Based on my understanding of LCA, I know there are two parameters (latent class probabilities and item-response probabilities) that are estimated using a likelihood similar to what is used for a finite mixture model. However, does this mean that this likelihood is the only one solved to estimate the parameters? Or is there a likelihood solved for each indicator and then another likelihood is solved for the entire latent variable using the parameter estimates from each indicator? Finally, is there a reference that describes this in more detail? Thanks!