I am using mixed modeling in SPSS to conduct a growth curves analysis of anxiety over 5 time points following a randomized intervention (brief counseling vs education session). I have determined that a model with random intercept, random linear time, and random quadratic time is the best way to model the data. This is the case for an unconditional model, as well as for the model to test my intervention (which it turns out does have a significant interaction with both linear and quadratic time). Those two models converge without issue, using an unstructured covariance matrix, but not with alternative covariance matrices. Here is the SPSS syntax for those two models:
*Unconditional Random Quadratic time. MIXED Anxiety with Time Quad_Time /FIXED INTERCEPT Time Quad_Time | SSTYPE(3) /RANDOM INTERCEPT Time Quad_Time | Subject(PID) COVTYPE(UN) /PRINT = SOLUTION HISTORY /METHOD = ML. *Random Quadratic Time with Intervention Group. MIXED Anxiety with Time Quad_Time Group /FIXED INTERCEPT Time Quad_Time Group Time*Group Quad_Time*Group | SSTYPE(3) /RANDOM INTERCEPT Time Quad_Time | Subject(PID) COVTYPE(UN) /PRINT = SOLUTION HISTORY /METHOD = ML.
I attempted to run both of these models using auto-regressive 1, Toeplitz, and compound symmetry covariance structures in order to figure out which covariance structure is the best fit. In all of these cases, SPSS produced the following error message:
The final Hessian matrix is not positive definite although all convergence criteria are satisfied. The MIXED procedure continues despite this warning. Validity of subsequent results cannot be ascertained.
I tried changing the convergence criteria (e.g., increasing MXSTEP, MXITER, and SCORING) but the issue still occurs. What might be happening? Why would a model fail to converge when switching to a more parsimonious covariance structure?