# [R-sig-ME] How to use mixed-effects models on multinomial data

Emmanuel Charpentier emmanuel.charpentier at sap.aphp.fr
Thu May 28 14:35:18 CEST 2009

```Le mercredi 27 mai 2009 à 18:08 +0200, Linda Mortensen a écrit :
> Dear list members,
>
> In the past, I have used the lmer function to model data sets with
> crossed random effects (i.e., of subjects and items) and with either a
> continuous response variable (reaction times) or a binary response
> variable (correct vs. incorrect response). For the reaction time data,
> I use the formula:
> lmer(response ~ predictor1 * predictor2 ....  + (1 + predictor1 *
> predictor2 .... | subject) + (1 + predictor1 * predictor2 .... |
> item), data)
> And for the binomial data, I use the formula:
> lmer(response ~ predictor1 * predictor2 ....  + (1 + predictor1 *
> predictor2 .... | subject) + (1 + predictor1 * predictor2 .... |
> item), data, family="binomial").
>
> I'm currently working on a data set for which the response variable is
> number of correct items with accuracy ranging from 0 to 5. So, here
> the response variable is not binomial but multinomial.

Huh ?

Treating it as a "pure class" variable loses the (essential) ordering
information. Unless this ordering information (which seems to an
ignorant outsider the most important information about your subjects) is
essentially irrelevant to you problem, I'd rather use your number of
correct items as a "rough" measure of a numeric variable, and accept, as
a first approximation, its non-continuity as part of the experimental
error.

This approximation may be too rough with only 5 items, though.
Furthermore, depending on your beliefs on the cognitive model involved
in giving a "correct" response, the distance between 0 and 1 correct
response(s) may be close to or very different from the distance between
4 and 5 correct responses, which is exactly what proportional risks
model (polr) tries to explain away.

V&R4 (p 204 & sqq), explains that an ordered logistic regression is but
a set of logistic regressions on the (nested) orders induced by the
ordered response. It points to a "seminal" paper : McCullagh (1980) :
regresion models for ordinal data (with discussion), JRSS B 42:109-42,
and to McCullagh's book (to which I do not have access).

Maybe working with glmer's mixed effect logistic regression as a
building block would allow to build somewhat inneficiently) something
close to what polr does ?

What do you think ?

>                                                             I want to
> stay within the mixed-effects model framework, but am not sure how to
> modify the lmer function formula so that it will work on ordered
> multinomial data. I am not even sure whether this function can handle
> this kind of data at all.
> I have tried to model the same data using the DPolmm function in the
> DPpackage, but this function doesn't seem to accept two random effect
> terms, at least it produces an error message when I enter "random
> = ..." twice.

I didn't know this one...

> Does anyone know which function to use here? Any advice is very much
> appreciated.
>
> If this mailing list does not deal with inquiries of this kind, I
> apologise, but would appreciate if someone would re-direct me to
> another more suitable list. Thanks.

IMHO, you are on the suitable list. But your problem isn't probably very
usual...

> Linda
>
>
> Linda Mortensen
> Post-doctoral research fellow
> Department of Psychology
> University of Copenhagen
> Øster Farimagsgade 2A
> 1353 Copenhagen K
> Denmark
> Tel.: +45 3532 4889
> E-mail: linda.mortensen at psy.ku.dk
>

```