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I am trying to select the correct model for analyzing data from a behavioral sciences experiment. The experiment consists of eight trials for each participant, and each experiment generates a score on the interval [0--8] for each participant. Each trial within the experiment can be conceived of as a binomial choice. The ideal model will give a prediction equation for the estimated score, using values for a small number of binary categorical explanatory variables.

I am inclined to assume a Poisson distribution for the response variable, with a log link, or a negative binomial distribution if overdispersion is an issue. However, the true distribution is truncated, since any score above 8 is not possible.

Is such an approach on the right track? Would it be wiser to treat each trial as a separate outcome, then do a binomial regression with a random effect for participant? (I have seen a similar question on this site, but would appreciate any advice beyond what is given there)

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Is the response variable continuous? If not, are the numbers cardinal (like counts), or ordinal (in order, like a Likert response scale), or just numbers assigned to different responses that aren't ordered? –  jbowman Feb 29 '12 at 3:06
    
@jbowman The numbers represent the number of times a particular response type is observed, so they are cardinal. –  jlovegren Feb 29 '12 at 3:24
    
@jbowman To give more context, each participant is asked to arrange eight rubber toys on a table; there are a small number of possible strategies for arranging each toy. The response variable is the number of animals for which a particular type of strategy is employed. –  jlovegren Feb 29 '12 at 12:26

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up vote 2 down vote accepted

I'd suggest using a generalized linear model for binomial data, i.e. grouped binary data, with the score 0-8 as the outcome and 8 as the binomial denominator.

As the 8 trials for the same participant aren't independent it's very possible you'll have over- (or under-) dispersion. The simplest way to deal with that within a GLM is to estimate the scale parameter from the data rather than fixing it at the theoretical value.

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Thanks, this is helpful. I think this would mean that the logit for a response of 5 (for example) would be 5/(8-5) = 5/3 (the binomial denominators cancel out). –  jlovegren Feb 29 '12 at 15:54
    
I mean log(5/3) –  jlovegren Feb 29 '12 at 16:03
    
Yes, but this should be calculated by your statistical software rather than you.. –  onestop Feb 29 '12 at 16:41
    
thanks, this works. –  jlovegren Feb 29 '12 at 17:07

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