Longitudinal CFA with categorical ite...
Message/Author
 Albert Farrell posted on Tuesday, April 14, 2015 - 7:53 am
I am running a longitudinal CFA on a 2-factor model treating Likert items as categorical. Data are missing by design. Each participant (N = 1,137) was randomized to 2 of 4 waves. All coverage > 16%. Fit indices are good (RMSEA = .013; CFI/TLI = .99). Estimates and SEs are reasonable. However, I get the warning.

THE MODEL ESTIMATION TERMINATED NORMALLY
WARNING: THE LATENT VARIABLE COVARIANCE MATRIX (PSI) IS NOT POSITIVE
DEFINITE. . . ..
PROBLEM INVOLVING VARIABLE RELVIC_C.

My syntax is:
Analysis:
Model:
!Wave A
OvVic_A by PBFS42_A* PBFS48_A PBFS65_A PBFS53_A
PBFS58_A PBFS44_A PBFS49_A PBFS54_A PBFS55_A;
RelVic_A by PBFS43_A* PBFS52_A PBFS61_A PBFS63_A PBFS64_A;
OvVic_A@1 RelVic_A@1;
!Wave B
OvVic_B by PBFS42_B* PBFS48_B PBFS65_B PBFS53_B
PBFS58_B PBFS44_B PBFS49_B PBFS54_B PBFS55_B;
RelVic_B by PBFS43_B* PBFS52_B PBFS61_B PBFS63_B PBFS64_B;
OvVic_B@1 RelVic_B@1;
syntax repeats for Wave C and D items

Factor variances are all 1 and largest correlation is .88. I get the same warning if I constrain thresholds and loadings over time. My intent is to test larger models with factors for additional items not in this model. Any help or suggestions would be greatly appreciated!
 Bengt O. Muthen posted on Tuesday, April 14, 2015 - 8:31 am
I would break the analysis down into smaller steps so you can see when this problem arises. First do each time point separately, then 2 at a time, etc.

Non-pos def factor correlation matrices can come from the many strict zero loadings which tend to inflate factor correlations. You can instead try the ESEM approach - see UG ex 5.27 modified for longitudinal instead of multi-group analysis.