Modeling Interactions Between Latent Variables in Research on Type D Personality: A Monte Carlo Simulation and Clinical Study of Depression and Anxiety

Abstract

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.

Keywords:

• Latent prediction model
• structural equation modeling
• SEM
• latent interaction
• nonnormality
• Type D personality
• depression
• anxiety

Notes

1 For instance, because the BIC is based on the log likelihood, Mplus only reports this fit index for models involving maximum likelihood estimation. Consequently, this fit index is not reported for our models involving weighted least squares estimation. Furthermore, when numerical integration is required (e.g., with the LMS method), means, variances, and covariances are not sufficient statistics for model estimation and chi-square and related fit statistics are not available. As a result, Mplus does for the LMS method not report the chi-square statistics and related indices (RMSEA, CFI, and TLI).

2 Originally, we compared these two models with a log-likelihood difference test. However, the resulting chi-square difference value was negative, and thus the test is invalid as these tests should result in a positive chi-square difference. We may add that such negative chi-square values can arise when using MLR estimation. As an alternative, we used the Wald test, which is available in MPLUS, to test the constraint that both interaction effects are equal to zero.

3 We used the parameter estimates resulting from the LMS method, because this is the default method in Mplus to model interaction effects.