Analyze Nominal Response Data with the Multinomial-Poisson Trick.

multpois

Jacob O. Wobbrock, University of Washington [email protected]

The goal of multpois is to use the multinomial-Poisson trick to provide for the analysis of nominal response data with or without repeated measures. Such responses, which often arise from surveys or experiments, consist of unordered categories. Although dichotomous responses can be analyzed with glm() or lme4::glmer() using the family=binomial option, there is no analogous family=multinomial option for polytomous responses. In the case of purely between-subjects data, nnet::multinom() can be used, but it cannot take random factors and therefore cannot handle repeated measures. To address this issue, the multpois package provides for the equivalent of a family=multinomial option in glm() or lme4::glmer() via the multinomial-Poisson trick, which converts nominal response data into counts of categorical alternatives and analyzes these counts using (mixed) Poisson regression. Omnibus tests of main effects and interactions are provided through analysis of variance-style output. Post hoc pairwise comparisons are also provided through contrast testing.

Installation

You can install the multpois package like so:

install.packages("multpois")

Example

This is a basic example which shows you how to solve a common problem:

library(multpois)
set.seed(123) # for repeatable results

## a generic 2x2 between-subjects example
ac = sample(c("yes","no","maybe"), size=15, replace=TRUE, prob=c(0.1, 0.6, 0.3))
ad = sample(c("yes","no","maybe"), size=15, replace=TRUE, prob=c(0.4, 0.4, 0.2))
bc = sample(c("yes","no","maybe"), size=15, replace=TRUE, prob=c(0.5, 0.1, 0.4))
bd = sample(c("yes","no","maybe"), size=15, replace=TRUE, prob=c(0.1, 0.5, 0.4))
df1 = data.frame(
  PId = factor(seq(1, 60, 1)),
  X1 = factor(c(rep("a",30), rep("b",30))),
  X2 = factor(rep(c(rep("c",15), rep("d",15)), times=2)),
  Y = factor(c(ac, ad, bc, bd), levels=c("yes","no","maybe"))
)
View(df1)
mosaicplot( ~ X1 + X2 + Y, data=df1, cex=1, col=c("lightgreen","pink","lightyellow"))
m = glm.mp(Y ~ X1*X2, data=df1)
Anova.mp(m, type=3)
glm.mp.con(m, pairwise ~ X1*X2, adjust="holm")

## a generic 2x2 within-subjects example
ac = sample(c("yes","no","maybe"), size=15, replace=TRUE, prob=c(0.2, 0.6, 0.2))
ad = sample(c("yes","no","maybe"), size=15, replace=TRUE, prob=c(0.4, 0.4, 0.2))
bc = sample(c("yes","no","maybe"), size=15, replace=TRUE, prob=c(0.5, 0.2, 0.3))
bd = sample(c("yes","no","maybe"), size=15, replace=TRUE, prob=c(0.2, 0.5, 0.3))
df2 = data.frame(
  PId = factor(rep(1:15, times=4)),
  X1 = factor(c(rep("a",30), rep("b",30))),
  X2 = factor(rep(c(rep("c",15), rep("d",15)), times=2)),
  Y = factor(c(ac, ad, bc, bd), levels=c("yes","no","maybe"))
)
View(df2)
mosaicplot( ~ X1 + X2 + Y, data=df2, cex=1, col=c("lightgreen","pink","lightyellow"))
m = glmer.mp(Y ~ X1*X2 + (1|PId), data=df2)
Anova.mp(m, type=3)
glmer.mp.con(m, pairwise ~ X1*X2, adjust="holm")