Probing curvilinear-by-linear interactions when the predictors are randomly sampled
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Probing curvilinear-by-linear interactions when the predictors are randomly sampled Yu Liu 1
# The Psychonomic Society, Inc. 2019
Abstract Curvilinear effects and curvilinear-by-linear interactions are hypothesized, tested, and probed in various fields of the social and behavioral sciences. When such effects are found, researchers traditionally have tested the simple slope, and more recently have utilized the Johnson–Neyman technique, often at the values of the sample statistics of the predictor(s). Both approaches implicitly assume that values on the predictors have been sampled according to a fixed sampling plan. More typically in social and behavioral research, however, values on the predictors can be more appropriately considered as randomly sampled from a multivariate population distribution. I show analytically and through simulation that for regression models containing a curvilinear-by-linear interaction, fixed and random regression models produce the same estimates but different standard errors of the simple slope at values of the sample statistics of the predictors. When values on the predictors are randomly sampled, treating them as fixed when testing the simple slope or generating conditional Johnson–Neyman confidence bands at values of the sample statistics of the predictors can lead to inflated Type I error rates and inaccurate coverage rates. Recommendations for researchers are provided, and directions for future research are discussed. Keywords Curvilinear interaction . Fixed regression . Random regression . Bootstrap . Fully Bayesian
Curvilinear effects and curvilinear-by-linear interactions are commonly hypothesized, tested, and probed in various fields of social and behavioral sciences. Examples include studies of job performance, job satisfaction, life satisfaction and turnover intention (Janssen, 2001), learning and performance in multidisciplinary teams (van der Vegt & Bunderson, 2005), creativity (Baer & Oldham, 2006), and voluntary turnover rates, organizational human resource management investment in employees, and workforce productivity and organizational financial performance (Shaw, Park, & Kim, 2013). When a significant interaction effect is found, researchers have traditionally followed-up the significant interaction effect by testing the simple slope of the effect of the focal predictor on the outcome at the values of the sample statistics of moderators, typically at the sample mean and one sample standard Electronic supplementary material The online version of this article (https://doi.org/10.3758/s13428-019-01276-4) contains supplementary material, which is available to authorized users. * Yu Liu [email protected] 1
Department of Psychological, Health, and Learning Sciences, University of Houston, Houston, TX, USA
deviation above and below the sample mean (see Aiken & West, 1991). The probing of significant interactions more recently has been conducted using the Johnson–Neyman technique, which has been extended to models with curvilinear effects (J. W. Miller, Stromeyer, &
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