The third step in our strategy was to develop a formal measurement model from which we could generate commensurate scale scores for depression. Although there are several options, we used an extension of traditional factor analytic and IRT methodology referred to as moderated nonlinear factor analysis (MNLFA; Bauer & Hussong, 2009). MNLFA assumes that observations are independent, so these models are also fit to the calibration sample. Given that model complexity in IDA applications of MNLFA can increase rapidly, we prefer a model building approach beginning with a simple model and adding complexity through iterative model tests.
