Interaction Effects in Multiple Regression.

Abstract

This monograph is concerned primarily with the statistical analysis of moderated relationships or as they are more commonly known interaction effects where all variables involved are continuous in nature. The focus is on analyzing interaction effects in the context of multiple regression and structural equation analyses. There currently exists a great deal of confusion about the analysis of moderated relationships involving continuous variables. The statistical and substantive literatures are replete with contradictory advice and admonitions about the best way to test models involving moderated relationships. Further the relevant statistical literature is scattered throughout a range of disciplines including sociology psychology political science economics biology and statistics. The major purpose of this monograph is to bring together this rather diverse literature and to explicate the central issues involved in conducting analyses of moderated relationships involving continuous variables. The principal finding is that interaction analysis is most straightforward when it is theoretically motivated; theory guides the specification of appropriate interaction models using multiple regression analysis. Traditional product terms with continuous variables assess interaction of a specific form namely bilinear interactions. The authors organize their analysis around 3 principal questions: 1) given the sample data can it be inferred that an interaction effect exists in the population; 2) if so what is the strength of the effect; and 3) if so what is the nature of the effect? When formulating research to test for interaction effects one should consider issues related to sample size (for purposes of power analysis) levels of measurement measurement error potential multicollinearity and other methodological/substantive issues discussed above. The monograph concludes with 10 empirical applications that have used multiple regression analysis for the analysis of moderated relationships.