Matti Cervin
A question about a latent growth curve model (LGCM). I work with a data set in which a large community sample has been assessed for psychopathology at three time points (baseline, 6 months, 12 months). I have six different measures covering different forms of psychopathology at each time point. So I fit a LGCM with random intercepts and random slopes for all measures (i.e., 6 intercepts and six slopes) and find that these psychopathology dimensions "travel together" to a high degree with some slpes being more related than others. All this is fine and the results are in line with theory about these phenomena. However, the overall model fit is quite poor:
CFI: 0.93 TLI: 0.87 SRMR: 0.04 RMSEA: 0.08
I suspect that this may be because of the high correlation between the indicators, e.g. depression and anxiety etc., at each time point, and because this covariance structure is not included in the model, I get a poor fit for the measurement model. However, when I include such a covariance structure, the fit indices are excellent. Further, when including covariance between indicators at each time point, the covariance between the slopes (i.e., the degree to which these things travel together) are reduced (overall, the standardized covariance coefficients goes from being in the ~0.70 range to the ~0.30 range).
What is your opinion on this? Should the covariance between indicators at each time point be included in the model? If so, how does this affect the interpretation of the results?
