I have a data set with a response variable with three outcomes (e.g. "zero", "one" or "two"). I want to see if this changes with the explanatory variable 'time'. Since the data is repeated measurements I will use a mixed-effect model with ID as random term. I was considering use glmer from 'lme4' package in R, and model separate binary logistic regression models with only two outcomes (model1: "Zero" vs "One" and model2: "Zero" vs "Two"). I know there is other software and Bayasian tools for multinomial logistic regression (with random effect), but I will prefer glmer from 'lme4' package due to parameterization and interpreting of the analyses.
So I kindly ask for the following:
1. I would like to get suggestions of references (articles and books) on this procedure of using separate binary logistic regression models for ordinal data.
2. Further, I would also like to get your opinion pros/cons of using sets of binomial vs. multinomial logistic regression.
Inngeneral I use SAS, but for R, you can go to
http://statistics.ats.ucla.edu/stat/r/dae/ologit.htm
Dear Ronny,
Both multinomial logistic regression and binary logistic regression models would ignore the ordering of the categories of your ordinal outcome variable. Therefore, I suggest you to use a multilevel ordinal logistic regression model.
You may find useful information in this thesis:
Isaac Sasson. (2012). Approaches to Modeling Self-rated Health in Longitudinal Studies: Best Practices and Recommendations for Multilevel Models
(the link to the full text is below)
Best regards and good luck with your research,
Zeljko
http://repositories.lib.utexas.edu/handle/2152/ETD-UT-2012-05-5236
Similar to Zeljko's suggestion, I'd first recommend examining whether your independent-dependent variable relationships adhere to a proportional odds model (see http://smr.sagepub.com/content/38/2/306.short).
If one or more independent variables can be fit using proportional odds (i.e., partial proportional odds), you could save yourself several degrees of freedom - which would otherwise be consumed without much gain in information in a multinomial or multiple binary logistics by in trying to model minute differences between the categories.
Programs such as gllamm in Stata and clmm2() in the R package ordinal fit such partial proportional odds models with random/mixed effects.
- joe
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