Journal
MULTIVARIATE BEHAVIORAL RESEARCH
Volume 52, Issue 4, Pages 445-464Publisher
ROUTLEDGE JOURNALS, TAYLOR & FRANCIS LTD
DOI: 10.1080/00273171.2017.1309261
Keywords
Bayesian; bootstrap; interaction; multiple regression; simple slope
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In multiple regression researchers often follow up significant tests of the interaction between continuous predictors X and Z with tests of the simple slope of Y on X at different sample-estimated values of the moderator Z (e.g., +/- 1 SD from the mean of Z). We show analytically that when X and Z are randomly sampled from the population, the variance expression of the simple slope at sample-estimated values of Z differs from the traditional variance expression obtained when the values of X and Z are fixed. A simulation study using randomly sampled predictors compared four approaches: (a) the Aiken and West (1991) test of simple slopes at fixed population values of Z, (b) the Aiken and West test at sample-estimated values of Z, (c) a 95% percentile bootstrap confidence interval approach, and (d) a fully Bayesian approach with diffuse priors. The results showed that approach (b) led to inflated Type 1 error rates and 95% confidence intervals with inadequate coverage rates, whereas other approaches maintained acceptable Type 1 error rates and adequate coverage of confidence intervals. Approach (c) had asymmetric rejection rates at small sample sizes. We used an empirical data set to illustrate these approaches.
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