Optimization-Based Model Fitting for Latent Class and Latent Profile Analyses

Statisticians typically estimate the parameters of latent class and latent profile models using the Expectation-Maximization algorithm. This paper proposes an alternative two-stage approach to model fitting. The first stage uses the modified k-means and hierarchical clustering algorithms to identify the latent classes that best satisfy the conditional independence assumption underlying the latent variable model. The second stage then uses mixture modeling treating the class membership as known. The proposed approach is theoretically justifiable, directly checks the conditional independence assumption, and converges much faster than the full likelihood approach when analyzing high-dimensional data. This paper also develops a new classification rule based on latent variable models. The proposed classification procedure reduces the dimensionality of measured data and explicitly recognizes the heterogeneous nature of the complex disease, which makes it perfect for analyzing high-throughput genomic data. Simulation studies and real data analysis demonstrate the advantages of the proposed method.