LPA assumuptions

#1
Do I need to meet the assumption of justly identified or over identification if my LPA has two continuous indicators (there are three classes in this LPA)? There are 10 free parameters. Thanks for any help provided.
 
#6
LPA is a subset of
structural equation modeling
, used to find groups or subtypes of cases in multivariate categorical data. These subtypes are called "latent profiles ".
A model with more unknowns (parameters) than equations (sample statistics) is not identified and will not be estimated by Mplus. A model with less unknowns than equations will be estimated if it is identified using maximum likelihood or weighted least squares. I have ten free parameters.
 
#7
For that reason, you would need to introduce regularization into your estimation procedure, either through a Bayesian prior or a penalty term on the absolute values of the coefficients in the model. In particular, to choose the proper penalty term check out lasso, ridge regression and their combination called "elastic nets". Then you would combine the ideas there with SEM. You might need to use a more flexible software than MPlus, like R or Matlab.