Bifactor modelling and the evaluation of scale scores

This chapter illustrates -with a real data example - a bifactor modelling approach for more broadly understanding an instrument's psychometric properties and their implications for its use. After introducing the item response data, it describes some preliminary analyses designed specifically to better understand sources of common variance, item content redundancy, and the degree to which the data depart from a unidimensional model. The emphasis primarily will be on model-based reliability indices that inform scale scoring. The chapter addresses the critical issues around the use of latent variable modelling to make judgments about how an instrument should be scored in both practice and research settings. An advantage of structural equation modelling (SEM) is that it allows the modelling of both general and group factors and corrects for errors of measurement. The psychometric literature bemoaning the misunderstandings, limits, and abuses of coefficient alpha to judge the precision of unit-weighted composite measurements is substantial.