[Application of the pi* 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 goodness-of-fit statistics with a known distribution. This paper describes the application of the pi* goodness-of-fit statistic to latent structure models. The statistic pi* 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 pi* is the population proportion in the residual class. This paper describes the estimation algorithms of pi* 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.