Choosing between the Bi-Factor and Second-Order Factor Models: A Direct Test Using Latent Variable Modeling

This paper is concerned with the process of selecting between the increasingly popular bi-factor model and the second-order factor model in measurement research. It is indicated that in certain settings widely used in empirical studies, the second-order model is nested in the bi-factor model and obtained from the latter after imposing appropriate parameter constraints. These restrictions can be directly tested within the framework of the latent variable modeling methodology employing widely circulated software. The outlined model selection procedure provides a readily applied means of choosing between the two models of growing interest to measurement scholars, and is illustrated using numerical data.