README.Rmd

---
output: github_document
---

<!-- README.md is generated from README.Rmd. Please edit that file -->

```{r setup, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  warning = FALSE,
  comment = "##",
  fig.path = "man/figures/README-",
  fig.height = 5,
  fig.width = 5
#  out.width = "100%"
)

library(vcdExtra)
```

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# vcdExtra <img src="man/figures/logo.png" style="float:right; height:200px;" />
## Extensions and additions to vcd: Visualizing Categorical Data 

Version 0.8-4

This package provides additional data sets, documentation, and many
functions designed to extend the [vcd](https://CRAN.R-project.org/package=vcd) package for *Visualizing Categorical Data*
and the [gnm](https://CRAN.R-project.org/package=gnm) package for *Generalized Nonlinear Models*. 
In particular, `vcdExtra` extends mosaic, assoc and sieve plots from vcd to handle `glm()` and 
`gnm()` models and
adds a 3D version in `mosaic3d()`.

`vcdExtra` is a support package for the book [*Discrete Data Analysis with R*](https://www.routledge.com/Discrete-Data-Analysis-with-R-Visualization-and-Modeling-Techniques-for/Friendly-Meyer/p/book/9781498725835) (DDAR) by Michael Friendly and David Meyer. There is also a
[web site for DDAR](http://ddar.datavis.ca) with all figures and code samples from the book.
It is also used in my graduate course, [Psy 6136: Categorical Data Analysis](https://friendly.github.io/psy6136/).

## Installation

Get the released version from CRAN:

     install.packages("vcdExtra")

The development version can be installed to your R library directly from the [GitHub repo](https://github.com/friendly/vcdExtra) via:

     if (!require(remotes)) install.packages("remotes")
     remotes::install_github("friendly/vcdExtra", build_vignettes = TRUE)


### Overview

The original purpose of this package was to serve as a sandbox for
introducing extensions of
mosaic plots and related graphical methods
that apply to loglinear models fitted using `MASS::loglm()`,
generalized linear models using
`stats::glm()` and the related, generalized _nonlinear_ models fitted
with `gnm()` in the [gnm](https://CRAN.R-project.org/package=gnm) package.

A related purpose was to fill in some holes in the analysis of
categorical data in R, not provided in base R, [vcd](https://CRAN.R-project.org/package=vcd), 
or other commonly used packages.

##### See also:
<a href="https://www.routledge.com/Discrete-Data-Analysis-with-R-Visualization-and-Modeling-Techniques-for/Friendly-Meyer/p/book/9781498725835"><img src="http://ddar.datavis.ca/images/ddar-cover.png" style="height:70px;"/></a>&nbsp; &nbsp; &nbsp; 
<a href="https://friendly.github.io/psy6136/"><img src="https://friendly.github.io/psy6136/icons/psy6136-highres.png" style="height:70px;" /></a>&nbsp; &nbsp; &nbsp; 
<a href="https://friendly.github.io/nestedLogit/"><img src="https://friendly.github.io/nestedLogit/logo.png" style="height:70px;" /></a>


* My book, [*Discrete Data Analysis with R: Visualization and Modeling Techniques for Categorical and Count Data*](https://www.routledge.com/Discrete-Data-Analysis-with-R-Visualization-and-Modeling-Techniques-for/Friendly-Meyer/p/book/9781498725835)

* My graduate course, [Psy 6136: Categorical Data Analysis](https://friendly.github.io/psy6136/)

* A companion package, [`nestedLogit`](https://friendly.github.io/nestedLogit/), for fitting nested dichotomy logistic regression models for a polytomous response.
 
#### vcdExtra Highlights

##### mosaic plot extensions
* The method `mosaic.glm()` 
extends the `mosaic.loglm()` method in the vcd
package to this wider class of models, e.g., models for ordinal factors, which can't
be handled with `MASS::loglm()`.
This method also works for
the generalized _nonlinear_ models fit with the [gnm](https://CRAN.R-project.org/package=gnm) package,
including models for square tables and models with multiplicative associations (RC models).

* `mosaic3d()`
introduces a 3D generalization of mosaic displays using the
[rgl](https://CRAN.R-project.org/package=rgl) package.

##### model extensions
* A new class, `glmlist`, is introduced for working with
collections of glm objects, e.g., `Kway()` for fitting
all K-way models from a basic marginal model, and `LRstats()`
for brief statistical summaries of goodness-of-fit for a collection of
models.

* Similarly, for loglinear models fit using `MASS::loglm()`, the function `seq_loglm()`
 fits a series of sequential models to the 1-, 2-, ... _n_-way marginal tables, corresponding to a variety of types of models for joint, conditional, mutual, ... independence. It
 returns an object of class `loglmlist`, each of which is a class `loglm` object.
 The function `seq_mosaic()` generates the mosaic plots and other plots in the
 `vcd::strucplot()` framework. 

* For **square tables** with ordered factors, `Crossings()` supplements the 
specification of terms in model formulas using
`gnm::Symm()`,
`gnm::Diag()`, 
`gnm::Topo(),` etc. in the [gnm](https://CRAN.R-project.org/package=gnm) package.

#### Other additions

* many new data sets; use `datasets("vcdExtra")` to see a list with titles and descriptions.
The vignette, `vignette("datasets", package="vcdExtra")` provides a classification of these
according to methods of analysis.

```{r vcdExtra-datasets}
vcdExtra::datasets("vcdExtra")[,1]
```

* a [collection of tutorial vignettes](https://cran.r-project.org/web/packages/vcdExtra/vignettes/). In the installed package, they can be viewed using `browseVignettes(package = "vcdExtra")`;

```{r vignettes}
tools::getVignetteInfo("vcdExtra")[,c("File", "Title")] |> knitr::kable()
```

* a few useful utility functions for manipulating categorical data sets and working with models for
categorical data. 


## Examples

These `README` examples simply provide illustrations of using some of the package functions in the
context of loglinear models for frequency tables fit using `glm()`, including
models for _structured associations_ taking ordinality into account.

The dataset `Mental` is a data frame frequency table representing the cross-classification of mental health status (`mental`) of 1660 young New York residents by their parents' socioeconomic status (`ses`).
Both are _ordered_ factors.

```{r ex-mental1}
data(Mental)
str(Mental)

# show as frequency table
(Mental.tab <- xtabs(Freq ~ ses+mental, data=Mental))
```


#### Independence model
Fit the independence model, `Freq ~ mental + ses`, using `glm(..., family = poisson)`
This model is equivalent to the `chisq.test(Mental)` for general association; it
does not take ordinality into account. `LRstats()` provides a compact summary of
fit statistics for one or more models.
```{r ex-mental2}
indep <- glm(Freq ~ mental + ses,
             family = poisson, data = Mental)
LRstats(indep)
```

`mosaic.glm()` is the mosaic method for `glm` objects.
The default mosaic display for these data:
```{r mental1}
mosaic(indep)
```

It is usually better to use _standardized residuals_ (`residuals_type="rstandard"`) in mosaic displays, rather than the default Pearson residuals.
Here we also add longer labels for the table factors (`set_varnames`)
and display the
values of residuals (`labeling=labeling_residuals`) in the cells. 

The strucplot `formula` argument, `~ ses + mental`
here gives the order of the factors in the mosaic display,
not the statistical model for independence. That is, the
unit square is first split by `ses`, then by `mental` within
each level of `ses`.
```{r mental2}
# labels for table factors
long.labels <- list(set_varnames = c(mental="Mental Health Status", 
                                     ses="Parent SES"))

mosaic(indep, formula = ~ ses + mental,
       residuals_type="rstandard",
       labeling_args = long.labels, 
       labeling=labeling_residuals)
```

The **opposite-corner** pattern of the residuals clearly shows that association
between Parent SES and mental health depends on the _ordered_ levels of the factors:
higher Parent SES is associated with better mental health status. A principal virtue
of mosaic plots is to show the pattern of association that remains
after a model has been fit, and thus help suggest a better model.

#### Ordinal models
Ordinal models use **numeric** scores for the row and/or column variables.
These models typically use equally spaced _integer_ scores.
The test for association here is analogous to a test of the correlation
between the frequency-weighted scores, carried out using `CMHtest()`.

In the data, `ses` and `mental` were declared to be ordered factors,
so using `as.numeric(Mental$ses)` is sufficient to create a new `Cscore`
variable. Similarly for the numeric version of `mental`, giving `Rscore`.

```{r mental-scores}
Cscore <- as.numeric(Mental$ses)
Rscore <- as.numeric(Mental$mental)
```


Using these, the term `Rscore:Cscore` represents an association
constrained to be **linear x linear**; that is, the slopes for profiles of
mental health status are assumed to vary linearly with those for Parent SES.
(This model asserts that only one parameter (a local odds ratio)
is sufficient to account for all association, and is also called the model of "uniform association".)


```{r mental3}
# fit linear x linear (uniform) association.  Use integer scores for rows/cols 
Cscore <- as.numeric(Mental$ses)
Rscore <- as.numeric(Mental$mental)

linlin <- glm(Freq ~ mental + ses + Rscore:Cscore,
              family = poisson, data = Mental)
mosaic(linlin, ~ ses + mental,
       residuals_type="rstandard", 
       labeling_args = long.labels, 
       labeling=labeling_residuals, 
       suppress=1, 
       gp=shading_Friendly,
       main="Lin x Lin model")
```

Note that the test for linear x linear association consumes only 1 degree of freedom,
compared to the `(r-1)*(c-1) = 15` degrees of freedom for general association.
```{r}
anova(linlin, test="Chisq")
```


Other models are possible between the independence model, `Freq ~ mental + ses`,
and the saturated model `Freq ~ mental + ses + mental:ses`.
The `update.glm()` method make these easy to specify, as addition of terms to
the independence model.
```{r}
# use update.glm method to fit other models

linlin <- update(indep, . ~ . + Rscore:Cscore)
roweff <- update(indep, . ~ . + mental:Cscore)
coleff <- update(indep, . ~ . + Rscore:ses)
rowcol <- update(indep, . ~ . + Rscore:ses + mental:Cscore)
```

**Compare the models**: 
For `glm` objects, the `print` and `summary` methods give too much information if all one wants to see is a brief summary of model goodness of fit, and there is no easy way to display a compact comparison of model goodness of fit for a collection of models fit to the same data.

`LRstats()` provides a brief summary for one or more models fit to the same dataset.
The likelihood ratio $\chi^2$ values (`LR Chisq`)test lack of fit.
By these tests, none of the ordinal models show significant lack of fit.
By the AIC and BIC statistics, the `linlin` model is the best, combining parsimony and goodness of fit.
```{r}
LRstats(indep, linlin, roweff, coleff, rowcol)
```
The `anova.glm()` function gives tests of nested models.
```{r}
anova(indep, linlin, roweff, test = "Chisq")

```


## References

Friendly, M. & Meyer, D. (2016). _Discrete Data Analysis with R: Visualization and Modeling Techniques for Categorical and Count Data_. Boca Raton, FL: Chapman & Hall/CRC.