADIJgBwAAYBAEOwAAAIMg2AEAABgEwQ4AAMAgCHYAAAAGQbADAAAwCIIdAACAQRDsAAMqXBxvMpka/GmruzeC30ClDE91ifndgDoEOwAAAIMg2AEAABgEwQ4AAMAgCHYAAAAGQbDTOcu57NXTBsVHtQlr7G/2aRDcKiZxxFu7CizaTYSLOVApk8mkXNi98IU+94Q39vPxbxzR6bGJbx++qvmWYS+VlaKL9UN1M9LFsJsCHSt4b0hrTxHxb9k18clnnnk6sUtLPxExhQ7851ltJsLFVFbqbHqciDQakpba3tvcrEOvfk/2fyg2zFdEJLDH/CMWl+0fv8GBStHF+qC6xHQx1CHY6VjVvskRIhL04Iq8n6vHKv+T3jtARFqlHtBgIlxMdaWsfxLMfn6hiUtyS22DZblv9QoSkYD+6y5pvHHUlepK0cV6obrEdDHUIdjp2LVT+7dtWv/O9txrNUcr1j7qISLd0///P+2qJ8LFVFfK+idBPLotOl1zuGrvxFYi4vvE2jKNdgw7qa4UXawXqktMF0MdL+c9qAtXM4fHJITHiIhYyouLLpSUXrMoIlLlHyhyuaSkRKS5kyfCxRytVIeEhLCaX5s69+zhO/9kxaFDx2RgR+32DXvZXym6WGdUNyNdDDsR7HRNuZCdMSNt6casnPPlVTccUhQtJsLFHKqUqU2bVrVHPMLDQ0VOFhYWOnWXcJCqStHFeqK6Geli2Itgp2Olu6f84f65Ryt9Wz/wwqjEmFbNAv29PURy/p4085Nffc2U6olwMQcr5RsQ4HnjkK+viFRUVGixXailolJ0sb6obka6GPYi2OnXudWvLDhaKW1Tth9Ij2/4y3jQ9uc0mggXc7RSldeu3Thk/WPg7+/vrD3CGeyvFF2sM6qbkS6GvXgfO/36+quvLCKRg5JrXtZFzuTmXtFoIlzM0UpZ8vPP1B5RCgoKRSQsLOyWE+Am9leKLtYZ1c1IF8NeBDv98vDwlOo75a+r3LcoI1vkV59ko3oiXMzhSh3cseNS7YE9e8pFAqKj2zpzn3CY3ZWii/VGdTPSxbATwU6/2t/dXkSObN18vPqJ0xXH1gwbuLF5fGsRKSwouH5pz//XjJSUlJSVB6vsnAj3Ul1iG09lx6xJW85Vj/2cn5m2/LhIoycGPGh2zXeAuqlDpehifbO/xHWfCNTmvndagaMuvPt0IxHxaBLd7/lRI4Y+fF+It9/vUndd3Dw0SET8Ivsmj1t9SFEUZf/EliIi/df9ZOdEuJnqEp9e2ENEQpNmjW1rvq3dA4OGjxoxJKH9bSYRaZqw/KQbvyXUVudK0cV6pbrEdDHUIdjpWsn+vw3v1a6Zv7e5QXCr2H7jVx24rCiK5fs1g6ObB/gEhN43I1tRbr5e1Hki3E5liY/PiRGRtlMPVJ37bO6wXu1Dg3zNfo0jYvtP3fA972pan9S5UnSxXqkuMV0MdUwKz8UAAAAwBJ5jBwAAYBAEOwAAAIMg2AEAABgEwQ4AAMAgCHYAAAAGQbADAAAwCIIdAACAQRDsAAAADIJgBwAAYBAEOwDOU7Zn3F2eJiufTrNzLDefUrThqaa2M0xN+v3j/A2HleJ9y5KigqrPCH8xW/t1Lef3vT3t2T6d2oQE+Xl7+wY2vaNDzydS5m46cqXu3zkA1A/u/kwzAIZS9mVqpKft8uLb5Y1jltqHiz8YEFJ99bmtb2ZBrYNXc9aO7das1r+bYeP2arzu5d2vdm9iuuXl0bvFY8uPXFPxQwAAd+EeOwDO5Nd11jup91gjVkX2zOGLT9T4OOor2yaMWn/OejswYX7GkNDqIz/lb5vZ9+7oQYu+PF/lynWL3h322PQ9F23nevo3bXFHSIBX9aZOfZD8+PSDP6vaEAC4A8EOgHP5/D4t86UobxERKc/68/Dl+bYDP+6YMvLtM9bbDXu/mZEU/sukY6smpG0/VSniE/Hw9GWjO7po3e+WvLrpovWmd1TK1pOXivLzCi+fzkqN9bWOVh1dnrHrFg/sAkD9RLAD4Gzm6BmZ0zqaRUTkx52TR646KyLlu6cmZ9iyVkD8m8uHt7hxmneLPi+9/13OlrSHI3xcs27+tm05tptBA2YvSGxhFhHxCun5l0mPVN9tV5yTc1bVbgDADQh2AJzP+96pmTNirRGrZNuk0Wvz9k5/Yant0VG/uNkrkiNqP60tMGbs+kNHPpr9+J3+Lly36ZA1h20OLnjA+5cDHmZzdbATT09PAQCdMCmK8ttnAYC9LEff6BH9UnaFiEij4OArRUUWERG/7vP//fmEO3/tn8rT87q0SP1KRETCxu09vbCLi9a97sK6/pGD3i8WEZHbx+85vaDbrV9dAQD1DffYAdCGZ7vUd2Z38xMRkUu2dCU+nWetfLFu6cpd61YeWTpkjC3ViXenlGRSHQD9INgB0IrHXWNff+72miONB88cF6n5ZceBda/un/dIfMqHthdU+HeetXJipAY7BACNEOwAaObU6tczC2oOFG+YuzKvvq5beWJdUpe41I/PW5+fEhg7ZcvWKfeaNdojAGiBYAdAI6cynp/wsfXDG7y8bK9FKN01OXnFmfq3rlL02Su9Og9anVsuIiKeYX0XZe2c0ytY250CgLMR7ABoIi/j+VRbvDLHvroj8ylbSLry0aRRazR8AxEV61ry33u2a5/X9lifV+cR2jtt5zdbxnRsoN0mAUAjBDsAzqfkZSSlfnxVRES87526IrXnwPS3Hm1sPViyefzoDTd+Rqzb1lUK3h8aN2DNiZ9ERKRhzPitBz+a3jOYayMAXeLiBcDZlLylSak7rfHK8+7JK1+O8hIJGbh0XmKg9YSLm8aO3VhcH9atPPx6/6Fr/2v91LDghxbtzlqQ0JzrIgDd4gIGwLmUH5YmTbHFK4/I8SumdbK9/iBs2LI3eje03j6/IWX8lksqV8idHx9hEzsj24F1qw7PGToju9T6RcTI9RvHRDn0/sgA4G68QTEAZ1J+WPLHqJSsUhERU+uUzw+n9/CveXRxXIcxX5SJiEjYsA9zVz1ovTPt6yWD531R/Zms5cc+3fyt9R1H/O7q/Wh0E9t4u6SMmX2CRL595c7o106IiEjI6F2Fi+NVrlu68clmT71XZjvHHBDk5yW30HX299tHNnPkhwIALqMAgLNUnVgYF1B9dblj5KdXbz7j6Lxu1z8JtuWIT360Dm8aXIfP7eqeflZRFEX55s9tqodCRu9Sv27Rsri6XCW7//WsZj8wAHAuHooF4CzK8fSkl7Nsj2yGDVs25/6bX1hqinxxxfQY24OkeRnDX/687KZz9LIuANQ7PBQLAABgENxjBwAAYBAEOwAAAIMg2AEAABgEwQ4AAMAgCHYAAAAGQbADAAAwCIIdAACAQRDsAAAADOJ/r1c4SazBzmgAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(ggplot2)\n",
    "library(ggthemes)\n",
    "library(scales)\n",
    "library(plyr)\n",
    "\n",
    "# Barplot\n",
    "# http://www.sthda.com/english/wiki/ggplot2-barplots-quick-start-guide-r-software-and-data-visualization\n",
    "# https://stackoverflow.com/questions/51892875/how-to-increase-the-space-between-grouped-bars-in-ggplot2\n",
    "df2 <- as.data.frame(xtabs(~ X1+X2+Y, data=df))\n",
    "df2$X12 = with(df2, interaction(X1, X2))\n",
    "df2$X12 = factor(df2$X12, levels=c(\"a.a\",\"a.b\",\"b.a\",\"b.b\"))\n",
    "df2 <- df2[order(df2$X1, df2$X2),] # sort df2 alphabetically by X1, X2\n",
    "ggplot(data=df2, aes(y=Freq, x=X12, fill=Y)) + theme_minimal() + \n",
    "  # set the font styles for the plot title and axis titles\n",
    "  theme(plot.title   = element_text(face=\"bold\",  color=\"black\", size=18, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.title.x = element_text(face=\"bold\",  color=\"black\", size=16, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.title.y = element_text(face=\"bold\",  color=\"black\", size=16, hjust=0.5, vjust=0.0, angle=90)) + \n",
    "  # set the font styles for the value labels that show on each axis\n",
    "  theme(axis.text.x  = element_text(face=\"plain\", color=\"black\", size=14, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.text.y  = element_text(face=\"plain\", color=\"black\", size=12, hjust=0.0, vjust=0.5, angle=0)) + \n",
    "  # set the font styles for the legend\n",
    "  theme(legend.title = element_text(face=\"bold\", color=\"black\", size=14, hjust=0.5, vjust=0.0, angle=0)) +\n",
    "  theme(legend.text  = element_text(face=\"plain\", color=\"black\", size=14, hjust=0.5, vjust=0.0, angle=0)) +\n",
    "  # create the barplots side-by-side\n",
    "  geom_col(width=0.75, position=position_dodge(width=0.75), alpha=0.60) +\n",
    "  # place text labels on each bar\n",
    "  geom_text(aes(label=Freq), position=position_dodge(width=0.75), vjust=1.2, color=\"black\", size=3.5) +\n",
    "  # set the labels for the title and each axis\n",
    "  labs(title=\"Y by X1, X2\", x=\"X1.X2\", y=\"Count\") + \n",
    "  # change the order of the bars on the x-axis\n",
    "  scale_x_discrete(limits=c(\"a.a\",\"a.b\",\"b.a\",\"b.b\")) + \n",
    "  # set the scale, breaks, and labels on the y-axis\n",
    "  scale_y_continuous(breaks=seq(0,17.5,by=5), labels=seq(0,17.5,by=5), limits=c(0,17.5), oob=rescale_none) + \n",
    "  # set the name, labels, and colors for the boxes\n",
    "  scale_fill_manual(name=\"Y\", labels=c(\"x\",\"y\"), values=c(\"#69b3a2\",\"#404080\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f880f694-a211-4dc1-9a9f-82c8a152e23d",
   "metadata": {},
   "source": [
    "## GLM for Multinomial Distribution Data\n",
    "\n",
    "* **Distribution:** Multinomial\n",
    "* **Link:** logit\n",
    "* **Typical Uses:** Multinomial Logistic Regression: polytomous responses (i.e. nominal responses with more two categories)\n",
    "* **Reporting:** \"Figure 14a shows the number of ‘x’, ‘y’, and ‘z’ outcomes for each level of X1 and X2. An analysis of variance based on multinomial logistic regression indicated a statistically significant effect on Y of X1 (χ2(2, N=60) = 10.46, p < .01), of X2 (χ2(2, N=60) = 15.21, p < .001), and a marginal X1×X2 interaction (χ2(2, N=60) = 5.09, p = .078).\""
   ]
  },
  {
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   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 20 × 4</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>S</th><th scope=col>X1</th><th scope=col>X2</th><th scope=col>Y</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td> 1</td><td>a</td><td>a</td><td>x</td></tr>\n",
       "\t<tr><th scope=row>2</th><td> 2</td><td>a</td><td>b</td><td>z</td></tr>\n",
       "\t<tr><th scope=row>3</th><td> 3</td><td>b</td><td>a</td><td>x</td></tr>\n",
       "\t<tr><th scope=row>4</th><td> 4</td><td>b</td><td>b</td><td>x</td></tr>\n",
       "\t<tr><th scope=row>5</th><td> 5</td><td>a</td><td>a</td><td>x</td></tr>\n",
       "\t<tr><th scope=row>6</th><td> 6</td><td>a</td><td>b</td><td>x</td></tr>\n",
       "\t<tr><th scope=row>7</th><td> 7</td><td>b</td><td>a</td><td>x</td></tr>\n",
       "\t<tr><th scope=row>8</th><td> 8</td><td>b</td><td>b</td><td>x</td></tr>\n",
       "\t<tr><th scope=row>9</th><td> 9</td><td>a</td><td>a</td><td>y</td></tr>\n",
       "\t<tr><th scope=row>10</th><td>10</td><td>a</td><td>b</td><td>x</td></tr>\n",
       "\t<tr><th scope=row>11</th><td>11</td><td>b</td><td>a</td><td>x</td></tr>\n",
       "\t<tr><th scope=row>12</th><td>12</td><td>b</td><td>b</td><td>z</td></tr>\n",
       "\t<tr><th scope=row>13</th><td>13</td><td>a</td><td>a</td><td>x</td></tr>\n",
       "\t<tr><th scope=row>14</th><td>14</td><td>a</td><td>b</td><td>y</td></tr>\n",
       "\t<tr><th scope=row>15</th><td>15</td><td>b</td><td>a</td><td>x</td></tr>\n",
       "\t<tr><th scope=row>16</th><td>16</td><td>b</td><td>b</td><td>x</td></tr>\n",
       "\t<tr><th scope=row>17</th><td>17</td><td>a</td><td>a</td><td>x</td></tr>\n",
       "\t<tr><th scope=row>18</th><td>18</td><td>a</td><td>b</td><td>x</td></tr>\n",
       "\t<tr><th scope=row>19</th><td>19</td><td>b</td><td>a</td><td>x</td></tr>\n",
       "\t<tr><th scope=row>20</th><td>20</td><td>b</td><td>b</td><td>x</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 20 × 4\n",
       "\\begin{tabular}{r|llll}\n",
       "  & S & X1 & X2 & Y\\\\\n",
       "  & <int> & <chr> & <chr> & <chr>\\\\\n",
       "\\hline\n",
       "\t1 &  1 & a & a & x\\\\\n",
       "\t2 &  2 & a & b & z\\\\\n",
       "\t3 &  3 & b & a & x\\\\\n",
       "\t4 &  4 & b & b & x\\\\\n",
       "\t5 &  5 & a & a & x\\\\\n",
       "\t6 &  6 & a & b & x\\\\\n",
       "\t7 &  7 & b & a & x\\\\\n",
       "\t8 &  8 & b & b & x\\\\\n",
       "\t9 &  9 & a & a & y\\\\\n",
       "\t10 & 10 & a & b & x\\\\\n",
       "\t11 & 11 & b & a & x\\\\\n",
       "\t12 & 12 & b & b & z\\\\\n",
       "\t13 & 13 & a & a & x\\\\\n",
       "\t14 & 14 & a & b & y\\\\\n",
       "\t15 & 15 & b & a & x\\\\\n",
       "\t16 & 16 & b & b & x\\\\\n",
       "\t17 & 17 & a & a & x\\\\\n",
       "\t18 & 18 & a & b & x\\\\\n",
       "\t19 & 19 & b & a & x\\\\\n",
       "\t20 & 20 & b & b & x\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 20 × 4\n",
       "\n",
       "| <!--/--> | S &lt;int&gt; | X1 &lt;chr&gt; | X2 &lt;chr&gt; | Y &lt;chr&gt; |\n",
       "|---|---|---|---|---|\n",
       "| 1 |  1 | a | a | x |\n",
       "| 2 |  2 | a | b | z |\n",
       "| 3 |  3 | b | a | x |\n",
       "| 4 |  4 | b | b | x |\n",
       "| 5 |  5 | a | a | x |\n",
       "| 6 |  6 | a | b | x |\n",
       "| 7 |  7 | b | a | x |\n",
       "| 8 |  8 | b | b | x |\n",
       "| 9 |  9 | a | a | y |\n",
       "| 10 | 10 | a | b | x |\n",
       "| 11 | 11 | b | a | x |\n",
       "| 12 | 12 | b | b | z |\n",
       "| 13 | 13 | a | a | x |\n",
       "| 14 | 14 | a | b | y |\n",
       "| 15 | 15 | b | a | x |\n",
       "| 16 | 16 | b | b | x |\n",
       "| 17 | 17 | a | a | x |\n",
       "| 18 | 18 | a | b | x |\n",
       "| 19 | 19 | b | a | x |\n",
       "| 20 | 20 | b | b | x |\n",
       "\n"
      ],
      "text/plain": [
       "   S  X1 X2 Y\n",
       "1   1 a  a  x\n",
       "2   2 a  b  z\n",
       "3   3 b  a  x\n",
       "4   4 b  b  x\n",
       "5   5 a  a  x\n",
       "6   6 a  b  x\n",
       "7   7 b  a  x\n",
       "8   8 b  b  x\n",
       "9   9 a  a  y\n",
       "10 10 a  b  x\n",
       "11 11 b  a  x\n",
       "12 12 b  b  z\n",
       "13 13 a  a  x\n",
       "14 14 a  b  y\n",
       "15 15 b  a  x\n",
       "16 16 b  b  x\n",
       "17 17 a  a  x\n",
       "18 18 a  b  x\n",
       "19 19 b  a  x\n",
       "20 20 b  b  x"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Example data\n",
    "# df has subjects (S), two between-Ss factors (X1,X2) each w/levels (a,b), and polytomous response (Y)\n",
    "df <- read.csv(\"data/2F2LBs_multinomial.csv\")\n",
    "head(df, 20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "e9ab602a-4b2d-4c58-994f-4155e81918ae",
   "metadata": {
    "tags": [],
    "vscode": {
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    }
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# weights:  15 (8 variable)\n",
      "initial  value 65.916737 \n",
      "iter  10 value 41.209129\n",
      "iter  20 value 41.110241\n",
      "iter  30 value 41.109293\n",
      "final  value 41.109253 \n",
      "converged\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A anova: 3 × 3</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>LR Chisq</th><th scope=col>Df</th><th scope=col>Pr(&gt;Chisq)</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>X1</th><td>10.456284</td><td>2</td><td>0.0053634826</td></tr>\n",
       "\t<tr><th scope=row>X2</th><td>15.212104</td><td>2</td><td>0.0004974317</td></tr>\n",
       "\t<tr><th scope=row>X1:X2</th><td> 5.092234</td><td>2</td><td>0.0783854422</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A anova: 3 × 3\n",
       "\\begin{tabular}{r|lll}\n",
       "  & LR Chisq & Df & Pr(>Chisq)\\\\\n",
       "  & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\tX1 & 10.456284 & 2 & 0.0053634826\\\\\n",
       "\tX2 & 15.212104 & 2 & 0.0004974317\\\\\n",
       "\tX1:X2 &  5.092234 & 2 & 0.0783854422\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A anova: 3 × 3\n",
       "\n",
       "| <!--/--> | LR Chisq &lt;dbl&gt; | Df &lt;dbl&gt; | Pr(&gt;Chisq) &lt;dbl&gt; |\n",
       "|---|---|---|---|\n",
       "| X1 | 10.456284 | 2 | 0.0053634826 |\n",
       "| X2 | 15.212104 | 2 | 0.0004974317 |\n",
       "| X1:X2 |  5.092234 | 2 | 0.0783854422 |\n",
       "\n"
      ],
      "text/plain": [
       "      LR Chisq  Df Pr(>Chisq)  \n",
       "X1    10.456284 2  0.0053634826\n",
       "X2    15.212104 2  0.0004974317\n",
       "X1:X2  5.092234 2  0.0783854422"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(nnet) # for multinom\n",
    "library(car) # for Anova\n",
    "df$S = factor(df$S)\n",
    "df$X1 = factor(df$X1)\n",
    "df$X2 = factor(df$X2)\n",
    "df$Y = factor(df$Y) # nominal response\n",
    "contrasts(df$X1) <- \"contr.sum\"\n",
    "contrasts(df$X2) <- \"contr.sum\"\n",
    "m = multinom(Y ~ X1*X2, data=df)\n",
    "Anova(m, type=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "6cfcfb5c-3acd-4290-ac3d-1a043d2d63f0",
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   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(ggplot2)\n",
    "library(ggthemes)\n",
    "library(scales)\n",
    "library(plyr)\n",
    "\n",
    "# Barplot\n",
    "# http://www.sthda.com/english/wiki/ggplot2-barplots-quick-start-guide-r-software-and-data-visualization\n",
    "# https://stackoverflow.com/questions/51892875/how-to-increase-the-space-between-grouped-bars-in-ggplot2\n",
    "df2 <- as.data.frame(xtabs(~ X1+X2+Y, data=df)) # build a freq table\n",
    "df2$X12 = with(df2, interaction(X1, X2))\n",
    "df2$X12 = factor(df2$X12, levels=c(\"a.a\",\"a.b\",\"b.a\",\"b.b\"))\n",
    "df2 <- df2[order(df2$X1, df2$X2),] # sort df2 alphabetically by X1, X2\n",
    "ggplot(data=df2, aes(x=X12, y=Freq, fill=Y)) + theme_minimal() + \n",
    "  # set the font styles for the plot title and axis titles\n",
    "  theme(plot.title   = element_text(face=\"bold\",  color=\"black\", size=18, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.title.x = element_text(face=\"bold\",  color=\"black\", size=16, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.title.y = element_text(face=\"bold\",  color=\"black\", size=16, hjust=0.5, vjust=0.0, angle=90)) + \n",
    "  # set the font styles for the value labels that show on each axis\n",
    "  theme(axis.text.x  = element_text(face=\"plain\", color=\"black\", size=14, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.text.y  = element_text(face=\"plain\", color=\"black\", size=12, hjust=0.0, vjust=0.5, angle=0)) + \n",
    "  # set the font styles for the legend\n",
    "  theme(legend.title = element_text(face=\"bold\", color=\"black\", size=14, hjust=0.5, vjust=0.0, angle=0)) +\n",
    "  theme(legend.text  = element_text(face=\"plain\", color=\"black\", size=14, hjust=0.5, vjust=0.0, angle=0)) +\n",
    "  # create the barplots side-by-side\n",
    "  geom_col(width=0.75, position=position_dodge(width=0.75), alpha=0.60) +\n",
    "  # place text labels on each bar\n",
    "  geom_text(aes(label=Freq), position=position_dodge(width=0.75), vjust=1.2, color=\"black\", size=3.5) +\n",
    "  # set the labels for the title and each axis\n",
    "  labs(title=\"Y by X1, X2\", x=\"X1.X2\", y=\"Count\") + \n",
    "  # change the order of the bars on the x-axis\n",
    "  scale_x_discrete(limits=c(\"a.a\",\"a.b\",\"b.a\",\"b.b\")) + \n",
    "  # set the scale, breaks, and labels on the y-axis\n",
    "  scale_y_continuous(breaks=seq(0,15,by=5), labels=seq(0,15,by=5), limits=c(0,15), oob=rescale_none) + \n",
    "  # set the name, labels, and colors for the boxes\n",
    "  scale_fill_manual(name=\"Y\", labels=c(\"x\",\"y\",\"z\"), values=c(\"#69b3a2\",\"#404080\",\"#e69f00\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3fdd1bc5-156e-4010-b571-afed6bfac534",
   "metadata": {},
   "source": [
    "## GLM for Ordinal Distribution Data\n",
    "\n",
    "* **Distribution:** Ordinal\n",
    "* **Link:** cumulative logit\n",
    "* **Typical Uses:** Ordinal Logistic Regression: ordinal responses (i.e. Likert scales)\n",
    "* **Reporting:** \"Figure 15a shows the distribution of Likert responses (1-7) for each combination of X1 and X2. An analysis of variance based on ordinal logistic regression indicated a statistically significant effect on Y of X2 (χ2(1, N=60) = 6.14, p < .05), but not of X1 (χ2(1, N=60) = 1.65, n.s.) or of the X1×X2 interaction (χ2(1, N=60) = 0.05, n.s.).\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "81f11bed-6672-4720-8340-5d32c9068d84",
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 20 × 4</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>S</th><th scope=col>X1</th><th scope=col>X2</th><th scope=col>Y</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;int&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td> 1</td><td>a</td><td>a</td><td>7</td></tr>\n",
       "\t<tr><th scope=row>2</th><td> 2</td><td>a</td><td>b</td><td>3</td></tr>\n",
       "\t<tr><th scope=row>3</th><td> 3</td><td>b</td><td>a</td><td>3</td></tr>\n",
       "\t<tr><th scope=row>4</th><td> 4</td><td>b</td><td>b</td><td>2</td></tr>\n",
       "\t<tr><th scope=row>5</th><td> 5</td><td>a</td><td>a</td><td>5</td></tr>\n",
       "\t<tr><th scope=row>6</th><td> 6</td><td>a</td><td>b</td><td>4</td></tr>\n",
       "\t<tr><th scope=row>7</th><td> 7</td><td>b</td><td>a</td><td>3</td></tr>\n",
       "\t<tr><th scope=row>8</th><td> 8</td><td>b</td><td>b</td><td>6</td></tr>\n",
       "\t<tr><th scope=row>9</th><td> 9</td><td>a</td><td>a</td><td>4</td></tr>\n",
       "\t<tr><th scope=row>10</th><td>10</td><td>a</td><td>b</td><td>2</td></tr>\n",
       "\t<tr><th scope=row>11</th><td>11</td><td>b</td><td>a</td><td>6</td></tr>\n",
       "\t<tr><th scope=row>12</th><td>12</td><td>b</td><td>b</td><td>3</td></tr>\n",
       "\t<tr><th scope=row>13</th><td>13</td><td>a</td><td>a</td><td>2</td></tr>\n",
       "\t<tr><th scope=row>14</th><td>14</td><td>a</td><td>b</td><td>5</td></tr>\n",
       "\t<tr><th scope=row>15</th><td>15</td><td>b</td><td>a</td><td>5</td></tr>\n",
       "\t<tr><th scope=row>16</th><td>16</td><td>b</td><td>b</td><td>1</td></tr>\n",
       "\t<tr><th scope=row>17</th><td>17</td><td>a</td><td>a</td><td>7</td></tr>\n",
       "\t<tr><th scope=row>18</th><td>18</td><td>a</td><td>b</td><td>5</td></tr>\n",
       "\t<tr><th scope=row>19</th><td>19</td><td>b</td><td>a</td><td>2</td></tr>\n",
       "\t<tr><th scope=row>20</th><td>20</td><td>b</td><td>b</td><td>4</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 20 × 4\n",
       "\\begin{tabular}{r|llll}\n",
       "  & S & X1 & X2 & Y\\\\\n",
       "  & <int> & <chr> & <chr> & <int>\\\\\n",
       "\\hline\n",
       "\t1 &  1 & a & a & 7\\\\\n",
       "\t2 &  2 & a & b & 3\\\\\n",
       "\t3 &  3 & b & a & 3\\\\\n",
       "\t4 &  4 & b & b & 2\\\\\n",
       "\t5 &  5 & a & a & 5\\\\\n",
       "\t6 &  6 & a & b & 4\\\\\n",
       "\t7 &  7 & b & a & 3\\\\\n",
       "\t8 &  8 & b & b & 6\\\\\n",
       "\t9 &  9 & a & a & 4\\\\\n",
       "\t10 & 10 & a & b & 2\\\\\n",
       "\t11 & 11 & b & a & 6\\\\\n",
       "\t12 & 12 & b & b & 3\\\\\n",
       "\t13 & 13 & a & a & 2\\\\\n",
       "\t14 & 14 & a & b & 5\\\\\n",
       "\t15 & 15 & b & a & 5\\\\\n",
       "\t16 & 16 & b & b & 1\\\\\n",
       "\t17 & 17 & a & a & 7\\\\\n",
       "\t18 & 18 & a & b & 5\\\\\n",
       "\t19 & 19 & b & a & 2\\\\\n",
       "\t20 & 20 & b & b & 4\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 20 × 4\n",
       "\n",
       "| <!--/--> | S &lt;int&gt; | X1 &lt;chr&gt; | X2 &lt;chr&gt; | Y &lt;int&gt; |\n",
       "|---|---|---|---|---|\n",
       "| 1 |  1 | a | a | 7 |\n",
       "| 2 |  2 | a | b | 3 |\n",
       "| 3 |  3 | b | a | 3 |\n",
       "| 4 |  4 | b | b | 2 |\n",
       "| 5 |  5 | a | a | 5 |\n",
       "| 6 |  6 | a | b | 4 |\n",
       "| 7 |  7 | b | a | 3 |\n",
       "| 8 |  8 | b | b | 6 |\n",
       "| 9 |  9 | a | a | 4 |\n",
       "| 10 | 10 | a | b | 2 |\n",
       "| 11 | 11 | b | a | 6 |\n",
       "| 12 | 12 | b | b | 3 |\n",
       "| 13 | 13 | a | a | 2 |\n",
       "| 14 | 14 | a | b | 5 |\n",
       "| 15 | 15 | b | a | 5 |\n",
       "| 16 | 16 | b | b | 1 |\n",
       "| 17 | 17 | a | a | 7 |\n",
       "| 18 | 18 | a | b | 5 |\n",
       "| 19 | 19 | b | a | 2 |\n",
       "| 20 | 20 | b | b | 4 |\n",
       "\n"
      ],
      "text/plain": [
       "   S  X1 X2 Y\n",
       "1   1 a  a  7\n",
       "2   2 a  b  3\n",
       "3   3 b  a  3\n",
       "4   4 b  b  2\n",
       "5   5 a  a  5\n",
       "6   6 a  b  4\n",
       "7   7 b  a  3\n",
       "8   8 b  b  6\n",
       "9   9 a  a  4\n",
       "10 10 a  b  2\n",
       "11 11 b  a  6\n",
       "12 12 b  b  3\n",
       "13 13 a  a  2\n",
       "14 14 a  b  5\n",
       "15 15 b  a  5\n",
       "16 16 b  b  1\n",
       "17 17 a  a  7\n",
       "18 18 a  b  5\n",
       "19 19 b  a  2\n",
       "20 20 b  b  4"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Example data\n",
    "# df has subjects (S), two between-Ss factors (X1,X2) each w/levels (a,b), and polytomous response (Y)\n",
    "df <- read.csv(\"data/2F2LBs_ordinal.csv\")\n",
    "head(df, 20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "5da0fa45-2cf7-464a-b9a1-50b64989caaf",
   "metadata": {
    "tags": [],
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A anova: 3 × 3</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>LR Chisq</th><th scope=col>Df</th><th scope=col>Pr(&gt;Chisq)</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>X1</th><td>1.65109008</td><td>1</td><td>0.19881063</td></tr>\n",
       "\t<tr><th scope=row>X2</th><td>6.14122538</td><td>1</td><td>0.01320658</td></tr>\n",
       "\t<tr><th scope=row>X1:X2</th><td>0.04980176</td><td>1</td><td>0.82340859</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A anova: 3 × 3\n",
       "\\begin{tabular}{r|lll}\n",
       "  & LR Chisq & Df & Pr(>Chisq)\\\\\n",
       "  & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\tX1 & 1.65109008 & 1 & 0.19881063\\\\\n",
       "\tX2 & 6.14122538 & 1 & 0.01320658\\\\\n",
       "\tX1:X2 & 0.04980176 & 1 & 0.82340859\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A anova: 3 × 3\n",
       "\n",
       "| <!--/--> | LR Chisq &lt;dbl&gt; | Df &lt;dbl&gt; | Pr(&gt;Chisq) &lt;dbl&gt; |\n",
       "|---|---|---|---|\n",
       "| X1 | 1.65109008 | 1 | 0.19881063 |\n",
       "| X2 | 6.14122538 | 1 | 0.01320658 |\n",
       "| X1:X2 | 0.04980176 | 1 | 0.82340859 |\n",
       "\n"
      ],
      "text/plain": [
       "      LR Chisq   Df Pr(>Chisq)\n",
       "X1    1.65109008 1  0.19881063\n",
       "X2    6.14122538 1  0.01320658\n",
       "X1:X2 0.04980176 1  0.82340859"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(MASS) # for polr\n",
    "library(car) # for Anova\n",
    "df$S = factor(df$S)\n",
    "df$X1 = factor(df$X1)\n",
    "df$X2 = factor(df$X2)\n",
    "df$Y = ordered(df$Y) # ordinal response\n",
    "contrasts(df$X1) <- \"contr.sum\"\n",
    "contrasts(df$X2) <- \"contr.sum\"\n",
    "m = polr(Y ~ X1*X2, data=df, Hess=TRUE)\n",
    "Anova(m, type=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "70042d7d-1dc8-4225-81c0-01dfa345bf1d",
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(ggplot2)\n",
    "library(ggthemes)\n",
    "library(scales)\n",
    "library(plyr)\n",
    "\n",
    "# Ordinal histograms-as-barplots\n",
    "# http://www.sthda.com/english/wiki/ggplot2-barplots-quick-start-guide-r-software-and-data-visualization\n",
    "# https://stackoverflow.com/questions/51892875/how-to-increase-the-space-between-grouped-bars-in-ggplot2\n",
    "df2 <- as.data.frame(xtabs(~ X1+X2+Y, data=df)) # build a freq table\n",
    "df2$X12 = with(df2, interaction(X1, X2))\n",
    "df2$X12 = factor(df2$X12, levels=c(\"a.a\",\"a.b\",\"b.a\",\"b.b\"))\n",
    "df2 <- df2[order(df2$X1, df2$X2),] # sort df2 alphabetically by X1, X2\n",
    "ggplot(data=df2, aes(x=Y, y=Freq, fill=X12)) + theme_minimal() + \n",
    "  # set the font styles for the plot title and axis titles\n",
    "  theme(plot.title   = element_text(face=\"bold\",  color=\"black\", size=18, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.title.x = element_text(face=\"bold\",  color=\"black\", size=16, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.title.y = element_text(face=\"bold\",  color=\"black\", size=14, hjust=0.5, vjust=0.0, angle=90)) + \n",
    "  # set the font styles for the value labels that show on each axis\n",
    "  theme(axis.text.x  = element_text(face=\"plain\", color=\"black\", size=12, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.text.y  = element_text(face=\"plain\", color=\"black\", size=12, hjust=0.0, vjust=0.5, angle=0)) + \n",
    "  # set the font styles for the legend\n",
    "  theme(legend.title = element_text(face=\"bold\", color=\"black\", size=14, hjust=0.5, vjust=0.0, angle=0)) +\n",
    "  theme(legend.text  = element_text(face=\"plain\", color=\"black\", size=14, hjust=0.5, vjust=0.0, angle=0)) +\n",
    "  # set the font style for the facet labels\n",
    "  theme(strip.text = element_text(face=\"bold\", color=\"black\", size=14, hjust=0.5)) + \n",
    "  # use a bar plot to just plot the value for each 1-7 in (X1,X2)\n",
    "  geom_col(width=0.95, alpha=0.60) + \n",
    "  #geom_bar(stat=\"identity\", width=0.95, alpha=0.60) + # equivalent\n",
    "  # place text labels on each bar\n",
    "  geom_text(aes(label=Freq), vjust=1.2, color=\"black\", size=3.5) +\n",
    "  # create a grid of plots by (X1,X2), one for each histogram\n",
    "  #facet_grid(X12 ~ .) +  # 4x1 stack\n",
    "  #facet_grid(. ~ X12) +  # 1x4 row\n",
    "  facet_grid(X2 ~ X1) +   # 2x2 grid\n",
    "  # determine the fill color values of each histogram\n",
    "  scale_fill_manual(values=c(\"#69b3a2\",\"#404080\", \"#e69f00\", \"darkred\")) + \n",
    "  # set the labels for the title, each axis, and the legend\n",
    "  labs(title=\"Responses by X1, X2\", x=\"Likert (1-7)\", y=\"Count\") + \n",
    "  guides(fill=guide_legend(title=\"X1.X2\")) + \n",
    "  # set the ranges and value labels for each axis\n",
    "  scale_x_discrete(labels=seq(1,7,by=1)) +\n",
    "  scale_y_continuous(breaks=seq(0,6,by=1), minor_breaks=seq(0,6,by=1), labels=seq(0,6,by=1), limits=c(0,6))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0dd10056-1b98-483d-8873-d967f3d963a9",
   "metadata": {},
   "source": [
    "## GLM for Poisson Distribution Data\n",
    "\n",
    "* **Distribution:** Poisson\n",
    "* **Link:** log\n",
    "* **Typical Uses:** Poisson Regression: counts, rare events (e.g. gesture recognition errors, 3-pointers per quarter, number of \"F\" grades)\n",
    "* **Reporting:** \"Figure 16a shows an interaction plot with ±1 standard deviation error bars for X1 and X2. An analysis of variance based on Poisson regression indicated a statistically significant effect on Y of the X1×X2 interaction (χ2(1, N=60) = 3.84, p < .05), but not of either X1 (χ2(1, N=60) = 0.17, n.s.) or X2 (χ2(1, N=60) = 1.19, n.s.).\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
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   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 20 × 4</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>S</th><th scope=col>X1</th><th scope=col>X2</th><th scope=col>Y</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;int&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td> 1</td><td>a</td><td>a</td><td>5</td></tr>\n",
       "\t<tr><th scope=row>2</th><td> 2</td><td>a</td><td>b</td><td>6</td></tr>\n",
       "\t<tr><th scope=row>3</th><td> 3</td><td>b</td><td>a</td><td>7</td></tr>\n",
       "\t<tr><th scope=row>4</th><td> 4</td><td>b</td><td>b</td><td>4</td></tr>\n",
       "\t<tr><th scope=row>5</th><td> 5</td><td>a</td><td>a</td><td>4</td></tr>\n",
       "\t<tr><th scope=row>6</th><td> 6</td><td>a</td><td>b</td><td>6</td></tr>\n",
       "\t<tr><th scope=row>7</th><td> 7</td><td>b</td><td>a</td><td>6</td></tr>\n",
       "\t<tr><th scope=row>8</th><td> 8</td><td>b</td><td>b</td><td>4</td></tr>\n",
       "\t<tr><th scope=row>9</th><td> 9</td><td>a</td><td>a</td><td>4</td></tr>\n",
       "\t<tr><th scope=row>10</th><td>10</td><td>a</td><td>b</td><td>9</td></tr>\n",
       "\t<tr><th scope=row>11</th><td>11</td><td>b</td><td>a</td><td>7</td></tr>\n",
       "\t<tr><th scope=row>12</th><td>12</td><td>b</td><td>b</td><td>2</td></tr>\n",
       "\t<tr><th scope=row>13</th><td>13</td><td>a</td><td>a</td><td>3</td></tr>\n",
       "\t<tr><th scope=row>14</th><td>14</td><td>a</td><td>b</td><td>3</td></tr>\n",
       "\t<tr><th scope=row>15</th><td>15</td><td>b</td><td>a</td><td>3</td></tr>\n",
       "\t<tr><th scope=row>16</th><td>16</td><td>b</td><td>b</td><td>7</td></tr>\n",
       "\t<tr><th scope=row>17</th><td>17</td><td>a</td><td>a</td><td>5</td></tr>\n",
       "\t<tr><th scope=row>18</th><td>18</td><td>a</td><td>b</td><td>4</td></tr>\n",
       "\t<tr><th scope=row>19</th><td>19</td><td>b</td><td>a</td><td>8</td></tr>\n",
       "\t<tr><th scope=row>20</th><td>20</td><td>b</td><td>b</td><td>3</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 20 × 4\n",
       "\\begin{tabular}{r|llll}\n",
       "  & S & X1 & X2 & Y\\\\\n",
       "  & <int> & <chr> & <chr> & <int>\\\\\n",
       "\\hline\n",
       "\t1 &  1 & a & a & 5\\\\\n",
       "\t2 &  2 & a & b & 6\\\\\n",
       "\t3 &  3 & b & a & 7\\\\\n",
       "\t4 &  4 & b & b & 4\\\\\n",
       "\t5 &  5 & a & a & 4\\\\\n",
       "\t6 &  6 & a & b & 6\\\\\n",
       "\t7 &  7 & b & a & 6\\\\\n",
       "\t8 &  8 & b & b & 4\\\\\n",
       "\t9 &  9 & a & a & 4\\\\\n",
       "\t10 & 10 & a & b & 9\\\\\n",
       "\t11 & 11 & b & a & 7\\\\\n",
       "\t12 & 12 & b & b & 2\\\\\n",
       "\t13 & 13 & a & a & 3\\\\\n",
       "\t14 & 14 & a & b & 3\\\\\n",
       "\t15 & 15 & b & a & 3\\\\\n",
       "\t16 & 16 & b & b & 7\\\\\n",
       "\t17 & 17 & a & a & 5\\\\\n",
       "\t18 & 18 & a & b & 4\\\\\n",
       "\t19 & 19 & b & a & 8\\\\\n",
       "\t20 & 20 & b & b & 3\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 20 × 4\n",
       "\n",
       "| <!--/--> | S &lt;int&gt; | X1 &lt;chr&gt; | X2 &lt;chr&gt; | Y &lt;int&gt; |\n",
       "|---|---|---|---|---|\n",
       "| 1 |  1 | a | a | 5 |\n",
       "| 2 |  2 | a | b | 6 |\n",
       "| 3 |  3 | b | a | 7 |\n",
       "| 4 |  4 | b | b | 4 |\n",
       "| 5 |  5 | a | a | 4 |\n",
       "| 6 |  6 | a | b | 6 |\n",
       "| 7 |  7 | b | a | 6 |\n",
       "| 8 |  8 | b | b | 4 |\n",
       "| 9 |  9 | a | a | 4 |\n",
       "| 10 | 10 | a | b | 9 |\n",
       "| 11 | 11 | b | a | 7 |\n",
       "| 12 | 12 | b | b | 2 |\n",
       "| 13 | 13 | a | a | 3 |\n",
       "| 14 | 14 | a | b | 3 |\n",
       "| 15 | 15 | b | a | 3 |\n",
       "| 16 | 16 | b | b | 7 |\n",
       "| 17 | 17 | a | a | 5 |\n",
       "| 18 | 18 | a | b | 4 |\n",
       "| 19 | 19 | b | a | 8 |\n",
       "| 20 | 20 | b | b | 3 |\n",
       "\n"
      ],
      "text/plain": [
       "   S  X1 X2 Y\n",
       "1   1 a  a  5\n",
       "2   2 a  b  6\n",
       "3   3 b  a  7\n",
       "4   4 b  b  4\n",
       "5   5 a  a  4\n",
       "6   6 a  b  6\n",
       "7   7 b  a  6\n",
       "8   8 b  b  4\n",
       "9   9 a  a  4\n",
       "10 10 a  b  9\n",
       "11 11 b  a  7\n",
       "12 12 b  b  2\n",
       "13 13 a  a  3\n",
       "14 14 a  b  3\n",
       "15 15 b  a  3\n",
       "16 16 b  b  7\n",
       "17 17 a  a  5\n",
       "18 18 a  b  4\n",
       "19 19 b  a  8\n",
       "20 20 b  b  3"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Example data\n",
    "# df has subjects (S), two factors (X1,X2) each w/levels (a,b), and count response (Y)\n",
    "df <- read.csv(\"data/2F2LBs_poisson.csv\")\n",
    "head(df, 20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "c1994c65-ad46-4def-9789-1f4fadd2fe24",
   "metadata": {
    "tags": [],
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   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A anova: 3 × 3</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>LR Chisq</th><th scope=col>Df</th><th scope=col>Pr(&gt;Chisq)</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>X1</th><td>0.1673829</td><td>1</td><td>0.68244826</td></tr>\n",
       "\t<tr><th scope=row>X2</th><td>1.1865585</td><td>1</td><td>0.27602485</td></tr>\n",
       "\t<tr><th scope=row>X1:X2</th><td>3.8423440</td><td>1</td><td>0.04997361</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A anova: 3 × 3\n",
       "\\begin{tabular}{r|lll}\n",
       "  & LR Chisq & Df & Pr(>Chisq)\\\\\n",
       "  & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\tX1 & 0.1673829 & 1 & 0.68244826\\\\\n",
       "\tX2 & 1.1865585 & 1 & 0.27602485\\\\\n",
       "\tX1:X2 & 3.8423440 & 1 & 0.04997361\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A anova: 3 × 3\n",
       "\n",
       "| <!--/--> | LR Chisq &lt;dbl&gt; | Df &lt;dbl&gt; | Pr(&gt;Chisq) &lt;dbl&gt; |\n",
       "|---|---|---|---|\n",
       "| X1 | 0.1673829 | 1 | 0.68244826 |\n",
       "| X2 | 1.1865585 | 1 | 0.27602485 |\n",
       "| X1:X2 | 3.8423440 | 1 | 0.04997361 |\n",
       "\n"
      ],
      "text/plain": [
       "      LR Chisq  Df Pr(>Chisq)\n",
       "X1    0.1673829 1  0.68244826\n",
       "X2    1.1865585 1  0.27602485\n",
       "X1:X2 3.8423440 1  0.04997361"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(car) # for Anova\n",
    "df$S = factor(df$S)\n",
    "df$X1 = factor(df$X1)\n",
    "df$X2 = factor(df$X2)\n",
    "contrasts(df$X1) <- \"contr.sum\"\n",
    "contrasts(df$X2) <- \"contr.sum\"\n",
    "m = glm(Y ~ X1*X2, data=df, family=poisson)\n",
    "Anova(m, type=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
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   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(ggplot2)\n",
    "library(ggthemes)\n",
    "library(scales)\n",
    "library(plyr)\n",
    "\n",
    "# Interaction plot\n",
    "# http://www.sthda.com/english/wiki/ggplot2-line-plot-quick-start-guide-r-software-and-data-visualization\n",
    "# http://www.sthda.com/english/wiki/ggplot2-error-bars-quick-start-guide-r-software-and-data-visualization\n",
    "# http://www.sthda.com/english/wiki/ggplot2-point-shapes\n",
    "# http://www.sthda.com/english/wiki/ggplot2-line-types-how-to-change-line-types-of-a-graph-in-r-software\n",
    "df2 <- ddply(df, ~ X1*X2, function(d) # make a summary data table\n",
    "  c(NROW(d$Y),\n",
    "    sum(is.na(d$Y)),\n",
    "    sum(!is.na(d$Y)),\n",
    "    mean(d$Y, na.rm=TRUE),\n",
    "    sd(d$Y, na.rm=TRUE),\n",
    "    median(d$Y, na.rm=TRUE),\n",
    "    IQR(d$Y, na.rm=TRUE)))\n",
    "colnames(df2) <- c(\"X1\",\"X2\",\"Rows\",\"NAs\",\"NotNAs\",\"Mean\",\"SD\",\"Median\",\"IQR\")\n",
    "ggplot(data=df2, aes(x=X1, y=Mean, color=X2, group=X2)) + theme_minimal() + \n",
    "  # set the font styles for the plot title and axis titles\n",
    "  theme(plot.title   = element_text(face=\"bold\",  color=\"black\", size=18, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.title.x = element_text(face=\"bold\",  color=\"black\", size=16, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.title.y = element_text(face=\"bold\",  color=\"black\", size=16, hjust=0.5, vjust=0.0, angle=90)) + \n",
    "  # set the font styles for the value labels that show on each axis\n",
    "  theme(axis.text.x  = element_text(face=\"plain\", color=\"black\", size=14, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.text.y  = element_text(face=\"plain\", color=\"black\", size=12, hjust=0.0, vjust=0.5, angle=0)) + \n",
    "  # set the font styles for the legend\n",
    "  theme(legend.title = element_text(face=\"bold\", color=\"black\", size=14, hjust=0.5, vjust=0.0, angle=0)) +\n",
    "  theme(legend.text  = element_text(face=\"plain\", color=\"black\", size=14, hjust=0.5, vjust=0.0, angle=0)) +\n",
    "  # create the plot lines, points, and error bars\n",
    "  geom_line(aes(linetype=X2), position=position_dodge(0.05)) + \n",
    "  geom_point(aes(shape=X2, size=X2), position=position_dodge(0.05)) + \n",
    "  geom_errorbar(aes(ymin=Mean-SD, ymax=Mean+SD), position=position_dodge(0.05), width=0.1) + \n",
    "  # place text labels on each bar\n",
    "  geom_text(aes(label=sprintf(\"%.2f (±%.2f)\", Mean, SD)), position=position_dodge(0.05), hjust=0.0, vjust=-1.0, color=\"black\", size=3.5) +\n",
    "  # set the labels for the title and each axis\n",
    "  labs(title=\"Y by X1, X2\", x=\"X1\", y=\"Y\") + \n",
    "  # set the ranges and value labels for each axis\n",
    "  scale_x_discrete(labels=c(\"a\",\"b\")) + \n",
    "  scale_y_continuous(breaks=seq(0,7,by=2), labels=seq(0,7,by=2), limits=c(0,7), oob=rescale_none) + \n",
    "  # set the name, labels, and colors for the traces\n",
    "  scale_color_manual(name=\"X2\", labels=c(\"a\",\"b\"), values=c(\"red\", \"blue\")) +\n",
    "  # set the size and shape of the points\n",
    "  scale_size_manual(values=c(4,4)) +\n",
    "  scale_shape_manual(values=c(16,10)) +\n",
    "  # set the linetype of the lines\n",
    "  scale_linetype_manual(values=c(\"solid\", \"longdash\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fdd07b2d-8085-480b-8c8b-193e80c2e7a1",
   "metadata": {},
   "source": [
    "## GLM for Zero-Inflated Poisson Distribution Data\n",
    "\n",
    "* **Distribution:** Zero-Inflated Poisson\n",
    "* **Link:** log\n",
    "* **Typical Uses:** Zero-Inflated Poisson Regression: counts, rare events with large proportion of zeroes\n",
    "* **Reporting:** \"Figure 17a shows histograms of Y by X1 and X2. An analysis of variance based on zero-inflated Poisson regression indicated a statistically significant effect on Y of the X1×X2 interaction (χ2(1, N=60) = 8.14, p < .01), and a marginal effect of X2 (χ2(1, N=60) = 3.11, p = .078). There was no statistically significant effect of X1 on Y (χ2(1, N=60) = 0.29, n.s.).\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "7f27d5e9-9573-43e1-bd84-09b900d397a9",
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    "vscode": {
     "languageId": "r"
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   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 20 × 4</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>S</th><th scope=col>X1</th><th scope=col>X2</th><th scope=col>Y</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;int&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td> 1</td><td>a</td><td>a</td><td>1</td></tr>\n",
       "\t<tr><th scope=row>2</th><td> 2</td><td>a</td><td>b</td><td>0</td></tr>\n",
       "\t<tr><th scope=row>3</th><td> 3</td><td>b</td><td>a</td><td>0</td></tr>\n",
       "\t<tr><th scope=row>4</th><td> 4</td><td>b</td><td>b</td><td>2</td></tr>\n",
       "\t<tr><th scope=row>5</th><td> 5</td><td>a</td><td>a</td><td>1</td></tr>\n",
       "\t<tr><th scope=row>6</th><td> 6</td><td>a</td><td>b</td><td>5</td></tr>\n",
       "\t<tr><th scope=row>7</th><td> 7</td><td>b</td><td>a</td><td>6</td></tr>\n",
       "\t<tr><th scope=row>8</th><td> 8</td><td>b</td><td>b</td><td>5</td></tr>\n",
       "\t<tr><th scope=row>9</th><td> 9</td><td>a</td><td>a</td><td>1</td></tr>\n",
       "\t<tr><th scope=row>10</th><td>10</td><td>a</td><td>b</td><td>0</td></tr>\n",
       "\t<tr><th scope=row>11</th><td>11</td><td>b</td><td>a</td><td>0</td></tr>\n",
       "\t<tr><th scope=row>12</th><td>12</td><td>b</td><td>b</td><td>8</td></tr>\n",
       "\t<tr><th scope=row>13</th><td>13</td><td>a</td><td>a</td><td>4</td></tr>\n",
       "\t<tr><th scope=row>14</th><td>14</td><td>a</td><td>b</td><td>1</td></tr>\n",
       "\t<tr><th scope=row>15</th><td>15</td><td>b</td><td>a</td><td>0</td></tr>\n",
       "\t<tr><th scope=row>16</th><td>16</td><td>b</td><td>b</td><td>0</td></tr>\n",
       "\t<tr><th scope=row>17</th><td>17</td><td>a</td><td>a</td><td>8</td></tr>\n",
       "\t<tr><th scope=row>18</th><td>18</td><td>a</td><td>b</td><td>5</td></tr>\n",
       "\t<tr><th scope=row>19</th><td>19</td><td>b</td><td>a</td><td>5</td></tr>\n",
       "\t<tr><th scope=row>20</th><td>20</td><td>b</td><td>b</td><td>3</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 20 × 4\n",
       "\\begin{tabular}{r|llll}\n",
       "  & S & X1 & X2 & Y\\\\\n",
       "  & <int> & <chr> & <chr> & <int>\\\\\n",
       "\\hline\n",
       "\t1 &  1 & a & a & 1\\\\\n",
       "\t2 &  2 & a & b & 0\\\\\n",
       "\t3 &  3 & b & a & 0\\\\\n",
       "\t4 &  4 & b & b & 2\\\\\n",
       "\t5 &  5 & a & a & 1\\\\\n",
       "\t6 &  6 & a & b & 5\\\\\n",
       "\t7 &  7 & b & a & 6\\\\\n",
       "\t8 &  8 & b & b & 5\\\\\n",
       "\t9 &  9 & a & a & 1\\\\\n",
       "\t10 & 10 & a & b & 0\\\\\n",
       "\t11 & 11 & b & a & 0\\\\\n",
       "\t12 & 12 & b & b & 8\\\\\n",
       "\t13 & 13 & a & a & 4\\\\\n",
       "\t14 & 14 & a & b & 1\\\\\n",
       "\t15 & 15 & b & a & 0\\\\\n",
       "\t16 & 16 & b & b & 0\\\\\n",
       "\t17 & 17 & a & a & 8\\\\\n",
       "\t18 & 18 & a & b & 5\\\\\n",
       "\t19 & 19 & b & a & 5\\\\\n",
       "\t20 & 20 & b & b & 3\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 20 × 4\n",
       "\n",
       "| <!--/--> | S &lt;int&gt; | X1 &lt;chr&gt; | X2 &lt;chr&gt; | Y &lt;int&gt; |\n",
       "|---|---|---|---|---|\n",
       "| 1 |  1 | a | a | 1 |\n",
       "| 2 |  2 | a | b | 0 |\n",
       "| 3 |  3 | b | a | 0 |\n",
       "| 4 |  4 | b | b | 2 |\n",
       "| 5 |  5 | a | a | 1 |\n",
       "| 6 |  6 | a | b | 5 |\n",
       "| 7 |  7 | b | a | 6 |\n",
       "| 8 |  8 | b | b | 5 |\n",
       "| 9 |  9 | a | a | 1 |\n",
       "| 10 | 10 | a | b | 0 |\n",
       "| 11 | 11 | b | a | 0 |\n",
       "| 12 | 12 | b | b | 8 |\n",
       "| 13 | 13 | a | a | 4 |\n",
       "| 14 | 14 | a | b | 1 |\n",
       "| 15 | 15 | b | a | 0 |\n",
       "| 16 | 16 | b | b | 0 |\n",
       "| 17 | 17 | a | a | 8 |\n",
       "| 18 | 18 | a | b | 5 |\n",
       "| 19 | 19 | b | a | 5 |\n",
       "| 20 | 20 | b | b | 3 |\n",
       "\n"
      ],
      "text/plain": [
       "   S  X1 X2 Y\n",
       "1   1 a  a  1\n",
       "2   2 a  b  0\n",
       "3   3 b  a  0\n",
       "4   4 b  b  2\n",
       "5   5 a  a  1\n",
       "6   6 a  b  5\n",
       "7   7 b  a  6\n",
       "8   8 b  b  5\n",
       "9   9 a  a  1\n",
       "10 10 a  b  0\n",
       "11 11 b  a  0\n",
       "12 12 b  b  8\n",
       "13 13 a  a  4\n",
       "14 14 a  b  1\n",
       "15 15 b  a  0\n",
       "16 16 b  b  0\n",
       "17 17 a  a  8\n",
       "18 18 a  b  5\n",
       "19 19 b  a  5\n",
       "20 20 b  b  3"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Example data\n",
    "# df has subjects (S), two factors (X1,X2) each w/levels (a,b), and count response (Y)\n",
    "df <- read.csv(\"data/2F2LBs_zipoisson.csv\")\n",
    "head(df, 20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "e0e7d895-5e84-4745-8e8d-982ea11d7ef1",
   "metadata": {
    "tags": [],
    "vscode": {
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    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Classes and Methods for R developed in the\n",
      "Political Science Computational Laboratory\n",
      "Department of Political Science\n",
      "Stanford University\n",
      "Simon Jackman\n",
      "hurdle and zeroinfl functions by Achim Zeileis\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A anova: 3 × 3</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>Df</th><th scope=col>Chisq</th><th scope=col>Pr(&gt;Chisq)</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>X1</th><td>1</td><td>0.2896066</td><td>0.590472759</td></tr>\n",
       "\t<tr><th scope=row>X2</th><td>1</td><td>3.1082852</td><td>0.077894931</td></tr>\n",
       "\t<tr><th scope=row>X1:X2</th><td>1</td><td>8.1401659</td><td>0.004329532</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A anova: 3 × 3\n",
       "\\begin{tabular}{r|lll}\n",
       "  & Df & Chisq & Pr(>Chisq)\\\\\n",
       "  & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\tX1 & 1 & 0.2896066 & 0.590472759\\\\\n",
       "\tX2 & 1 & 3.1082852 & 0.077894931\\\\\n",
       "\tX1:X2 & 1 & 8.1401659 & 0.004329532\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A anova: 3 × 3\n",
       "\n",
       "| <!--/--> | Df &lt;dbl&gt; | Chisq &lt;dbl&gt; | Pr(&gt;Chisq) &lt;dbl&gt; |\n",
       "|---|---|---|---|\n",
       "| X1 | 1 | 0.2896066 | 0.590472759 |\n",
       "| X2 | 1 | 3.1082852 | 0.077894931 |\n",
       "| X1:X2 | 1 | 8.1401659 | 0.004329532 |\n",
       "\n"
      ],
      "text/plain": [
       "      Df Chisq     Pr(>Chisq) \n",
       "X1    1  0.2896066 0.590472759\n",
       "X2    1  3.1082852 0.077894931\n",
       "X1:X2 1  8.1401659 0.004329532"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(pscl) # for zeroinfl\n",
    "library(car) # for Anova\n",
    "df$S = factor(df$S)\n",
    "df$X1 = factor(df$X1)\n",
    "df$X2 = factor(df$X2)\n",
    "contrasts(df$X1) <- \"contr.sum\"\n",
    "contrasts(df$X2) <- \"contr.sum\"\n",
    "m = zeroinfl(Y ~ X1*X2, data=df, dist=\"poisson\")\n",
    "Anova(m, type=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "c23ee66d-0c60-4ce1-899a-2eecc994a9bd",
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   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "“\u001b[1m\u001b[22mThe dot-dot notation (`..count..`) was deprecated in ggplot2 3.4.0.\n",
      "\u001b[36mℹ\u001b[39m Please use `after_stat(count)` instead.”\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(ggplot2)\n",
    "library(ggthemes)\n",
    "library(scales)\n",
    "library(plyr)\n",
    "\n",
    "# Histograms\n",
    "# http://www.sthda.com/english/wiki/ggplot2-histogram-plot-quick-start-guide-r-software-and-data-visualization\n",
    "ggplot(data=df, aes(x=Y, fill=X1, color=X2)) + theme_minimal() + \n",
    "  # set the font styles for the plot title and axis titles\n",
    "  theme(plot.title   = element_text(face=\"bold\",  color=\"black\", size=18, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.title.x = element_text(face=\"bold\",  color=\"black\", size=16, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.title.y = element_text(face=\"bold\",  color=\"black\", size=16, hjust=0.5, vjust=0.0, angle=90)) + \n",
    "  # set the font styles for the value labels that show on each axis\n",
    "  theme(axis.text.x  = element_text(face=\"plain\", color=\"black\", size=12, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.text.y  = element_text(face=\"plain\", color=\"black\", size=12, hjust=0.0, vjust=0.5, angle=0)) + \n",
    "  # set the font style for the facet labels\n",
    "  theme(strip.text = element_text(face=\"bold\", color=\"black\", size=14, hjust=0.5)) + \n",
    "  # remove the legend\n",
    "  theme(legend.position=\"none\") + \n",
    "  # create the histogram; the alpha value ensures overlaps can be seen\n",
    "  geom_histogram(binwidth=1, breaks=seq(-0.5,10.5,by=1), alpha=0.25) + \n",
    "  stat_bin(aes(y=..count.., label=..count..), binwidth=1, geom=\"text\", vjust=-0.5) + \n",
    "  # create stacked plots by X, one for each histogram\n",
    "  facet_grid(X1+X2 ~ .) + \n",
    "  # determine the outline and fill color values of each histogram\n",
    "  scale_color_manual(values=c(\"darkblue\",\"darkred\")) + \n",
    "  scale_fill_manual(values=c(\"#69b3a2\",\"#404080\")) + \n",
    "  # set the labels for the title and each axis\n",
    "  labs(title=\"Y by X1, X2\", x=\"Y\", y=\"Count\") + \n",
    "  # set the ranges and value labels for each axis\n",
    "  scale_x_continuous(breaks=seq(-0.5,10.5,by=1), labels=seq(0,11,by=1), limits=c(-0.5,10.5)) +\n",
    "  scale_y_continuous(breaks=seq(0,8,by=2), labels=seq(0,8,by=2), limits=c(0,8))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "670b193a-2073-4343-996a-549c3017fed2",
   "metadata": {},
   "source": [
    "## GLM for Negative Binomial Distribution Data\n",
    "\n",
    "* **Distribution:** Negative Binomial\n",
    "* **Link:** log\n",
    "* **Typical Uses:** Negative Binomial Regression: Same as Poisson but for use in the presence of overdispersion\n",
    "* **Reporting:** \"Figure 18a shows an interaction plot with ±1 standard deviation error bars for X1 and X2. An analysis of variance based on negative binomial regression indicated a statistically significant effect on Y of X1 (χ2(1, N=60) = 13.46, p < .001), but not of X2 (χ2(1, N=60) = 0.07, n.s.) or the X1×X2 interaction (χ2(1, N=60) = 0.92, n.s.).\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "ab5d3b8f-8ae8-401e-8cb0-371befb509b6",
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 20 × 4</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>S</th><th scope=col>X1</th><th scope=col>X2</th><th scope=col>Y</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;int&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td> 1</td><td>a</td><td>a</td><td> 1</td></tr>\n",
       "\t<tr><th scope=row>2</th><td> 2</td><td>a</td><td>b</td><td> 1</td></tr>\n",
       "\t<tr><th scope=row>3</th><td> 3</td><td>b</td><td>a</td><td> 2</td></tr>\n",
       "\t<tr><th scope=row>4</th><td> 4</td><td>b</td><td>b</td><td> 9</td></tr>\n",
       "\t<tr><th scope=row>5</th><td> 5</td><td>a</td><td>a</td><td> 0</td></tr>\n",
       "\t<tr><th scope=row>6</th><td> 6</td><td>a</td><td>b</td><td> 1</td></tr>\n",
       "\t<tr><th scope=row>7</th><td> 7</td><td>b</td><td>a</td><td> 1</td></tr>\n",
       "\t<tr><th scope=row>8</th><td> 8</td><td>b</td><td>b</td><td> 7</td></tr>\n",
       "\t<tr><th scope=row>9</th><td> 9</td><td>a</td><td>a</td><td> 2</td></tr>\n",
       "\t<tr><th scope=row>10</th><td>10</td><td>a</td><td>b</td><td> 2</td></tr>\n",
       "\t<tr><th scope=row>11</th><td>11</td><td>b</td><td>a</td><td> 6</td></tr>\n",
       "\t<tr><th scope=row>12</th><td>12</td><td>b</td><td>b</td><td> 1</td></tr>\n",
       "\t<tr><th scope=row>13</th><td>13</td><td>a</td><td>a</td><td> 2</td></tr>\n",
       "\t<tr><th scope=row>14</th><td>14</td><td>a</td><td>b</td><td> 3</td></tr>\n",
       "\t<tr><th scope=row>15</th><td>15</td><td>b</td><td>a</td><td> 3</td></tr>\n",
       "\t<tr><th scope=row>16</th><td>16</td><td>b</td><td>b</td><td> 1</td></tr>\n",
       "\t<tr><th scope=row>17</th><td>17</td><td>a</td><td>a</td><td> 2</td></tr>\n",
       "\t<tr><th scope=row>18</th><td>18</td><td>a</td><td>b</td><td> 3</td></tr>\n",
       "\t<tr><th scope=row>19</th><td>19</td><td>b</td><td>a</td><td>10</td></tr>\n",
       "\t<tr><th scope=row>20</th><td>20</td><td>b</td><td>b</td><td> 4</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 20 × 4\n",
       "\\begin{tabular}{r|llll}\n",
       "  & S & X1 & X2 & Y\\\\\n",
       "  & <int> & <chr> & <chr> & <int>\\\\\n",
       "\\hline\n",
       "\t1 &  1 & a & a &  1\\\\\n",
       "\t2 &  2 & a & b &  1\\\\\n",
       "\t3 &  3 & b & a &  2\\\\\n",
       "\t4 &  4 & b & b &  9\\\\\n",
       "\t5 &  5 & a & a &  0\\\\\n",
       "\t6 &  6 & a & b &  1\\\\\n",
       "\t7 &  7 & b & a &  1\\\\\n",
       "\t8 &  8 & b & b &  7\\\\\n",
       "\t9 &  9 & a & a &  2\\\\\n",
       "\t10 & 10 & a & b &  2\\\\\n",
       "\t11 & 11 & b & a &  6\\\\\n",
       "\t12 & 12 & b & b &  1\\\\\n",
       "\t13 & 13 & a & a &  2\\\\\n",
       "\t14 & 14 & a & b &  3\\\\\n",
       "\t15 & 15 & b & a &  3\\\\\n",
       "\t16 & 16 & b & b &  1\\\\\n",
       "\t17 & 17 & a & a &  2\\\\\n",
       "\t18 & 18 & a & b &  3\\\\\n",
       "\t19 & 19 & b & a & 10\\\\\n",
       "\t20 & 20 & b & b &  4\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 20 × 4\n",
       "\n",
       "| <!--/--> | S &lt;int&gt; | X1 &lt;chr&gt; | X2 &lt;chr&gt; | Y &lt;int&gt; |\n",
       "|---|---|---|---|---|\n",
       "| 1 |  1 | a | a |  1 |\n",
       "| 2 |  2 | a | b |  1 |\n",
       "| 3 |  3 | b | a |  2 |\n",
       "| 4 |  4 | b | b |  9 |\n",
       "| 5 |  5 | a | a |  0 |\n",
       "| 6 |  6 | a | b |  1 |\n",
       "| 7 |  7 | b | a |  1 |\n",
       "| 8 |  8 | b | b |  7 |\n",
       "| 9 |  9 | a | a |  2 |\n",
       "| 10 | 10 | a | b |  2 |\n",
       "| 11 | 11 | b | a |  6 |\n",
       "| 12 | 12 | b | b |  1 |\n",
       "| 13 | 13 | a | a |  2 |\n",
       "| 14 | 14 | a | b |  3 |\n",
       "| 15 | 15 | b | a |  3 |\n",
       "| 16 | 16 | b | b |  1 |\n",
       "| 17 | 17 | a | a |  2 |\n",
       "| 18 | 18 | a | b |  3 |\n",
       "| 19 | 19 | b | a | 10 |\n",
       "| 20 | 20 | b | b |  4 |\n",
       "\n"
      ],
      "text/plain": [
       "   S  X1 X2 Y \n",
       "1   1 a  a   1\n",
       "2   2 a  b   1\n",
       "3   3 b  a   2\n",
       "4   4 b  b   9\n",
       "5   5 a  a   0\n",
       "6   6 a  b   1\n",
       "7   7 b  a   1\n",
       "8   8 b  b   7\n",
       "9   9 a  a   2\n",
       "10 10 a  b   2\n",
       "11 11 b  a   6\n",
       "12 12 b  b   1\n",
       "13 13 a  a   2\n",
       "14 14 a  b   3\n",
       "15 15 b  a   3\n",
       "16 16 b  b   1\n",
       "17 17 a  a   2\n",
       "18 18 a  b   3\n",
       "19 19 b  a  10\n",
       "20 20 b  b   4"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Example data\n",
    "# df has subjects (S), two factors (X1,X2) each w/levels (a,b), and count response (Y)\n",
    "df <- read.csv(\"data/2F2LBs_negbin.csv\")\n",
    "head(df, 20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "fd902cec-eb39-4245-a176-55671b7cb241",
   "metadata": {
    "tags": [],
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A anova: 3 × 3</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>LR Chisq</th><th scope=col>Df</th><th scope=col>Pr(&gt;Chisq)</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>X1</th><td>13.4596339</td><td>1</td><td>0.0002437513</td></tr>\n",
       "\t<tr><th scope=row>X2</th><td> 0.0663977</td><td>1</td><td>0.7966558091</td></tr>\n",
       "\t<tr><th scope=row>X1:X2</th><td> 0.9247341</td><td>1</td><td>0.3362350241</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A anova: 3 × 3\n",
       "\\begin{tabular}{r|lll}\n",
       "  & LR Chisq & Df & Pr(>Chisq)\\\\\n",
       "  & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\tX1 & 13.4596339 & 1 & 0.0002437513\\\\\n",
       "\tX2 &  0.0663977 & 1 & 0.7966558091\\\\\n",
       "\tX1:X2 &  0.9247341 & 1 & 0.3362350241\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A anova: 3 × 3\n",
       "\n",
       "| <!--/--> | LR Chisq &lt;dbl&gt; | Df &lt;dbl&gt; | Pr(&gt;Chisq) &lt;dbl&gt; |\n",
       "|---|---|---|---|\n",
       "| X1 | 13.4596339 | 1 | 0.0002437513 |\n",
       "| X2 |  0.0663977 | 1 | 0.7966558091 |\n",
       "| X1:X2 |  0.9247341 | 1 | 0.3362350241 |\n",
       "\n"
      ],
      "text/plain": [
       "      LR Chisq   Df Pr(>Chisq)  \n",
       "X1    13.4596339 1  0.0002437513\n",
       "X2     0.0663977 1  0.7966558091\n",
       "X1:X2  0.9247341 1  0.3362350241"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(MASS) # for glm.nb\n",
    "library(car) # for Anova\n",
    "df$S = factor(df$S)\n",
    "df$X1 = factor(df$X1)\n",
    "df$X2 = factor(df$X2)\n",
    "contrasts(df$X1) <- \"contr.sum\"\n",
    "contrasts(df$X2) <- \"contr.sum\"\n",
    "m = glm.nb(Y ~ X1*X2, data=df)\n",
    "Anova(m, type=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "b25eb59d-b027-49a6-bc02-0b5896423790",
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(ggplot2)\n",
    "library(ggthemes)\n",
    "library(scales)\n",
    "library(plyr)\n",
    "\n",
    "# Interaction plot\n",
    "# http://www.sthda.com/english/wiki/ggplot2-line-plot-quick-start-guide-r-software-and-data-visualization\n",
    "# http://www.sthda.com/english/wiki/ggplot2-error-bars-quick-start-guide-r-software-and-data-visualization\n",
    "# http://www.sthda.com/english/wiki/ggplot2-point-shapes\n",
    "# http://www.sthda.com/english/wiki/ggplot2-line-types-how-to-change-line-types-of-a-graph-in-r-software\n",
    "df2 <- ddply(df, ~ X1*X2, function(d) # make a summary data table\n",
    "  c(NROW(d$Y),\n",
    "    sum(is.na(d$Y)),\n",
    "    sum(!is.na(d$Y)),\n",
    "    mean(d$Y, na.rm=TRUE),\n",
    "    sd(d$Y, na.rm=TRUE),\n",
    "    median(d$Y, na.rm=TRUE),\n",
    "    IQR(d$Y, na.rm=TRUE)))\n",
    "colnames(df2) <- c(\"X1\",\"X2\",\"Rows\",\"NAs\",\"NotNAs\",\"Mean\",\"SD\",\"Median\",\"IQR\")\n",
    "ggplot(data=df2, aes(x=X1, y=Mean, color=X2, group=X2)) + theme_minimal() + \n",
    "  # set the font styles for the plot title and axis titles\n",
    "  theme(plot.title   = element_text(face=\"bold\",  color=\"black\", size=18, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.title.x = element_text(face=\"bold\",  color=\"black\", size=16, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.title.y = element_text(face=\"bold\",  color=\"black\", size=16, hjust=0.5, vjust=0.0, angle=90)) + \n",
    "  # set the font styles for the value labels that show on each axis\n",
    "  theme(axis.text.x  = element_text(face=\"plain\", color=\"black\", size=14, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.text.y  = element_text(face=\"plain\", color=\"black\", size=12, hjust=0.0, vjust=0.5, angle=0)) + \n",
    "  # set the font styles for the legend\n",
    "  theme(legend.title = element_text(face=\"bold\", color=\"black\", size=14, hjust=0.5, vjust=0.0, angle=0)) +\n",
    "  theme(legend.text  = element_text(face=\"plain\", color=\"black\", size=14, hjust=0.5, vjust=0.0, angle=0)) +\n",
    "  # create the plot lines, points, and error bars\n",
    "  geom_line(aes(linetype=X2), position=position_dodge(0.05)) + \n",
    "  geom_point(aes(shape=X2, size=X2), position=position_dodge(0.05)) + \n",
    "  geom_errorbar(aes(ymin=Mean-SD, ymax=Mean+SD), position=position_dodge(0.05), width=0.1) + \n",
    "  # place text labels on each bar\n",
    "  geom_text(aes(label=sprintf(\"%.2f (±%.2f)\", Mean, SD)), position=position_dodge(0.05), hjust=0.0, vjust=-1.0, color=\"black\", size=3.5) +\n",
    "  # set the labels for the title and each axis\n",
    "  labs(title=\"Y by X1, X2\", x=\"X1\", y=\"Y\") + \n",
    "  # set the ranges and value labels for each axis\n",
    "  scale_x_discrete(labels=c(\"a\",\"b\")) + \n",
    "  scale_y_continuous(breaks=seq(0,10,by=2), labels=seq(0,10,by=2), limits=c(0,10), oob=rescale_none) + \n",
    "  # set the name, labels, and colors for the traces\n",
    "  scale_color_manual(name=\"X2\", labels=c(\"a\",\"b\"), values=c(\"red\", \"blue\")) +\n",
    "  # set the size and shape of the points\n",
    "  scale_size_manual(values=c(4,4)) +\n",
    "  scale_shape_manual(values=c(16,10)) +\n",
    "  # set the linetype of the lines\n",
    "  scale_linetype_manual(values=c(\"solid\", \"longdash\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "807420d2-fc59-4523-a62d-50675eb92f53",
   "metadata": {},
   "source": [
    "## GLM for Zero-Inflated Negative Binomial Distribution Data\n",
    "\n",
    "* **Distribution:** Zero-Inflated Negative Binomial\n",
    "* **Link:** log\n",
    "* **Typical Uses:** Zero-Inflated Negative Binomial Regression: Same as Zero-Inflated Poisson but for use in the presence of overdispersion\n",
    "* **Reporting:** \"Figure 19a shows histograms of Y by X1 and X2. An analysis of variance based on zero-inflated negative binomial regression indicated no statistically significant effects on Y of X1 (χ2(1, N=60) = 0.43, n.s.), X2 (χ2(1, N=60) = 1.28, n.s.), or the X1×X2 interaction (χ2(1, N=60) = 0.10, n.s.).\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "1bab1e43-5dfd-466b-9ad5-258caaf98677",
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 20 × 4</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>S</th><th scope=col>X1</th><th scope=col>X2</th><th scope=col>Y</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;int&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td> 1</td><td>a</td><td>a</td><td> 3</td></tr>\n",
       "\t<tr><th scope=row>2</th><td> 2</td><td>a</td><td>b</td><td> 1</td></tr>\n",
       "\t<tr><th scope=row>3</th><td> 3</td><td>b</td><td>a</td><td>13</td></tr>\n",
       "\t<tr><th scope=row>4</th><td> 4</td><td>b</td><td>b</td><td> 0</td></tr>\n",
       "\t<tr><th scope=row>5</th><td> 5</td><td>a</td><td>a</td><td> 0</td></tr>\n",
       "\t<tr><th scope=row>6</th><td> 6</td><td>a</td><td>b</td><td> 1</td></tr>\n",
       "\t<tr><th scope=row>7</th><td> 7</td><td>b</td><td>a</td><td> 0</td></tr>\n",
       "\t<tr><th scope=row>8</th><td> 8</td><td>b</td><td>b</td><td> 2</td></tr>\n",
       "\t<tr><th scope=row>9</th><td> 9</td><td>a</td><td>a</td><td> 0</td></tr>\n",
       "\t<tr><th scope=row>10</th><td>10</td><td>a</td><td>b</td><td> 6</td></tr>\n",
       "\t<tr><th scope=row>11</th><td>11</td><td>b</td><td>a</td><td> 0</td></tr>\n",
       "\t<tr><th scope=row>12</th><td>12</td><td>b</td><td>b</td><td> 0</td></tr>\n",
       "\t<tr><th scope=row>13</th><td>13</td><td>a</td><td>a</td><td> 0</td></tr>\n",
       "\t<tr><th scope=row>14</th><td>14</td><td>a</td><td>b</td><td> 0</td></tr>\n",
       "\t<tr><th scope=row>15</th><td>15</td><td>b</td><td>a</td><td> 2</td></tr>\n",
       "\t<tr><th scope=row>16</th><td>16</td><td>b</td><td>b</td><td> 0</td></tr>\n",
       "\t<tr><th scope=row>17</th><td>17</td><td>a</td><td>a</td><td> 4</td></tr>\n",
       "\t<tr><th scope=row>18</th><td>18</td><td>a</td><td>b</td><td> 4</td></tr>\n",
       "\t<tr><th scope=row>19</th><td>19</td><td>b</td><td>a</td><td> 7</td></tr>\n",
       "\t<tr><th scope=row>20</th><td>20</td><td>b</td><td>b</td><td> 0</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 20 × 4\n",
       "\\begin{tabular}{r|llll}\n",
       "  & S & X1 & X2 & Y\\\\\n",
       "  & <int> & <chr> & <chr> & <int>\\\\\n",
       "\\hline\n",
       "\t1 &  1 & a & a &  3\\\\\n",
       "\t2 &  2 & a & b &  1\\\\\n",
       "\t3 &  3 & b & a & 13\\\\\n",
       "\t4 &  4 & b & b &  0\\\\\n",
       "\t5 &  5 & a & a &  0\\\\\n",
       "\t6 &  6 & a & b &  1\\\\\n",
       "\t7 &  7 & b & a &  0\\\\\n",
       "\t8 &  8 & b & b &  2\\\\\n",
       "\t9 &  9 & a & a &  0\\\\\n",
       "\t10 & 10 & a & b &  6\\\\\n",
       "\t11 & 11 & b & a &  0\\\\\n",
       "\t12 & 12 & b & b &  0\\\\\n",
       "\t13 & 13 & a & a &  0\\\\\n",
       "\t14 & 14 & a & b &  0\\\\\n",
       "\t15 & 15 & b & a &  2\\\\\n",
       "\t16 & 16 & b & b &  0\\\\\n",
       "\t17 & 17 & a & a &  4\\\\\n",
       "\t18 & 18 & a & b &  4\\\\\n",
       "\t19 & 19 & b & a &  7\\\\\n",
       "\t20 & 20 & b & b &  0\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 20 × 4\n",
       "\n",
       "| <!--/--> | S &lt;int&gt; | X1 &lt;chr&gt; | X2 &lt;chr&gt; | Y &lt;int&gt; |\n",
       "|---|---|---|---|---|\n",
       "| 1 |  1 | a | a |  3 |\n",
       "| 2 |  2 | a | b |  1 |\n",
       "| 3 |  3 | b | a | 13 |\n",
       "| 4 |  4 | b | b |  0 |\n",
       "| 5 |  5 | a | a |  0 |\n",
       "| 6 |  6 | a | b |  1 |\n",
       "| 7 |  7 | b | a |  0 |\n",
       "| 8 |  8 | b | b |  2 |\n",
       "| 9 |  9 | a | a |  0 |\n",
       "| 10 | 10 | a | b |  6 |\n",
       "| 11 | 11 | b | a |  0 |\n",
       "| 12 | 12 | b | b |  0 |\n",
       "| 13 | 13 | a | a |  0 |\n",
       "| 14 | 14 | a | b |  0 |\n",
       "| 15 | 15 | b | a |  2 |\n",
       "| 16 | 16 | b | b |  0 |\n",
       "| 17 | 17 | a | a |  4 |\n",
       "| 18 | 18 | a | b |  4 |\n",
       "| 19 | 19 | b | a |  7 |\n",
       "| 20 | 20 | b | b |  0 |\n",
       "\n"
      ],
      "text/plain": [
       "   S  X1 X2 Y \n",
       "1   1 a  a   3\n",
       "2   2 a  b   1\n",
       "3   3 b  a  13\n",
       "4   4 b  b   0\n",
       "5   5 a  a   0\n",
       "6   6 a  b   1\n",
       "7   7 b  a   0\n",
       "8   8 b  b   2\n",
       "9   9 a  a   0\n",
       "10 10 a  b   6\n",
       "11 11 b  a   0\n",
       "12 12 b  b   0\n",
       "13 13 a  a   0\n",
       "14 14 a  b   0\n",
       "15 15 b  a   2\n",
       "16 16 b  b   0\n",
       "17 17 a  a   4\n",
       "18 18 a  b   4\n",
       "19 19 b  a   7\n",
       "20 20 b  b   0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Example data\n",
    "# df has subjects (S), two between-Ss factors (X1,X2) each w/levels (a,b), and count response (Y)\n",
    "df <- read.csv(\"data/2F2LBs_zinegbin.csv\")\n",
    "head(df, 20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "f7df92e2-e5f1-4701-afd1-a645dfce4f1d",
   "metadata": {
    "tags": [],
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A anova: 3 × 3</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>Df</th><th scope=col>Chisq</th><th scope=col>Pr(&gt;Chisq)</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>X1</th><td>1</td><td>0.42588152</td><td>0.5140168</td></tr>\n",
       "\t<tr><th scope=row>X2</th><td>1</td><td>1.28178400</td><td>0.2575676</td></tr>\n",
       "\t<tr><th scope=row>X1:X2</th><td>1</td><td>0.09911078</td><td>0.7528994</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A anova: 3 × 3\n",
       "\\begin{tabular}{r|lll}\n",
       "  & Df & Chisq & Pr(>Chisq)\\\\\n",
       "  & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\tX1 & 1 & 0.42588152 & 0.5140168\\\\\n",
       "\tX2 & 1 & 1.28178400 & 0.2575676\\\\\n",
       "\tX1:X2 & 1 & 0.09911078 & 0.7528994\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A anova: 3 × 3\n",
       "\n",
       "| <!--/--> | Df &lt;dbl&gt; | Chisq &lt;dbl&gt; | Pr(&gt;Chisq) &lt;dbl&gt; |\n",
       "|---|---|---|---|\n",
       "| X1 | 1 | 0.42588152 | 0.5140168 |\n",
       "| X2 | 1 | 1.28178400 | 0.2575676 |\n",
       "| X1:X2 | 1 | 0.09911078 | 0.7528994 |\n",
       "\n"
      ],
      "text/plain": [
       "      Df Chisq      Pr(>Chisq)\n",
       "X1    1  0.42588152 0.5140168 \n",
       "X2    1  1.28178400 0.2575676 \n",
       "X1:X2 1  0.09911078 0.7528994 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(pscl) # for zeroinfl\n",
    "library(car) # for Anova\n",
    "df$S = factor(df$S)\n",
    "df$X1 = factor(df$X1)\n",
    "df$X2 = factor(df$X2)\n",
    "contrasts(df$X1) <- \"contr.sum\"\n",
    "contrasts(df$X2) <- \"contr.sum\"\n",
    "m = zeroinfl(Y ~ X1*X2, data=df, dist=\"negbin\")\n",
    "Anova(m, type=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "3db6fe94-5810-485f-a842-ba651b878d88",
   "metadata": {
    "vscode": {
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    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(ggplot2)\n",
    "library(ggthemes)\n",
    "library(scales)\n",
    "library(plyr)\n",
    "\n",
    "# Histograms\n",
    "# http://www.sthda.com/english/wiki/ggplot2-histogram-plot-quick-start-guide-r-software-and-data-visualization\n",
    "ggplot(data=df, aes(x=Y, fill=X1, color=X2)) + theme_minimal() + \n",
    "  # set the font styles for the plot title and axis titles\n",
    "  theme(plot.title   = element_text(face=\"bold\",  color=\"black\", size=18, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.title.x = element_text(face=\"bold\",  color=\"black\", size=16, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.title.y = element_text(face=\"bold\",  color=\"black\", size=16, hjust=0.5, vjust=0.0, angle=90)) + \n",
    "  # set the font styles for the value labels that show on each axis\n",
    "  theme(axis.text.x  = element_text(face=\"plain\", color=\"black\", size=12, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.text.y  = element_text(face=\"plain\", color=\"black\", size=12, hjust=0.0, vjust=0.5, angle=0)) + \n",
    "  # set the font style for the facet labels\n",
    "  theme(strip.text = element_text(face=\"bold\", color=\"black\", size=14, hjust=0.5)) + \n",
    "  # remove the legend\n",
    "  theme(legend.position=\"none\") + \n",
    "  # create the histogram; the alpha value ensures overlaps can be seen\n",
    "  geom_histogram(binwidth=1, breaks=seq(-0.5,13.5,by=1), alpha=0.25) + \n",
    "  stat_bin(aes(y=..count.., label=..count..), binwidth=1, geom=\"text\", vjust=-0.5) + \n",
    "  # create stacked plots by X, one for each histogram\n",
    "  facet_grid(X1+X2 ~ .) + \n",
    "  # determine the outline and fill color values of each histogram\n",
    "  scale_color_manual(values=c(\"darkblue\",\"darkred\")) + \n",
    "  scale_fill_manual(values=c(\"#69b3a2\",\"#404080\")) + \n",
    "  # set the labels for the title and each axis\n",
    "  labs(title=\"Y by X1, X2\", x=\"Y\", y=\"Count\") + \n",
    "  # set the ranges and value labels for each axis\n",
    "  scale_x_continuous(breaks=seq(-0.5,13.5,by=1), labels=seq(0,14,by=1), limits=c(-0.5,13.5)) +\n",
    "  scale_y_continuous(breaks=seq(0,10,by=2), labels=seq(0,10,by=2), limits=c(0,10))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9131502c-d8d8-4877-a567-063fae72b9ff",
   "metadata": {},
   "source": [
    "## GLM for Gamma and Expontential Distribution Data\n",
    "\n",
    "* **Distribution:** Gamma and Exponential\n",
    "* **Link:** inverse or log when 1/0 is undefined\n",
    "* **Typical Uses:** Gamma Regression: Exponentially distributed responses (e.g. income, wait times)\n",
    "* **Reporting:** \"Figure 20a shows an interaction plot with ±1 standard deviation error bars for X1 and X2. An analysis of variance based on Gamma regression indicated no statistically significant effect on Y of X1 (χ2(1, N=60) = 0.40, n.s.) or X2 (χ2(1, N=60) = 0.58, n.s.), but the X1×X2 interaction was marginal (χ2(1, N=60) = 3.26, p = .071).\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "2ecf9d5f-0638-4b6a-b6f2-eb61f7e95871",
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 20 × 4</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>S</th><th scope=col>X1</th><th scope=col>X2</th><th scope=col>Y</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td> 1</td><td>a</td><td>a</td><td> 7.210222</td></tr>\n",
       "\t<tr><th scope=row>2</th><td> 2</td><td>a</td><td>b</td><td> 4.511329</td></tr>\n",
       "\t<tr><th scope=row>3</th><td> 3</td><td>b</td><td>a</td><td> 8.750533</td></tr>\n",
       "\t<tr><th scope=row>4</th><td> 4</td><td>b</td><td>b</td><td> 4.636170</td></tr>\n",
       "\t<tr><th scope=row>5</th><td> 5</td><td>a</td><td>a</td><td> 5.059694</td></tr>\n",
       "\t<tr><th scope=row>6</th><td> 6</td><td>a</td><td>b</td><td> 3.906251</td></tr>\n",
       "\t<tr><th scope=row>7</th><td> 7</td><td>b</td><td>a</td><td> 4.144064</td></tr>\n",
       "\t<tr><th scope=row>8</th><td> 8</td><td>b</td><td>b</td><td> 2.890245</td></tr>\n",
       "\t<tr><th scope=row>9</th><td> 9</td><td>a</td><td>a</td><td>11.229607</td></tr>\n",
       "\t<tr><th scope=row>10</th><td>10</td><td>a</td><td>b</td><td> 5.079605</td></tr>\n",
       "\t<tr><th scope=row>11</th><td>11</td><td>b</td><td>a</td><td> 4.408323</td></tr>\n",
       "\t<tr><th scope=row>12</th><td>12</td><td>b</td><td>b</td><td> 9.266559</td></tr>\n",
       "\t<tr><th scope=row>13</th><td>13</td><td>a</td><td>a</td><td> 3.851376</td></tr>\n",
       "\t<tr><th scope=row>14</th><td>14</td><td>a</td><td>b</td><td> 6.323390</td></tr>\n",
       "\t<tr><th scope=row>15</th><td>15</td><td>b</td><td>a</td><td> 3.870606</td></tr>\n",
       "\t<tr><th scope=row>16</th><td>16</td><td>b</td><td>b</td><td> 3.884600</td></tr>\n",
       "\t<tr><th scope=row>17</th><td>17</td><td>a</td><td>a</td><td> 4.155613</td></tr>\n",
       "\t<tr><th scope=row>18</th><td>18</td><td>a</td><td>b</td><td> 3.056740</td></tr>\n",
       "\t<tr><th scope=row>19</th><td>19</td><td>b</td><td>a</td><td> 6.283452</td></tr>\n",
       "\t<tr><th scope=row>20</th><td>20</td><td>b</td><td>b</td><td> 3.060357</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 20 × 4\n",
       "\\begin{tabular}{r|llll}\n",
       "  & S & X1 & X2 & Y\\\\\n",
       "  & <int> & <chr> & <chr> & <dbl>\\\\\n",
       "\\hline\n",
       "\t1 &  1 & a & a &  7.210222\\\\\n",
       "\t2 &  2 & a & b &  4.511329\\\\\n",
       "\t3 &  3 & b & a &  8.750533\\\\\n",
       "\t4 &  4 & b & b &  4.636170\\\\\n",
       "\t5 &  5 & a & a &  5.059694\\\\\n",
       "\t6 &  6 & a & b &  3.906251\\\\\n",
       "\t7 &  7 & b & a &  4.144064\\\\\n",
       "\t8 &  8 & b & b &  2.890245\\\\\n",
       "\t9 &  9 & a & a & 11.229607\\\\\n",
       "\t10 & 10 & a & b &  5.079605\\\\\n",
       "\t11 & 11 & b & a &  4.408323\\\\\n",
       "\t12 & 12 & b & b &  9.266559\\\\\n",
       "\t13 & 13 & a & a &  3.851376\\\\\n",
       "\t14 & 14 & a & b &  6.323390\\\\\n",
       "\t15 & 15 & b & a &  3.870606\\\\\n",
       "\t16 & 16 & b & b &  3.884600\\\\\n",
       "\t17 & 17 & a & a &  4.155613\\\\\n",
       "\t18 & 18 & a & b &  3.056740\\\\\n",
       "\t19 & 19 & b & a &  6.283452\\\\\n",
       "\t20 & 20 & b & b &  3.060357\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 20 × 4\n",
       "\n",
       "| <!--/--> | S &lt;int&gt; | X1 &lt;chr&gt; | X2 &lt;chr&gt; | Y &lt;dbl&gt; |\n",
       "|---|---|---|---|---|\n",
       "| 1 |  1 | a | a |  7.210222 |\n",
       "| 2 |  2 | a | b |  4.511329 |\n",
       "| 3 |  3 | b | a |  8.750533 |\n",
       "| 4 |  4 | b | b |  4.636170 |\n",
       "| 5 |  5 | a | a |  5.059694 |\n",
       "| 6 |  6 | a | b |  3.906251 |\n",
       "| 7 |  7 | b | a |  4.144064 |\n",
       "| 8 |  8 | b | b |  2.890245 |\n",
       "| 9 |  9 | a | a | 11.229607 |\n",
       "| 10 | 10 | a | b |  5.079605 |\n",
       "| 11 | 11 | b | a |  4.408323 |\n",
       "| 12 | 12 | b | b |  9.266559 |\n",
       "| 13 | 13 | a | a |  3.851376 |\n",
       "| 14 | 14 | a | b |  6.323390 |\n",
       "| 15 | 15 | b | a |  3.870606 |\n",
       "| 16 | 16 | b | b |  3.884600 |\n",
       "| 17 | 17 | a | a |  4.155613 |\n",
       "| 18 | 18 | a | b |  3.056740 |\n",
       "| 19 | 19 | b | a |  6.283452 |\n",
       "| 20 | 20 | b | b |  3.060357 |\n",
       "\n"
      ],
      "text/plain": [
       "   S  X1 X2 Y        \n",
       "1   1 a  a   7.210222\n",
       "2   2 a  b   4.511329\n",
       "3   3 b  a   8.750533\n",
       "4   4 b  b   4.636170\n",
       "5   5 a  a   5.059694\n",
       "6   6 a  b   3.906251\n",
       "7   7 b  a   4.144064\n",
       "8   8 b  b   2.890245\n",
       "9   9 a  a  11.229607\n",
       "10 10 a  b   5.079605\n",
       "11 11 b  a   4.408323\n",
       "12 12 b  b   9.266559\n",
       "13 13 a  a   3.851376\n",
       "14 14 a  b   6.323390\n",
       "15 15 b  a   3.870606\n",
       "16 16 b  b   3.884600\n",
       "17 17 a  a   4.155613\n",
       "18 18 a  b   3.056740\n",
       "19 19 b  a   6.283452\n",
       "20 20 b  b   3.060357"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Example data\n",
    "# df has subjects (S), two factors (X1,X2) each w/levels (a,b), and continuous response (Y)\n",
    "df <- read.csv(\"data/2F2LBs_gamma.csv\")\n",
    "head(df, 20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "e3a493dc-1ff9-4bd7-8013-75fe6fe970ef",
   "metadata": {
    "tags": [],
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A anova: 3 × 3</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>LR Chisq</th><th scope=col>Df</th><th scope=col>Pr(&gt;Chisq)</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>X1</th><td>0.3971864</td><td>1</td><td>0.52854588</td></tr>\n",
       "\t<tr><th scope=row>X2</th><td>0.5791674</td><td>1</td><td>0.44663887</td></tr>\n",
       "\t<tr><th scope=row>X1:X2</th><td>3.2574933</td><td>1</td><td>0.07109773</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A anova: 3 × 3\n",
       "\\begin{tabular}{r|lll}\n",
       "  & LR Chisq & Df & Pr(>Chisq)\\\\\n",
       "  & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\tX1 & 0.3971864 & 1 & 0.52854588\\\\\n",
       "\tX2 & 0.5791674 & 1 & 0.44663887\\\\\n",
       "\tX1:X2 & 3.2574933 & 1 & 0.07109773\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A anova: 3 × 3\n",
       "\n",
       "| <!--/--> | LR Chisq &lt;dbl&gt; | Df &lt;dbl&gt; | Pr(&gt;Chisq) &lt;dbl&gt; |\n",
       "|---|---|---|---|\n",
       "| X1 | 0.3971864 | 1 | 0.52854588 |\n",
       "| X2 | 0.5791674 | 1 | 0.44663887 |\n",
       "| X1:X2 | 3.2574933 | 1 | 0.07109773 |\n",
       "\n"
      ],
      "text/plain": [
       "      LR Chisq  Df Pr(>Chisq)\n",
       "X1    0.3971864 1  0.52854588\n",
       "X2    0.5791674 1  0.44663887\n",
       "X1:X2 3.2574933 1  0.07109773"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(car) # for Anova\n",
    "df$S = factor(df$S)\n",
    "df$X1 = factor(df$X1)\n",
    "df$X2 = factor(df$X2)\n",
    "contrasts(df$X1) <- \"contr.sum\"\n",
    "contrasts(df$X2) <- \"contr.sum\"\n",
    "m = glm(Y ~ X1*X2, data=df, family=Gamma)\n",
    "# family=Gamma(link=\"log\") is often used\n",
    "Anova(m, type=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "a1cdea5c-1dfb-4bde-a821-7a8ad151e888",
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(ggplot2)\n",
    "library(ggthemes)\n",
    "library(scales)\n",
    "library(plyr)\n",
    "\n",
    "# Interaction plot\n",
    "# http://www.sthda.com/english/wiki/ggplot2-line-plot-quick-start-guide-r-software-and-data-visualization\n",
    "# http://www.sthda.com/english/wiki/ggplot2-error-bars-quick-start-guide-r-software-and-data-visualization\n",
    "# http://www.sthda.com/english/wiki/ggplot2-point-shapes\n",
    "# http://www.sthda.com/english/wiki/ggplot2-line-types-how-to-change-line-types-of-a-graph-in-r-software\n",
    "df2 <- ddply(df, ~ X1*X2, function(d) # make a summary data table\n",
    "  c(NROW(d$Y),\n",
    "    sum(is.na(d$Y)),\n",
    "    sum(!is.na(d$Y)),\n",
    "    mean(d$Y, na.rm=TRUE),\n",
    "    sd(d$Y, na.rm=TRUE),\n",
    "    median(d$Y, na.rm=TRUE),\n",
    "    IQR(d$Y, na.rm=TRUE)))\n",
    "colnames(df2) <- c(\"X1\",\"X2\",\"Rows\",\"NAs\",\"NotNAs\",\"Mean\",\"SD\",\"Median\",\"IQR\")\n",
    "ggplot(data=df2, aes(x=X1, y=Mean, color=X2, group=X2)) + theme_minimal() + \n",
    "  # set the font styles for the plot title and axis titles\n",
    "  theme(plot.title   = element_text(face=\"bold\",  color=\"black\", size=18, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.title.x = element_text(face=\"bold\",  color=\"black\", size=16, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.title.y = element_text(face=\"bold\",  color=\"black\", size=16, hjust=0.5, vjust=0.0, angle=90)) + \n",
    "  # set the font styles for the value labels that show on each axis\n",
    "  theme(axis.text.x  = element_text(face=\"plain\", color=\"black\", size=14, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.text.y  = element_text(face=\"plain\", color=\"black\", size=12, hjust=0.0, vjust=0.5, angle=0)) + \n",
    "  # set the font styles for the legend\n",
    "  theme(legend.title = element_text(face=\"bold\", color=\"black\", size=14, hjust=0.5, vjust=0.0, angle=0)) +\n",
    "  theme(legend.text  = element_text(face=\"plain\", color=\"black\", size=14, hjust=0.5, vjust=0.0, angle=0)) +\n",
    "  # create the plot lines, points, and error bars\n",
    "  geom_line(aes(linetype=X2), position=position_dodge(0.05)) + \n",
    "  geom_point(aes(shape=X2, size=X2), position=position_dodge(0.05)) + \n",
    "  geom_errorbar(aes(ymin=Mean-SD, ymax=Mean+SD), position=position_dodge(0.05), width=0.1) + \n",
    "  # place text labels on each bar\n",
    "  geom_text(aes(label=sprintf(\"%.2f (±%.2f)\", Mean, SD)), position=position_dodge(0.05), hjust=0.0, vjust=-1.0, color=\"black\", size=3.5) +\n",
    "  # set the labels for the title and each axis\n",
    "  labs(title=\"Y by X1, X2\", x=\"X1\", y=\"Y\") + \n",
    "  # set the ranges and value labels for each axis\n",
    "  scale_x_discrete(labels=c(\"a\",\"b\")) + \n",
    "  scale_y_continuous(breaks=seq(0,9,by=2), labels=seq(0,9,by=2), limits=c(0,9), oob=rescale_none) + \n",
    "  # set the name, labels, and colors for the traces\n",
    "  scale_color_manual(name=\"X2\", labels=c(\"a\",\"b\"), values=c(\"red\", \"blue\")) +\n",
    "  # set the size and shape of the points\n",
    "  scale_size_manual(values=c(4,4)) +\n",
    "  scale_shape_manual(values=c(16,10)) +\n",
    "  # set the linetype of the lines\n",
    "  scale_linetype_manual(values=c(\"solid\", \"longdash\"))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "4.2.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}