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Hello. I want to run a difftest to examine gender differences in a longitudinal, crosslagged model. Some latent variables have categorical indicators and I'm using the theta parameterization because my model is not supported by delta (I believe because certain latent vars are both exognenous and endogenous). In your course notes, several steps are outlined for multiple group analysis with categorical outcomes: In the lessrestrictive H1 model, all parameters are free except factors means which are fixed to zero and scale factors which are fixed to one in all groups. In the morerestrictive H0 model, factor loadings and thresholds are fixed to be equal, with factor means fixed to zero/scale factors fixed to one in 1st group and free in other groups. However, these steps are relevant to delta but not theta parameterization since, with theta parameterization, you cannot fix scale factors as specified, right? With theta, I can fix residual variancesshould I substitute "residual variances" for "scale factors" in the steps outlined above or are there different steps/constraints I should be using? I read web note 4 and some other materials about either difftests or theta but am still not clear on the constraints/settings for difftests with both theta and categorical indicators... Any help would be much appreciated! Dana 


Yes, you should substitute residual variances for scale factors. There is a section in Chapter 13 at the end of the discussion of multiple group analysis that describes the models to use for testing measurement invariance for the Theta paramaterization. 


Thanks for your reply! I did see and try the steps in that section. However, the H1 model for the difftest wouldn't identify (although the singlegroup model did identify in the overall sample and when running each gender separately), so I wondered if there were other constraints I needed to include... 


No, there are not. You would need to send your input, data, output, and your license number to support@statmodel.com so we can see what you are doing. 

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