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I am now using Version 5, and I fit a model to 10 binary indicators using MLR, which the manual says will give 2PL output. In that output, two chisquare statistics appear as ChiSquare Test of Model Fit for the Binary and Ordered Categorical (Ordinal) Outcomes** What null hypothesis do these chisquares test? One is a Pearson, and one is an LR chisquare. They do not appear to be testing the fit of the 2PL model per se. Sorry if this question has been asked before, but I couldn't find it on the list. Roger Millsap 


These are tests of the observed versus expected multiway frequency tables for the categorical indicators. 


Hi Linda, If I could follow up on this: when you say "expected", under what model are the expected frequencies generated? They do not seem to be generated under a singlefactor model for binary indicators. Or are they? The chisquares are much different from the fit of the singlefactor model under WLSMV, for example. Thanks, Roger 


In both cases expected is the H0 model such as a 1factor model. The frequency table chisquares (Pearson and LR) have higher df since they test against the full distribution whereas WLS tests against only bivariates  so df's are different (WLSMV df, as opposed to WLS and WLSM, is of course totally different since it is estimated). The p values should be comparable. As usual, freq table Pearson/LR can suffer from low cell count problems. 


Hi Bengt, The pvalues in my example are not even close to comparable. I'm fitting a singlefactor to 10 binary items with N=937. No missing data. For the MLR run, the two chisquares are: Pearson chi=1039.751 df=1002 p=.1983 LR chi=589.487 df=1002 p=1.0000 For the singlefactor run with WLSMV: WLSMV chi=54.598 df=31 p=.0055 Clearly, the IRTMLR results lead to a vastly different conclusion about fit. What is the explanation? If you want the data and programs, I can send them. Roger 


Typically when the Pearson and LR chisquares for a frequency table are as different as in this MLR run, neither can be trusted most likely due to many freq table cells with (close to) zero cell counts. Adding Tech10 to the MLR run should expose this. The WLSMV chisquare can work better in such situations since it collapses to bivariate tables. If that doesn't explain it, please send materials to support. 


Hi Bengt, I think that your conjecture is correct. When I cut the number of items down to 57, the pvalues are much more comparable. Once I get up to 10 items, the divergence is there and there are many cells with zero's. I guess that the lesson is to use the singlefactor WLSMV to test the model if the number of items exceeds what can be supported with the N. Thanks, Roger 


Dear Drs. Muthen, I am testing a model, in which the independent variable (IV) is categorical with 4 groups (4 groups of children with different social profiles). The grouping variable is gender. I use version 5 now. 1. How do I specify that the independent (w1_socgr) variable is categorical? When I run this model command: W3_anti BY W3_devfA W3_police W3_drugA; W2_soci BY W2_coopA W2_assrA W2_contA; W2_soci ON w1_socgr; W3_anti ON w1_socgr W2_soci; it looks like w1_socgr is being correlated with w2_soci (a latent variable of social competence at w2)? If I choose w1_socgr as a grouping variable, how do I test for gender differences and how do I retain the three wave nature of the design? 2. One of the indicators for the outcome variable (antisocial at wave 3) is actually a count variable treated as a continuous variable (# of times the adolescent in contact with police). It has about 50% missing + many zero’s. Could I recode the variable into a dichotomous variable? What else could I do? 3. The results indicate that w2_soci is a mediator for girls, but not for boys, in that the path from w2_soci to w3_anti is significant only for girls. Do I have to run a test constraining that path to be equal across groups to test for significance? How do I specify that in the command? Thank you for a wonderful forum, 


You need to represent a fourcategory nominal variable by three dummy variables and include these dummy variables as covariates in your model. You can treat the variable as a count or dichotomize it. You could try both. It depends on what question you are trying to answer. The ztest given for each group tests whether the coefficient is different from zero. A difference test tests whether the coefficients are different from each other. 

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