Abstract
ABSTRACT This study focuses on three popular methods to model interactions between two constructs containing measurement error in predicting an observed binary outcome: logistic regression using (1) observed scores, (2) factor scores, and (3) Structural Equation Modeling (SEM). It is still unclear how they compare with respect to bias and precision in the estimated interaction when item scores underlying the interaction constructs are skewed and ordinal. In this article, we investigated this issue using both a Monte Carlo simulation and an empirical illustration of the effect of Type D personality on cardiac events. Our results indicated that the logistic regression using SEM performed best in terms of bias and confidence interval coverage, especially at sample sizes of 500 or larger. Although for most methods bias increased when item scores were skewed and ordinal, SEM produced relatively unbiased interaction effect estimates when items were modeled as ordered categorical.
Highlights
In the medical and behavioral sciences, researchers often inves tigate the effect of predictor variables on a binary outcome variable
In a previous Monte Carlo simulation study (Lodder et al, 2019), we found that when item scores are ordinal and non-normally distributed, using MLR estimation adequately controls the false positive rate when estimating the interaction between two latent variables on a continuous latent outcome variable, while WLS estimation resulted in an inflated false positive rate
As the Type D personality effect is hypothesized to reflect an interaction between its components negative affect and social inhibition (Smith, 2011), we studied four methods to model this interaction effect: (1) logistic regression, modeling the interaction as a multiplication of sum scores, (2) logistic regres sion, modeling the interaction as a multiplication of factor scores, (3) latent logistic regression, modeling the interaction using the Latent Moderated Structural equations (LMS) approach in a structural equation model treat ing the ordinal item scores as continuous, and (4) latent logistic regression using LMS, but modeling the item scores at their appropriate measurement level
Summary
In the medical and behavioral sciences, researchers often inves tigate the effect of predictor variables on a binary outcome variable. There are several ways to assess the interaction between two variables on a binary outcome measure, researchers typically use a logistic regression analysis. In the logistic regression model, the interaction effect is assessed by multiplying the observed scores of two (or more) constructs involved in the interaction, and including the resulting product variable as a predictor (e.g., see Field, 2010; Tabachnick & Fidell, 2007). The two interacting constructs are commonly unobserved (latent) and measured with question naires containing items measured on an ordinal scale. The scores on these items are typically summed and the resulting sum score is assumed to represent the construct of interest. We will argue that this is especially true for interaction effects
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