Predictive power of school motivation clusters in secondary education

In many applications of cluster analysis in educational research, the solutions found have very limited predictive power for relevant outcomes. In this paper, we explore whether the clusterings found have more predictive power (in terms of explained variance) if relevant outcomes are included in the estimation procedure, using a real-world data set on school motivation. We compare various normal mixture models with different distal outcomes involved such as no outcome variable, a single outcome, all outcomes. All models were estimated using the simultaneous estimation (one-step) procedure for distal outcomes in Latent GOLD. Partial eta squared (휂2푝) was used to assess predictive power. Including relevant outcomes will in most cases increase the predictive power of the models. Furthermore, the increase in power is more substantial, in the absolute sense, when the correlation between the outcome variable and input variables is higher.