Which analysis for categorical repeated design?

Hello there,

I am looking for an appropriate analysis to analyze polytomous categorical data from a repeated mixed design.

More specifically:
There were 5 groups of subjects; each subject provided 4 datapoints; each datapoint could be one of 3 categories.

In other words:
1 between factor, taking on 5 levels
1 within factor, taking on 4 levels
The DV is a choice of category

Cochran's Q is not appropriate as it can only handle dichotomous data, and cannot accomodate the between factor.

Multinomial logistic regression cannot handle the repeated measures aspect.

Any ideas?



TS Contributor

This is sort of tough, because there really aren't any statistical methods that meld together the different aspects of your study (that I know of...)

However, you should just try breaking up the analysis into a couple of steps, maybe one step would be the between-groups comparison (i.e., is one group more likely to make a particular choice). The other step would be looking at correlations between a particular choice and other choices...

If you can give us some insight as to the purpose of the study (i.e., what was the research problem; exactly what were you trying to prove / disprove), that would help direct the appropriate analysis(es).

Otherwise, if your study was exploratory, then unfortunately, the analysis will be exploratory as well - but that could lead to interesting follow-on studies if you see patterns worth noting.

Categorical between-within design

Dear John,

thanks for your response.
i will try and describe the study to you.

It was a psychology experiment.

As outlined before, each participant made 1 choice in each of 4 conditions.
The within factor can be called TIME (the timing of a stimulus changed with 4 discrete steps across the 4 conditions)

The clear hypothesis was that increases in TIME lead to a shift from choice A to choice B. There was also a third alternative option, C. The hypothesis was that proportion of C choices shoud stay constant across variations in TIME.

More specifically, the hypothesis was that with low values of TIME, A should be chosen most, and indeed, from eyeballing the data, this clearly happened. As TIME increases, participants should gradually shift from A to B, while C should hardly ever be chosen. Again, eyeballing suggests that indeed this happened.

So much for the within subject factor.

The between factor, let's call it CONTRAST, varied the a-priori attractiveness of choices A and B. More specifically, in some between-condiitons, A and B were very close in attractiveness, while in other conditions, A was much more attractive than B.
The hypothesis here was that in those groups were A is much more attractive than B, variations in TIME would affect choices less, i.e. A will be chosen, regardless of TIME; on contrast, in those conditions where A and B are very close together, choices should shift from A to B more readily.

This is a very abstract rendition of the actual experiment, but I think it conveys the general picture. If you are really keen, I could attach a PDF of a 6-page conference paper describing the experiment

What I have done so far, is collapse over the between factor, and form dichotomous choice variables for each option, i.e. AChoice@Time1, AChoice@Time2, etc.
I have then calculated Cochran's Q for ACHoice, BChoice, and CChoice, and can support the within hypothesis. However, this seems a bit messy to me, because
a) I completely lose the between subjects information
b) the dichotomous Choice variables are naturally NOT independent of each other
c) I have to do multiple tests (though I did correct the alpha)
d) Cochran's Q does not actually check for trends

My next thought was to try multinomial logistic regression, and use "SUBJECT" as a stratification variable, and TIME as a factor.
This seems like I am forcing a within design on the regression -- do yuo think this is acceptable?

thanks very much,
similar problem

I also have a problem trying to work out how to analyse my categorical data.
My experiment was entirely within-subject (2 x 2) and in each of the four conditions the participants were asked to rate two things. Participants were coded as either
1. showing a decrease between the two ratings
2. showing an increase
3. ratings remaining the same.

I'm not sure which statistical test is appropriate in this case.
Any suggestions?


TS Contributor

As this is a very-rarely seen design, it's difficult to make a suggestion. Any design where both variables are within-subject is rarely seen in texts or in practice, and it's even more unusual to have one with a categorical response.

What I originally suggested to Marc was to visit UCLA's Department of Statistics free statistical "e-consulting" site:


The professors there have more experience dealing with unusual aspects of experimental design.

Just post a detailed question and they usually get back in 1-2 days.