I'm running an SEM model (a latent curve model with structured residuals) to estimate the relationship between repeated measurements of two variables. Four of my latent variables each predict several observed variables. Initial model fit was very poor, so, following modification indices, I added code to estimate the means of these latent variables. I now have much better fit. However, I don't have a good understanding of what these changes mean for my model. I have two questions:
- Why might estimating the means of latent variables affect model fit?
2.What is the difference in interpretation of a model with and without the means of the latent variables estimated?