A Fisher-scoring algorithm for fitting latent class models with individual covariates

Describes a modified Fisher scoring algorithm for fitting a wide variety of latent class models for categorical responses when both the class weights and the conditional distributions of the responses depend on individual covariates through a multinomial logit. A simple expression for computing the score vector and the empirical information matrix is presented; it is shown that this matrix is positive definite under mild conditions. The Fisher scoring algorithm combines the empirical information matrix to update the step direction with a line search to optimize the step length. The algorithm converges for almost any choice of starting values. An application to the field of education transmission seems to suggest that, while parents' education affects the child latent ability, their pressure affects directly the child's achievements.