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Hello Drs. Muthen, I am interested in testing a path model with two ordinal variables predicting a count variable (range = 090). I must choose between the poisson and zeroinflated poisson distributions. To make this choice, I would like to test for overdispersion using MPlus if at all possible. Is it possible to test for overdispersion within Mplus? If so, could you provide a stepbystep regarding how to do so? Thanks, Jim 


You can run it both ways and see which model has the best loglikelihood. Also, if the model with inflation has an inflation constant of 15, then you don't need inflation. 


Hi Linda, Thank you for your response. Two followup questions: "You can run it both ways and see which model has the best loglikelihood" I was hoping for a method that could test the statistical significance of the difference in loglikelihood between these two models (e.g., likelihood ratio test). My understanding is that the poisson and zip models are not nested, so typically the difference in fit between these models is evaluated using the vuong statistic. Is this approach possible using Mplus? "If the model with inflation has an inflation constant of 15, then you don't need inflation." Could you please explain what the inflation constant signifies and why a cutoff of 15 would lead one to favor the poisson moodel? Secondly, is this a heuristic or is this cutoff based on research? Relatedly, how would one defend this decision? Thanks, Jim 


The Mplus User's Guide describes this modeling in examples 7.2 and 7.25. Ex 7.2 describes the inflation matter in Mplus terms. You see there that "the binary inflation variable u#1  describes the probability of being unable to assume any value except zero". This is talking about being in the inflation class. So when the mean (or intercept) in the logit scale goes large negative (15 say), you find that the probability of being in the inflation class is essentially zero. The Poisson and the ZIP are nested as far as I understand, but with the caveat that you have Poisson as a special case with the probability of being in the inflation class being zero  so not fulfilling the LR chisquare requirement of parameters being within the admissible space. If you do ZIP analysis as in 7.25 you work with 2 classes and therefore it would seem that you can instead use the Vuong approach of testing k1 vs k classes, which is Tech11 in Mplus, or a bootstrapped LRT approach, which is Tech14 in Mplus. These approaches are described in the User's Guide and also applied in latent class settings in the Nylund et al paper on our web site under Recent Papers. Note that Mplus deletes the first class in testing k1 vs k classes, so you want to put the inflation class first. I have not tested out this approach, however. 


Dear Linda and/or Bengt Is there a way to have an overdispersion parameter in a multilevel logistic model in Mplus? This is possible in SAS GLIMMIX as applied to binary outcomes. As far as I have been able to find in the Mplus manual and in output, a dispersion parameter can only be requested for the count outcomes. Thanks very much, JP 


Do you mean adding a random effect to the logit expression on Level1? If so, yes, this can be done saying f by; where f is the random effect and regressing the categorical outcome on f with fixed slope 1, y on f@1; The variance of f is estimated. 


Thanks Bengt...I will try this out. JP 

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