Treating binary variables as conitnuous using cfa

[Esther Szekely]

Hello, I am posting this for a friend. Any advice is much appreciated.

"I initially ran cfa (specifying a hierarchical second-order model) using WLSMV as estimator, but without further specifying binary variables as ordered. I then realized that the majority of my manifest variables were binary, thus included the "ordered" statement and changed to std.ov=FALSE, but standardized the continuous variables before fitting the model on a set of m=40 imputed data sets.

Since then, I receive a lot of warnings and error messages from lavaan.

This issue arises in two separate analyses of mine.

1) In the first analyses, 80% of my variables are binary, when treat the binary variables as ordered, in many of the imputed data sets the analysis results in Heywood cases or non-convergence. Interestingly, this was not the case when I treated the binary variables as continuous (i.e., std.ov=TRUE, did not specify them as ORDERED and used WLSMV as estimator). When I ignored the data sets with Heywood cases, the overall fit (based on CFI scaled, TLI scaled, rmsea, etc.) became much worse than previously, when I treated my binary variables as continuous (i.e., std.ov=TRUE, no ORDERED statment, and estimator=WLSMV).

2) In the second model, 50% of my variables are binary, I run m=40 sets of imputations using mice and when I run my cfa model on these data sets, specifying the binary variables as ORDERED, using WLSMV as estimator I receive the following warning: "estimation polyserial correlation did not converge" for many of my binary variables, and "correlation between variables x and y is (nearly) 1.0", and "Negative pooled test statistic was set to zero, so fit will appear to be arbitrarily perfect. Robust corrections uninformative, not returned."

I had none of these issues before starting to consider my binary variables as "ordered".

Therefore, my question is: is it O.K. if I treat my binary variables as continuous? And is there a reason why I should expect models to be that unstable/problematic when using so many ordered variables? It is puzzling why I suddenly run into all these issues when I properly specify binary variables as" ordered" relative to when I treated them as continuous.

Thank you for any assistance in advance!"