Inferring the structure of latent class models using a genetic algorithm

Present optimization techniques in latent class analysis apply the expectation maximization algorithm or the Newton-Raphson algorithm for optimizing the parameter values of a prespecified model. These techniques can be used to find maximum likelihood estimates of the parameters, given the specified structure of the model, which is defined by the number of classes and, possibly, fixation and equality constraints. The model structure is usually chosen on theoretical grounds. A large variety of structurally different latent class models can be compared using goodness-of-fit indices of the chi-square family, Akaike's information criterion, the Bayesian information criterion, and various other statistics. However, finding the optimal structure for a given goodness-of-fit index often requires a lengthy search in which all kinds of model structures are tested. Moreover, solutions may depend on the choice of initial values for the parameters. This article presents a new method by which one can simultaneously infer the model structure from the data and optimize the parameter values. The method consists of a genetic algorithm in which any goodness-of-fit index can be used as a fitness criterion. In a number of test cases in which data sets from the literature were used, it is shown that this method provides models that fit equally well as or better than the models suggested in the original articles.