Noa Cohen posted on Saturday, May 09, 2015 - 11:52 am
I was trying to run a CFA with two latent variables and this message came up:
WARNING: THE LATENT VARIABLE COVARIANCE MATRIX (PSI) IS NOT POSITIVE DEFINITE. THIS COULD INDICATE A NEGATIVE VARIANCE/RESIDUAL VARIANCE FOR A LATENT VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE BETWEEN TWO LATENT VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO LATENT VARIABLES.CHECK THE TECH4 OUTPUT FOR MORE INFORMATION. PROBLEM INVOLVING VARIABLE F2.
TECHNICAL 4 OUTPUT:
ESTIMATES DERIVED FROM THE MODEL
ESTIMATED MEANS FOR THE LATENT VARIABLES F1 F2 ________ ________ 1 0.000 0.000
ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES F1 F2 ________ ________ F1 0.652 F2 0.610 0.536
ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES F1 F2 ________ ________ F1 1.000 F2 1.032 1.000
Could you please tell me what the problem is and how do I fix it?
I'd like to compare CFA-models with one, two or three factors. There are alltogether six indicator variables and they are all binary. When I spesify the three factor model (with two indicators in each factor) I get the "LATENT VARIABLE COVARIANCE MATRIX (PSI) IS NOT POSITIVE DEFINITE" error message and it turns out that one of the correlations between the factors is >1.
My questions are: Can I still compare this three-factor model (despite the error message) using DIFFTEST option with two-factor model (where the two highly correlated factor are combined) - i.e. is the chi-square value trust worthy in the presence of that error message?
Or can I use ML estimator (instead of WLSMV), then I would get "error free" models with comparable BIC values, but is it okay to use ML estimator with binary factor indicators?
Okay, thank you. I suppose I can report that correlation above 1.0 suggests that the two factors should be combined? I'd like to report this somehow, because there is a current debate on this (two vs. three factors) I'd like to contribute to.
What about ML estimator and comparisons using BIC? When I use ML, there aren't any errors and correlations are below 1. But I'm wondering whether I can use ML with categorical indicators.
Ok, thank you for your answer. While ML with CATEGORICAL gives logistic regression as the default, I suppose the factor loadings and correlations between factors are to interpreted as usual (I'm reading STYDX output)?