A Parametric Bootstrap Procedure to Perform Statistical Tests in a LCA of Anti-Social Behaviour

In this paper we focus on latent class analysis of a large data set. The data deal with antisocial behaviour which is measured by 24 dichotomous variables. Latent class analysis of such huge data sets is unusual. One of the reasons is that latent class analysis defines models for contingency tables, so, if there is a set of k dichotomous items, then a table of 2 cells is modeled. It will be clear that, in general, the cells of the contingency table will be reasonably filled only for small k. Therefore, for large k we cannot rely on asymptotic results, meaning that the usual testing procedures cannot be applied. Furthermore, since the better known computer programs MLLSA (Clogg, 1977) and LCAG (Hagenaars and Luijkx, 1990) require the 2 k frequencies as input, usage of these computer programs for such examples leads to the tedious creation of the correct input file and computer storage problems.