Some issues associated with the use of moderated regression

Abstract

In recent years, some degree of controversy has arisen over the methods that researchers should employ in the detection of moderating effects. More specifically, both M. R. Blood and G. M. Mullet (1977, Where have all the moderators gone?: The perils of type II error, Tech. Rep. No. 11, College of Industrial Management, Georgia Institute of Technology) and H. J. Arnold (1982, Organizational Behavior and Human Performance, 29, 143–174) have challenged the use of “conventional” moderated regression (e.g., S. Zedeck (1971, Psychological Bulletin, 76, 295–310) as an appropriate method for the analysis of moderating effects. Blood and Mullet, for example, have argued that conventional moderated regression is an overly “conservative” technique that is generally incapable of detecting moderating effects—even in data bases “constructed” so as to have strong interaction components. To remedy this problem, they suggest a “backward entry” regression analysis in which the interaction term is the first variable entered into the regression. Also critical of conventional moderated regression, Arnold argues that the same analytic strategy is inappropriate in instances where the researcher's concern is to demonstrate differing “degrees” of correlation between two variables for moderator variable based “subgroups.” The purpose of the present paper is to show that both the arguments of Blood and Mullet and those of Arnold are incorrect. The difficulties associated with the backward entry procedure are demonstrated through the use of Monte Carlo simulation methods. Results of the simulations revealed that the moderated regression analytic procedure is well suited to the detection of statistical interactions (i.e., moderating effects)—even in data bases constructed so as to have (a) very strong main effects for both the independent variable and the moderator variable, (b) dependent variables having large error components, (c) independent and moderator variables having only modest reliability levels, and (d) partially redundant (multicollinear) independent and moderator variables. The errors inherent in the recent arguments of Arnold are shown to result from (a) an unduly restrictive definition of the “degree of relationship” concept, and (b) a seeming belief that differences in correlation coefficients have necessary implications for the accuracy with which scores on one variables can be predicted on the basis of knowledge of scores on another variable. Implications of the present study's analyses are offered.