Iteration of Partially Specified Target Matrices: Applications in Exploratory and Bayesian Confirmatory Factor Analysis

We describe and evaluate a factor rotation algorithm, iterated target rotation (ITR). Whereas target rotation (Browne, 2001) requires a user to specify a target matrix a priori based on theory or prior research, ITR begins with a standard analytic factor rotation (i.e., an empirically informed target) followed by an iterative search procedure to update the target matrix. In Study 1, Monte Carlo simulations were conducted to evaluate the performance of ITR relative to analytic rotations from the Crawford-Ferguson family with population factor structures varying in complexity. Simulation results: (a) suggested that ITR analyses will be particularly useful when evaluating data with complex structures (i.e., multiple cross-loadings) and (b) showed that the rotation method used to define an initial target matrix did not materially affect the accuracy of the various ITRs. In Study 2, we: (a) demonstrated the application of ITR as a way to determine empirically informed priors in a Bayesian confirmatory factor analysis (BCFA; Muthen & Asparouhov, 2012) of a rater-report alexithymia measure (Haviland, Warren, & Riggs, 2000) and (b) highlighted some of the challenges when specifying empirically based priors and assessing item and overall model fit.