index.Rmd

---
title: "Psy 6136: Categorical Data Analysis"
author: "Michael Friendly"
date: "Winter, 2026"
output:
  html_document:
    toc: true
    toc_depth: 2
    toc_float: yes
    css: assets/styles.css
    includes:
      after_body: footer.html
      in_header: header.html
---


<center>
<img src="icons/psy6136-highres.png" width="120px" style="margin-right: 2em;">
<img src="icons/psy6136-qr.png" width="120px" style="margin-left: 2em;"/>
</center>

```{r setup, echo=FALSE}
source("assets/div_heading.R")
```


## Course Description 

This course is designed as a broad, applied introduction to the statistical analysis of categorical (or discrete) data, such as counts, proportions, nominal variables, ordinal variables, discrete variables with few values, continuous variables grouped into a small number of categories, etc. 

* The course begins with methods designed for cross-classified table of counts, (i.e., contingency tables), using simple chi square-based methods. 

* It progresses to generalized linear models, for which log-linear models provide a natural extension of simple chi square-based methods. 

* This framework is then extended to comprise logit and logistic regression models for binary responses and generalizations of these models for polytomous (multicategory) outcomes.

Throughout, there is a strong emphasis on associated **graphical methods** for visualizing categorical data, checking model assumptions, etc. Lab sessions will familiarize the student with software using R for carrying out these analyses.

Course and lecture topics are listed below, in a visual overview. 

* See the [Course schedule](schedule.html) for details of readings, lecture notes, R scripts, etc.
* For students, see [Assignments](about.html#assign) and [Evaluation](about.html#evaluation)

<img src="icons/construction.png" height=20> These web pages will be revised as the course proceeds. If you find a link that doesn't work, or could be replaced by something better or more recent, 
[please let me know by filing an issue](https://github.com/friendly/psy6136/issues).
<img src="icons/construction.png" height=20> 


## Overview & Introduction {#overview}

Let's get started! I'll talk about the organization of the course, what is expected, and resouces for 
learning. Then, provide an overview of methods and models for catgegorical data and the role
of graphical methods in understanding and communicating results.


![](images/headers/bertifier.png)


<!--
```{r topics1, results='asis', echo=FALSE}
div_heading("topics")
```
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<!-- #### <img src="icons/list.png" height=20> Topics:   -->

#### 📌 Topics:

- Course outline, books, R
- What is categorical data?
- Categorical data analysis: methods & models
- Graphical methods


<!--
```{r lecture1, results='asis', echo=FALSE}
div_heading("lecture")
```
-->

#### <img src="icons/PDF_icon.png" height=20> Lecture notes   

- [1up PDF](lectures/01-Overview.pdf) || [4up PDF](lectures/01-Overview-2x2.pdf) || [PPT](lectures/01-Overview.pptx)


<!-- #### Readings: `r icon::fa("book-reader", color="blue")`  -->

<!--
```{r readings1, results='asis', echo=FALSE}
div_heading("readings")
```
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#### <img src="icons/book.png" height=20> Readings: 

**Bold face** items are considered essential. When there are assignments,
some supplementary readings are also mentioned there.

- **DDAR**: [Ch 1](VCDR/chapter01.pdf); [Ch 2](VCDR/chapter02.pdf)
- **Agresti**, Ch 1
- See [Supplementary resources](resources.html#week1) for this week.

<!-- #### Assignment: `r icon::fa("building", color="brown")` -->
```{r asn1, results='asis', echo=FALSE}
div_heading("assign")
```
- [Assignment 1](assign/assign1.pdf)


## Discrete Distributions {#discrete}

Discrete distributions are the gateway drug for categorical data analysis. Meet some 
--- binomial, Poisson, Negative Binomial, and others --- who will
become your friends as you learn to analyze discrete data.

More importantly, learn some nifty graphical methods for fitting these distributions
and understanding why a given one might not fit well. 

![](images/headers/dpois-xyplot.png)

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<!-- #### <img src="icons/list.png" height=20> Topics:   -->

#### 📌 Topics:


- Discrete distributions: Basic ideas
- Fitting discrete distributions
- Graphical methods: Rootograms, Ord plots
- Robust distribution plots
- Looking ahead

<!-- #### Lecture notes  `r icon::fa("file-pdf", color="red")`
```{r lecture2, results='asis', echo=FALSE}
div_heading("lecture")
```
-->


#### <img src="icons/PDF_icon.png" height=20> Lecture notes   

- [1up PDF](lectures/02-Discrete.pdf) || [4up PDF](lectures/02-Discrete-2x2.pdf)

<!-- #### Readings: `r icon::fa("book-reader", color="blue")`  -->


#### <img src="icons/book.png" height=20> Readings: 


- **DDAR**: [Ch 3](VCDR/chapter03.pdf)
- See [Supplementary resources](resources.html#week2) for this week.

```{r asn2, results='asis', echo=FALSE}
div_heading("assign")
```
- [Assignment 2](assign/assign2.pdf)


```{r quiz2, results='asis', echo=FALSE}
div_heading("quiz")
```

- [Quiz 2 - Discrete distributions](quiz/02-discrete.html)


## Two-way Tables {#twoway}

How can we test for independence and measure the strength of association in two way tables?
Get acquainted with some standard tests and statistics: Pearson $\chi^2$, Odds ratio,
Cramer's $V$, Cohen's $\kappa$ and even Bangdiwal's $W$.

More importantly, how can we _visualize_ association? We'll meet fourfold plots, sieve diagrams,
spine plots.  Much of this is prep for understanding how to formulate, test and visualize
models for categorical data.

![](images/headers/twoway.png)

<!--
```{r topics3, results='asis', echo=FALSE}
div_heading("topics")
```
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#### 📌 Topics:

- Overview: $2 \times 2$, $r \times c$, ordered tables
- Independence
- Visualizing association
- Ordinal factors
- Square tables: Observer agreement
- Looking ahead: models


<!-- #### Lecture notes  `r icon::fa("file-pdf", color="red")`
```{r lecture3, results='asis', echo=FALSE}
div_heading("lecture")
```
-->

#### <img src="icons/PDF_icon.png" height=20> Lecture notes   

- [1up PDF](lectures/03-Twoway1.pdf) || [4up PDF](lectures/03-Twoway1-2x2.pdf)
- [Tutorial on two way tables](tutorials/twoway.pdf)

<!-- #### Readings: `r icon::fa("book-reader", color="blue")`  -->
<!--
<div style="display:flex">
  <i class="fas fa-book-reader" style="color:blue; font-size: 1.25em;"></i> &nbsp;
  <h4>Readings</h4>
</div>
-->

#### <img src="icons/book.png" height=20> Readings: 

- **DDAR**: [Ch 4](VCDR/chapter04.pdf)
- **Agresti, Ch 2**
- See [Supplementary resources](resources.html#week3) for this week.

```{r quiz3, results='asis', echo=FALSE}
div_heading("quiz")
```

```{r asn3, results='asis', echo=FALSE}
div_heading("assign")
```
- [Assignment 3](assign/assign3.pdf)
 
- [Quiz 3 - Two-way tables](quiz/03-twoway.html)



## Loglinear models & mosaic displays {#loglin}


```
༄˖°.🍂࿔*:･
  Some people think nothing is prettier
  Than algebra of models log-linear.
    But I've got the hots
    For my mosaic plots
  With all those squares in the interior.
  --- by Michael Greenacre (see his [Statistical Songs](https://www.youtube.com/StatisticalSongs))
```

![](images/headers/loglin.png)


<!--
```{r topics4, results='asis', echo=FALSE}
div_heading("topics")
```
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#### 📌 Topics:

- Mosaic displays: Basic ideas
- Loglinear models
- Model-based methods: Fitting & graphing
- Mosaic displays: Visual fitting
- survival on the _Titanic_
- Sequential plots & models

<!-- #### Lecture notes  `r icon::fa("file-pdf", color="red")`
```{r lecture4, results='asis', echo=FALSE}
div_heading("lecture")
```
-->

#### <img src="icons/PDF_icon.png" height=20> Lecture notes   

- [1up PDF](lectures/04-Loglin.pdf) || [4up PDF](lectures/04-Loglin-2x2.pdf)

<!--
```{r readings4, results='asis', echo=FALSE}
div_heading("readings")
```
-->

#### <img src="icons/book.png" height=20> Readings: 

- **DDAR**: [Ch 5](VCDR/chapter05.pdf)
- **Agresti, 2.7; Ch 7**
- See [Supplementary resources](resources.html#week4) for this week.

```{r asn4, results='asis', echo=FALSE}
div_heading("assign")
```
- [Assignment 4](assign/assign4.pdf)
 

```{r quiz4, results='asis', echo=FALSE}
div_heading("quiz")
```

- [Quiz 4 - Loglinear models](quiz/04-loglin.html)


## Correspondence Analysis {#corresp}

```
༄˖°.🍂࿔*:･
  Benzécri brought data mystique
  With his elegant SVD technique.
    So I've got the hots
    For correspondence plots
  Where profiles show what the rows seek.
```

Correspondence analysis (CA) is one of the first things I think of when I meet a new frequency table and
want to get a quick look at the relations among the row and column categories.
Very much like PCA for quantitative data, think of CA as a **multivariate juicer** that takes a 
high-dimensional data set and squeezes it into a 2D (or 3D) space that best accounts for the
associations (Pearson $\chi^2$) between the row and column categories.
The category scores on the dimensions are in fact the best numerical values that can be defined.
They can be used to permute the categories in mosaic displays to make the pattern of associations
as clear as possible.

![](images/headers/corresp.png)

<!--
```{r topics5, results='asis', echo=FALSE}
div_heading("topics")
```
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#### 📌 Topics:

- CA: Basic ideas
- Singular value decomposition (SVD)
- Optimal category scores
- Multiway tables: MCA

<!-- #### Lecture notes  `r icon::fa("file-pdf", color="red")`
```{r lecture5, results='asis', echo=FALSE}
div_heading("lecture")
```
-->


#### <img src="icons/PDF_icon.png" height=20> Lecture notes   


- [1up PDF](lectures/05-Corresp.pdf) || [4up PDF](lectures/05-Corresp-2x2.pdf)

<!--
```{r readings5, results='asis', echo=FALSE}
div_heading("readings")
```
-->



#### <img src="icons/book.png" height=20> Readings: 

- **DDAR**: [Ch 6](VCDR/chapter06.pdf)
- See [Supplementary resources](resources.html#week5) for this week.

```{r quiz5, results='asis', echo=FALSE}
div_heading("quiz")
```

- [Quiz 5 - Correspondence analysis](quiz/05-corresp.html)

## Logistic regression

```
༄˖°.🍂࿔*:･
 For responses that come just in two,
  Linear models just will not do.
    With glm() and a smile
    In binomial style,
  The S-curve reveals what is true.
```

Logistic regression provides an entry to model-based methods for categorical data
analysis. These provide estimates and tests for predictor variables of a
binary outcome, but more importantly, allow graphs of a fitted outcome together
with confidence bands representing uncertainty,

![](images/headers/logistic.png)

<!--
```{r topics6, results='asis', echo=FALSE}
div_heading("topics")
```
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#### 📌 Topics:


- Model-based methods: Overview
- Logistic regression: one predictor, multiple predictors, fitting
- Visualizing logistic regression
- Effect plots
- Case study: Racial profiling
- Model diagnostics

<!-- #### Lecture notes  `r icon::fa("file-pdf", color="red")`
```{r lecture6, results='asis', echo=FALSE}
div_heading("lecture")
```
-->

#### <img src="icons/PDF_icon.png" height=20> Lecture notes   

- [1up PDF](lectures/06-Logistic.pdf) || [4up PDF](lectures/06-Logistic-2x2.pdf)


#### <img src="icons/book.png" height=20> Readings: 

- **DDAR**: [Ch 7](VCDR/chapter07.pdf)
- See [Supplementary resources](resources.html#week6) for this week.

```{r quiz6, results='asis', echo=FALSE}
div_heading("quiz")
```

- [Quiz 6 - Logistic regression](quiz/06-logistic.html)

## Logistic regression: Extensions

The ideas behind logistic regression can be extended in a variety of ways.
The effects of predictors on a binary response can incorporate non-linear terms
and interactions. When the outcome is **polytomous** (more than two categories),
and the response categories are ordered,
the _proportional odds model_ provides a simple framework.
Other methods for polytomous outcomes include _nested dichotomies_ and
the general _multinomial_ logistic regression model.

![](images/headers/logistic2.png)


<!--
```{r topics7, results='asis', echo=FALSE}
div_heading("topics")
```
-->

<!-- #### <img src="icons/list.png" height=20> Topics:   -->

#### 📌 Topics:

- Case study: Survival in the Donner party
- Polytomous response models
  + Proportional odds model
  + Nested dichotomies
  + Multinomial models

<!-- #### Lecture notes  `r icon::fa("file-pdf", color="red")`
```{r lecture7, results='asis', echo=FALSE}
div_heading("lecture")
```
-->

#### <img src="icons/PDF_icon.png" height=20> Lecture notes   

- [1up PDF](lectures/07-Logistic2.pdf) || [4up PDF](lectures/07-Logistic2-2x2.pdf)
- Bonus lecture: [Deep Questions of Data Visualization](lectures/DeepQuestions.pdf)

#### <img src="icons/book.png" height=20> Readings: 

- **DDAR**: [Ch 8](VCDR/chapter08.pdf)
- See [Supplementary resources](resources.html#week7) for this week.

```{r quiz7, results='asis', echo=FALSE}
div_heading("quiz")
```

- [Quiz 7 - Logistic regression: Extensions](quiz/07-logistic2.html)

## Extending loglinear models

Here we return to loglinear models to consider extensions to the `glm()` framework.
Models for ordinal factors have greater power when associations reflect their ordered nature.
The `gnm` package extends these to generalized _non-linear_ models.
For **square tables**, we can fit a variety of specialized models, including
_quasi-independence_, _symmetry_ and _quasi-symmetry_.

![](images/headers/loglin2.png)

<!--
```{r topics8, results='asis', echo=FALSE}
div_heading("topics")
```
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<!-- #### <img src="icons/list.png" height=20> Topics:   -->

#### 📌 Topics:

- Logit models for response variables
- Models for ordinal factors
- RC models, estimating row/col scores
- Models for square tables
- More complex models

<!-- #### Lecture notes  `r icon::fa("file-pdf", color="red")`  
```{r lecture8, results='asis', echo=FALSE}
div_heading("lecture")
```
-->

#### <img src="icons/PDF_icon.png" height=20> Lecture notes   

- [1up PDF](lectures/08-Loglin2.pdf) || [4up PDF](lectures/08-Loglin2-2x2.pdf)


#### <img src="icons/book.png" height=20> Readings: 

- **DDAR**: [Ch 10](VCDR/chapter10.pdf)

```{r quiz8, results='asis', echo=FALSE}
div_heading("quiz")
```

- [Quiz 8 - Extending Loglinear Models](quiz/08-loglin2.html)


## GLMs for count data

Here we consider generalized linear models more broadly, with emphasis on those for 
a count or frequency response variable in the Poisson family.
Some extensions allow for **overdispersion**, including the _quasi-poisson_
and _negative binomial_ model.  When the data exhibits a greater frequency of
0 counts, **zero-inflated** versions of these models come to the rescue.

![](images/headers/countdata.png)


<!--
```{r topics9, results='asis', echo=FALSE}
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```
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#### 📌 Topics:

- Generalized linear models: Families & links
- GLMs for count data
- Model diagnostics
- Overdispersion
- Excess zeros

<!-- #### Lecture notes  `r icon::fa("file-pdf", color="red")`  -->
<!--
```{r lecture9, results='asis', echo=FALSE}
div_heading("lecture")
```
-->

#### <img src="icons/PDF_icon.png" height=20> Lecture notes   

- [1up PDF](lectures/09-CountData.pdf) || [4up PDF](lectures/09-CountData-2x2.pdf)
- See [Supplementary resources](resources.html#week9) for this week.
- [Notes on Negative Binomial: Interpreting the overdispersion parameter](notes/09-negbin.html)

#### <img src="icons/book.png" height=20> Readings: 

- **DDAR**: [Ch 11](VCDR/chapter11.pdf)

```{r quiz9, results='asis', echo=FALSE}
div_heading("quiz")
```

- [Quiz 9 - GLMs for Count Data](quiz/09-countdata.html)



## Models and graphs for log odds and log odds ratios

Logit models for a binary response simplify the specification and interpretation
of loglinear models. In the same way, a model for a
polytomous response can be simplified by considering a set of log odds
defined for the set of adjacent categories.
Similarly, when there are two response variables, models for their log odds
ratios provide a new way to look at their associations in a structured way.

![](images/headers/log-odds.png)

<!--
```{r topics10, results='asis', echo=FALSE}
div_heading("topics")
```
-->

#### 📌 Topics:

- Logit models -> log odds models
- Generalized log odds ratios
- Models for bivariate responses

<!-- #### Lecture notes  `r icon::fa("file-pdf", color="red")`  -->
<!--
```{r lecture10, results='asis', echo=FALSE}
div_heading("lecture")
```
-->

#### <img src="icons/PDF_icon.png" height=20> Lecture notes   

- [1up PDF](lectures/10-Log-Odds.pdf) || [4up PDF](lectures/10-Log-Odds-2x2.pdf)

```{r readings10, results='asis', echo=FALSE}
div_heading("readings")
```

- Friendly & Meyer (2015), [General Models and Graphs for Log Odds and Log
Odds Ratios](https://www.datavis.ca/papers/CARME2015-2x2.pdf)

## Wrapup & summary: The Last Waltz

A brief summary of the course.

![](images/headers/last-waltz.png)

<!--
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```
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#### 📌 Topics:


- Course goals
- What have I tried to teach?
- Whirlwind course summary
- Your turn: what did you like/dislike about the course?

<!-- #### Lecture notes  `r icon::fa("file-pdf", color="red")`  -->
<!--
```{r lecture99, results='asis', echo=FALSE}
div_heading("lecture")
```
-->

#### <img src="icons/PDF_icon.png" height=20> Lecture notes   

- [1up PDF](lectures/99-Summary.pdf) || [4up PDF](lectures/99-Summary-2x2.pdf)