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I have conducted a CFA using WLS (and WLSMV) on dichotomous variables. The model is a bifactor (or generalspecific) model with 10 variables loading on the general and 5 variables each loading on two specific factors. Now there are two things in the results that I find puzzling: 1. One of the standardised loadings for the specific factor is .71 (i.e. quite high) but not statistically significant. How is this possible? 2. The pvalues for the unstandardized as compared to the standardised coefficients are sometimes different (??) Many thanks for your help! 


1. It is the size of the standard error in relation to the parameter that determines significance. Also, the parameter distribution may not be normal. 2. The sampling distribution of the raw and standardized loadings are not the same causing the pvalues to differ. 


Thanks so much for your quick response! To follow up on this: Yes, the distribution is probably not normal as the observed variables are dichotomous (1,0) and skewed. However, my understanding was the WLS estimation would handle this. From another discussion thread one of your responses was: “The Mplus estimates for paths from predictors to an observed categorical dependent variable are probit regression coefficients. Typically, only their signs and significance are noted.” From that I am assuming that neither standardised nor unstandardized coefficients are reported but just the sign of the effect. However, I am now not sure which significance levels are the correct ones to report (if any)? 


Categorical data methodology handles floor and ceiling effects of categorical variables. This is related to the distribution of the variable. I am talking about the sampling distributions of the parameter estimates being nonnormal. You would report the significance of the parameter you decide to report. 

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