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I have a simple path model: x > u > y where u is binary and y continuous; estimator is WLSMV. What are the equations that Plot3 graphs use when presenting the estimated values of u and y? (e.g., the probit probability estimates of u  outlined in ch13 of the UG  do not seem to accord with the graph of estimated values of u). 


The u and y predicted values are not plotted. It is the unconditional values. 


Ok, a followup question. I am looking at the sample correlation for two endogenous binary variables (with covariates) estimated under WLSMV. This should be the correlation of the residuals from probit models. What kind of residuals are they (e.g., anscombe, pearson)  how are they calculated? 


This is a residual covariance between the latent response variables underlying the observed categorical variables. See the following reference for details: Muthén, B. (1984). A general structural equation model with dichotomous, ordered categorical, and continuous latent variable indicators. Psychometrika, 49, 115132. 

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