Hello, I have a latent autoregressive cross-lagged model where one type of variable is continuous whereas the other is binary. I run it with integration=montecarlo and obtain the estimates (log odds ratios, I believe, when the outcome is binary, and B when the outcome is continuous). However, with this model I am unable to receive standardized estimates to compare the cross-lagged effects (i.e., I can't compare the log odds ratios to the Bs)and I do not receive absolute model fit indices.
To overcome this, I rerun the model without the "categorical are" statement which, I believe, makes it into a linear probability model, and I can receive standardized estimates which make the effects where there is a binary and a continuous outcome comparable. Also, I receive RMSEA, CFI, and TLI as absolute model fit indices.
Is this the correct approach to be able to compare the effects and receive absolute model fit indices where one type of outcome is binary and the other continuous?
I would not recommend treating the binary outcomes as continuous.
To get fit statistics and standardization, you might consider using WLSMV instead of ML. WLSMV estimates linear regressions involving the continuous latent response variables underlying the binary observed variables.
Nevertheless, I think it is doubtful if it is meaningful to compare the size of cross-lagged effects for two such different DVs. Sign and significance is probably the only thing one should consider.
Also, standard fit statistics are not necessarily needed. You can always formulate neighboring models that are somewhat less restrictive than your model and then compare them by doing a likelihood-ratio chi-square test.
Thank you so much for your quick response. First, I tried using the WLSMV estimator, but it gave me an error that the model can ONLY be done with montecarlo integration. When I tried to rerun the WLSMV model with montecarlo integration, it gave me an error that it CANNOT be done with montecarlo integration.
Also, I tried the other idea of comparing more or less restrictive models, but when I tried to set the cross-lag from my binary variable to my continuous variable equal to the cross-lag from my continuous variable to my binary variable, model would not run because "equalities between parameters are not possible in this situation".