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@1RelVic_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@1RelVic_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!
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.