Version 0.8-0
This package provides additional data sets, documentation, and a few
functions designed to extend the
vcd package for Visualizing
Categorical Data and the 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 now a support package for the book Discrete Data
Analysis with
R
(DDAR) by Michael Friendly and David Meyer. There is also a web site
for DDAR with all figures and code samples from
the book.
The main purpose of this package is to serve as a sandbox for
introducing extensions of mosaic plots and related graphical methods
that apply to loglinear models fitted using glm() and related,
generalized nonlinear models fitted with gnm() in the
gnm package. A related purpose
is to fill in some holes in the analysis of categorical data in R, not
provided in base R, vcd, or
other commonly used packages.
-
The method
mosaic.glm()extends themosaic.loglm()method in the vcd package to this wider class of models. This method also works for the generalized nonlinear models fit with the gnm package, including models for square tables and models with multiplicative associations. -
mosaic3d()introduces a 3D generalization of mosaic displays using the rgl package. -
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, andLRstats()for brief statistical summaries of goodness-of-fit for a collection of models. -
For square tables with ordered factors,
Crossings()supplements the specification of terms in model formulas usingSymm(),Diag(),Topo(),etc. in the gnm package. -
In addition, there are
- many new data sets; use
datasets("vcdExtra")to see a list; - a tutorial
vignette.
In the installed package, it can be viewed using
vignette("vcd-tutorial", package = "vcdExtra"); - a few useful utility functions for manipulating categorical data sets and working with models for categorical data.
- many new data sets; use
Get the released version from CRAN:
install.packages("vcdExtra")
The development version can be installed to your R library directly from the GitHub repo via:
if (!require(remotes)) install.packages("remotes")
remotes::install_github("friendly/vcdExtra", build_vignettes = TRUE)
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.
data(Mental)
str(Mental)
## 'data.frame': 24 obs. of 3 variables:
## $ ses : Ord.factor w/ 6 levels "1"<"2"<"3"<"4"<..: 1 1 1 1 2 2 2 2 3 3 ...
## $ mental: Ord.factor w/ 4 levels "Well"<"Mild"<..: 1 2 3 4 1 2 3 4 1 2 ...
## $ Freq : int 64 94 58 46 57 94 54 40 57 105 ...
# show as frequency table
(Mental.tab <- xtabs(Freq ~ ses+mental, data=Mental))
## mental
## ses Well Mild Moderate Impaired
## 1 64 94 58 46
## 2 57 94 54 40
## 3 57 105 65 60
## 4 72 141 77 94
## 5 36 97 54 78
## 6 21 71 54 71These examples illustrate fitting loglinear models using glm() and
models for structured associations taking ordinality into account.
Fit the independence model, Freq ~ mental+ses. This does not take
ordinality into account.
indep <- glm(Freq ~ mental+ses,
family = poisson, data = Mental)
LRstats(indep)
## Likelihood summary table:
## AIC BIC LR Chisq Df Pr(>Chisq)
## indep 209.59 220.19 47.418 15 3.155e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1mosaic.glm() is the mosaic method for glm objects. The default
mosaic display for these data:
mosaic(indep)
It is usually better to use standardized residuals in mosaic displays. Here we also add longer labels for the table factors and display the values of residuals in the cells.
The formula, ~ 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.
# labels for table factors
long.labels <- list(set_varnames = c(mental="Mental Health Status",
ses="Parent SES"))
mosaic(indep, ~ 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.
Ordinal models use numeric scores for the row and/or column variables. The simplest models use equally spaced integer scores.
Using these, the term Rscore:Cscore represents an association
constrained to be linear x linear; that is, the slopes for mental
health status is assumed to vary linearly with Parent SES.
# 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.
anova(linlin, test="Chisq")
## Analysis of Deviance Table
##
## Model: poisson, link: log
##
## Response: Freq
##
## Terms added sequentially (first to last)
##
##
## Df Deviance Resid. Df Resid. Dev Pr(>Chi)
## NULL 23 217.400
## mental 3 113.525 20 103.875 < 2.2e-16 ***
## ses 5 56.457 15 47.418 6.543e-11 ***
## Rscore:Cscore 1 37.523 14 9.895 9.035e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Other 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.
# 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
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.
LRstats(indep, linlin, roweff, coleff, rowcol)
## Likelihood summary table:
## AIC BIC LR Chisq Df Pr(>Chisq)
## indep 209.59 220.19 47.418 15 3.155e-05 ***
## linlin 174.07 185.85 9.895 14 0.7698
## roweff 174.45 188.59 6.281 12 0.9013
## coleff 179.00 195.50 6.829 10 0.7415
## rowcol 179.22 198.07 3.045 8 0.9315
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1The anova.glm() function gives tests of nested models.
anova(indep, linlin, roweff, test = "Chisq")
## Analysis of Deviance Table
##
## Model 1: Freq ~ mental + ses
## Model 2: Freq ~ mental + ses + Rscore:Cscore
## Model 3: Freq ~ mental + ses + mental:Cscore
## Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1 15 47.418
## 2 14 9.895 1 37.523 9.035e-10 ***
## 3 12 6.281 2 3.614 0.1641
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Friendly, M. & Meyer, D. (2016). Discrete Data Analysis with R: Visualization and Modeling Techniques for Categorical and Count Data. Boca Raton, FL: Chapman & Hall/CRC.