Dealing with multiple local modalities in latent class profile analysis

Parameters for latent class profile analysis (LCPA) are easily estimated by maximum likelihood via the EM algorithm or Bayesian method via Markov chain Monte Carlo. However, the local maximum problem is a long-standing issue in any hill-climbing optimization technique for the LCPA model. To deal with multiple local modalities, two probabilistic optimization techniques using the deterministic annealing framework are proposed. The deterministic annealing approaches are implemented with an efficient recursive formula in the step for the parameter update. The proposed methods are applied to the data from the National Longitudinal Survey of Youth 1997 (NLSY97), a survey that explores the transition from school to work and from adolescence to adulthood in the United States.