My goal is to fit a LCSM over 3 measurement time points . To establish basic model structure, I first fit a latent state model with three time points and autocorrelated neighboring error variables:
MODEL: reas1 by LPS3_T1 LPS4_T1; reas2 by LPS3_T2 LPS4_T2; reas3 by LPS3_T3 LPS4_T3;
! specification of autocorrelated error variables LPS4_T1 with LPS4_T2; LPS4_T2 with LPS4_T3; LPS3_T1 with LPS3_T2; LPS3_T2 with LPS3_T3;
I received the following error message:
WARNING: THE LATENT VARIABLE COVARIANCE MATRIX (PSI) IS NOT POSITIVE DEFINITE. THIS COULD INDICATE A NEGATIVE/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 REAS2.
The same happened for other factors with two indicators that I wanted to fit - but not for a factor with three indicators (this fit very well). The same problem occurred for all models: the latent variables were correlated > than 1. When I started to fix these correlations to 1, the problem just shifted to other variables and yielded negative variances...
I wonder if the problem lies in my model specification for the two-indicator solution, or is it possible that this simple model does not fit my data?