Below is a short summary of a new study I published with my collaborators in the Journal Multivariate Behavioral Research.
Modeling Interactions Between Latent Variables in Research on Type D Personality: A Monte Carlo Simulation and Clinical Study of Depression and Anxiety
Several approaches exist to model interactions between latent variables. However, it is unclear how these perform when item scores are skewed and ordinal. Research on Type D personality serves as a good case study for that matter. In Study 1, we fitted a multivariate interaction model to predict depression and anxiety with Type D personality, operationalized as an interaction between its two subcomponents negative affectivity (NA) and social inhibition (SI). We constructed this interaction according to four approaches: (1) sum score product; (2) single product indicator; (3) matched product indicators; and (4) latent moderated structural equations (LMS). In Study 2, we compared these interaction models in a simulation study by assessing for each method the bias and precision of the estimated interaction effect under varying conditions. In Study 1, all methods showed a significant Type D effect on both depression and anxiety, although this effect diminished after including the NA and SI quadratic effects. Study 2 showed that the LMS approach performed best with respect to minimizing bias and maximizing power, even when item scores were ordinal and skewed. However, when latent traits were skewed LMS resulted in more false-positive conclusions, while the Matched PI approach adequately controlled the false-positive rate.
Lodder, P., Denollet, J., Emons, W. H., Nefs, G., Pouwer, F., Speight, J., & Wicherts, J. M. (2019). Modeling Interactions Between Latent Variables in Research on Type D Personality: A Monte Carlo Simulation and Clinical Study of Depression and Anxiety. Multivariate behavioral research, 1-29.