@Stephen:  I just noticed your affiliation has changed, and you're now an Assistant Prof.  Congrats! 

Meanwhile, if Rebecca wants to attempt repeated measures multinomial logistic regression via SPSS, I think GENLINMIXED is the only option.  (GENLIN can estimate ordinal logistic regression models, with GEE to account for the repeated measures; but it cannot estimate multinomial logistic regression models with repeated measures.)  From the Command Syntax Reference manual, under GENLINMIXED > TARGET_OPTIONS Subcommand:

MULTINOMIAL. Multinomial probability distribution. The target can be numeric or string, and it must have at least two distinct, valid data values. This is the default probability distribution if the target is categorical. Note that the form of the model will depend on the measurement level of the target.

– A nominal target will result in a nominal multinomial model in which a separate set of model parameters are estimated for each category of the target (except the reference category). The parameter estimates for a given predictor show the relationship between that predictor and the likelihood of each category of the target, relative to the reference category.

– An ordinal target will result in an ordinal multinomial model in which the traditional intercept term is replaced with a set of threshold parameters that relate to the cumulative probability of the target categories.

A good resource for GENLINMIXED is the book by Heck, Thomas & Tababa (see link below). 

HTH.

http://www2.hawaii.edu/~ltabata/mlm/HTT2012.html

As far as I know [caveat: it's been several years since I looked into this, so the situation may have changed] this is actually a nontrivial problem. Generally speaking, if you want regression with repeated measures then you do a mixed effects model. However, for a multinomial outcome, there actually do not seem to be many implementations of this. The closest thing I ever found was https://hlplab.wordpress.com/2009/05/07/multinomial-random-effects-models-in-r/, which appears to do what you need, but you need to know some bayesian model fitting concepts to understand how to do this (that's what stopped me from really figuring this out back when I had a similar problem as you).

An easier option could be to just decompose the outcome into one or more binary outcomes and do separate models. e.g., if the response options are A, B, and C, you could do one model just analyzing people's likelihood of choosing A (as opposed to B or C), yada yada.

@Stephen:  I just noticed your affiliation has changed, and you're now an Assistant Prof.  Congrats! 

Meanwhile, if Rebecca wants to attempt repeated measures multinomial logistic regression via SPSS, I think GENLINMIXED is the only option.  (GENLIN can estimate ordinal logistic regression models, with GEE to account for the repeated measures; but it cannot estimate multinomial logistic regression models with repeated measures.)  From the Command Syntax Reference manual, under GENLINMIXED > TARGET_OPTIONS Subcommand:

MULTINOMIAL. Multinomial probability distribution. The target can be numeric or string, and it must have at least two distinct, valid data values. This is the default probability distribution if the target is categorical. Note that the form of the model will depend on the measurement level of the target.

– A nominal target will result in a nominal multinomial model in which a separate set of model parameters are estimated for each category of the target (except the reference category). The parameter estimates for a given predictor show the relationship between that predictor and the likelihood of each category of the target, relative to the reference category.

– An ordinal target will result in an ordinal multinomial model in which the traditional intercept term is replaced with a set of threshold parameters that relate to the cumulative probability of the target categories.

A good resource for GENLINMIXED is the book by Heck, Thomas & Tababa (see link below). 

HTH.

http://www2.hawaii.edu/~ltabata/mlm/HTT2012.html

You may wish to test for auto correlation

Please let me know if the following references/sites are useful to you:

1.  IBM SPSS Regression 22

ftp://public.dhe.ibm.com/software/analytics/spss/.../22.../IBM_SPSS_Regression.pdfCached

number of cases, while the Multinomial Logistic Regression procedure internally ... Note: If you have repeated measurements of binary data, or records that are ...

2.  Multinomial Logistic Regression

https://it.unt.edu/sites/default/files/mlr_jds_aug2011.pdf

by J Starkweather - ‎Cited by 54 - ‎Related articles

Multinomial logistic regression is used to predict categorical placement in or the probability ... Multinomial logistic regression is a simple extension of binary logistic .... in Biostatistics: Linear, Logistic, Survival, and Repeated Measures Models.

3.  Your Statistical Tool Belt - Social Science Research Commons

https://ssrc.indiana.edu/doc/wimdocs/2013-09-

27_dickinson_toolbelt_slides.pdfCached

by S Dickinson - ‎Cited by 1 - ‎Related articles

A Guide to Doing Statistics in Second Language Research Using SPSS , by Jenifer Larson-Hall .... DV is Categorical Correlated Data Repeated Measures Logistic. Regression. ... Multinomial Logistic Regression. Comparison ..... Tutorial “demo” slideshow for SPSS commands in 'Diet Study RM ANOVA_demo.pdf'. Demo:.

Dennis

Dennis Mazur

Thanks everyone for useful responses and references ! think I am going to decompose the outcome into binary variables and perform fit binomial models.

Although will be reading into the references you all suggested!