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

For latent class models where the class weights depend on individual covariates, we derive a simple expression for computing the score vector and a convenient hybrid between the observed and the expected information matrices which is always positive defnite. These ingredients, combined with a maximization algorithm based on line search, provides an efficient tool for maximum likelihood estimation. In particular, the proposed algorithm is such that the log-likelihood never decreases from one step to the next and the choice of starting values is not crucial for reaching a local maximum. We show how the same algorithm may be used for numerical investigation of the effect of model mispecifications. An application to education transmission is used as an illustration.