LSAM, GSAM or factor scores?

[Lucas Udby]

Hi all,

I am analyzing how parental self-efficacy changes across the first postpartum year (N = 2150, 4 waves, six indicators per wave; Likert 1-6). After establishing partial-scalar longitudinal measurement invariance (full syntax attached), I compared a progressive sequence of longitudinal structures to find the best representation of change:

-         Baseline comparison of a time-invariant trait model (stable efficacy) versus a pure autoregressive (AR) model (short-term carry-over).

-         Addition of latent growth curves—linear, quadratic, and a freed-loading growth model.

-          Estimation of hybrid models that blend the best elements of the above.

I use MLR estimator because there is moderate multivariate non-normality. In isolation, the measurement model fits the data well (rCFI .981, rTLI = .978, rRMSEA = .031, and SRMR .04). The trouble begins when I combine the measurement model with the structural specifications. All joint structural models converge but are rank-deficient, they do, however, produce sensible parameter estimates that align with the factor score results. I have tried many sensible tweaks to diagnose the problem (simplify measurement model, less constrictive in structural part, remove item residual cross-time correlations), but it is difficult for me to isolate it.

Now, I am playing around with the Structural-After-Measurement (SAM) approach. Unfortunately, I have a hard time figuring out if SAM is even tangible in my case (complex measurement model + longitudinal structural change). I can get the global SAM to work, but it would be nice to get isolated fit for the structural part, since I am comparing multiple structural models of change on the same measurement model.

My questions are therefore:

-          Can the SAM approach in lavaan support my needs (trait, growth, and AR terms with mild multivariate non-normality), and if so, how should I specify the SAM?

-          If SAM is out of reach, is relying on factor scores an acceptable pragmatic solution in this context, and if so, what is the best way to compensate for the lost measurement uncertainty?

I have attached syntax for my measurement model + longitudinal specifications for the first 5 structural models.

Any guidance or references you can share would be greatly appreciated.

Best regards,

Lucas