It is my understanding that for latent class analysis (LCA) the log likelihood can be calculated by summing the log likelihoods for each case (combination of values of the categorical predictors). For example if we have X1, X2, and X3 as binary variables the likelihood would be the sum of n * ln(P(X1,X2,X3)) where n is the number of observations with the given combination of values for X1, X2, and X3 and we calculate a probability for each combination of values (e.g X1 = 1, X2 = 1, X3 = 1; X1=1, X2 = 1, X3 = 0;....)
However I am not sure how to extend this to latent profile analysis (LPA) where variables are continuous. I know most programs for performing LPA provide this final summery statistic but I would like to understand how to calculate each likelihood. Thank you so much in advance!
