Abstract
Application of the π* goodness-of-fit index to latent structure models. Testing model fit for latent structure models (latent trait models and latent class models) is difficult because of the lack of goodnessof-fit statistics with a known distribution. This paper describes the application of the π* ,goodness-offit statistic to latent structure models. The statistic π* is based on the concept of latent classes and has a natural interpretation when applied to these models. This statistic assumes that the population is made up of several classes that follow a parametric model, and a residual class outside the model. The value of π* is the population proportion in the residual class. This paper describes the estimation algorithms of π* for latent trait and latent class models and an empirical example with a scale of study habits. There are two latent classes in these data: bad and regular students, which are related to the student's responsibility.
