On the Use of Elbow Plot Method for Class Enumeration in Factor Mixture Models

Application of factor mixture models (FMMs) requires determining the correct number of latent classes. A number of studies have examined the performance of several information criterion (IC) indices, but as yet none have studied the effectiveness of the elbow plot method. In this study, therefore, the effectiveness of the elbow plot method was compared with the lowest value criterion and the difference method calculated from five commonly used IC indices. Results of a simulation study showed the elbow plot method to detect the generating model at least 90% of the time for two- and three-class FMMs. Results also showed the elbow plot method did not perform well for two-factor and four-class conditions. The performance of the elbow plot method was generally better than that of the lowest IC value criterion and difference method under two- and three-class conditions. For the four-latent class conditions, there were no meaningful differences between the results of the elbow plot method and the lowest value criterion method. On the other hand, the difference method outperformed the other two methods in conditions with two factors and four classes.