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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:

  1. 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?

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If you free the means of the latents, and your model is still identified, then your model was not correctly set up in the first place.

You can identify the means of the latent variables by constraining the intercepts of the measured variables, or constraining the means (or intercepts) or the latent variables. If you do both, your model fit will (probably) be horrible.

If you paste some code, that might help us to understand what happened.

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