# [R] ordered logistic regression with random effects. Howto?

From: Paul Johnson <pauljohn32_at_gmail.com>
Date: Mon, 07 May 2007 21:03:08 -0500

I'd like to estimate an ordinal logistic regression with a random effect for a grouping variable. I do not find a pre-packaged algorithm for this. I've found methods glmmML (package: glmmML) and lmer (package: lme4) both work fine with dichotomous dependent variables. I'd like a model similar to polr (package: MASS) or lrm (package: Design) that allows random effects.

I was thinking there might be a trick that might allow me to use a program written for a dichotomous dependent variable with a mixed effect to estimate such a model. The proportional odds logistic regression is often written as a sequence of dichotomous comparisons. But it seems to me that, if it would work, then somebody would have proposed it already.

Ching-Fan Sheu, "Fitting mixed-effects models for repeated ordinal outcomes with the NLMIXED procedure" Behavior Research Methods, Instruments, & Computers, 2002, 34(2): 151-157.

the other gives an approach that works in SAS's NLMIXED procedure. In this approach, one explicitly writes down the probability that each level will be achieved (using the linear predictor and constants for each level). I THINK I could find a way to translate this approach into a model that can be fitted with either nlme or lmer. Has someone done it?

What other strategies for fitting mixed ordinal models are there in R?

Finally, a definitional question. Is a multi-category logistic regression (either ordered or not) a member of the glm family? I had thought the answer is no, mainly because glm and other R functions for glms never mention multi-category qualitative dependent variables and also because the distribution does not seem to fall into the exponential family. However, some textbooks do include the multicategory models in the GLM treatment.

```--
Paul E. Johnson
Professor, Political Science
1541 Lilac Lane, Room 504
University of Kansas

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