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Activity Number: 414
Type: Contributed
Date/Time: Tuesday, August 5, 2014 : 2:00 PM to 3:50 PM
Sponsor: Section on Bayesian Statistical Science
Abstract #312483
Title: Probing Interactions in Multiple Regression: Frequentist Versus Bayesian Approaches
Author(s): Yu Liu*+ and Roy Levy and Stephen G. West
Companies: Arizona State University and Arizona State University and Arizona State University
Keywords: Bayesian ; simple slope ; interaction ; conditional slope ; regression ; bootstrap
Abstract:

Applied researchers often follow up significant tests of the b3 interaction term in multiple regression, Y=b0+b1*X+b2*Z+b3*XZ+e, with tests of the simple (conditional) slope at values of 1 SD above and below the mean of Z. The values of M and SD of Z used to determine these values are treated as fixed rather than random in the standard frequentist approach. This simulation study compares the standard frequentist test of simple slopes with bootstrapping and a fully Bayesian approach at sample sizes of 50, 200, 400, and 1600, with 1000 replications per sample size. Both the Bayesian and bootstrapping approaches take the uncertainty in the sample estimates of the M and SD of Z into account. Simulation results show that the frequentist solutions can be inaccurate depending on the distributions of the M and SD of Z and those of b1 and b3; accuracy did not improve with increased sample size. Percentile bootstrapping resulted in accurate solutions even for smaller sample sizes. For the Bayesian approach, the posterior distribution with non-informative priors approached the population distribution as sample size increased.


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