A Theoretical Note on the Stochastics of Moderated Multiple Regression

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Abstract
An examination of the stochastics of moderated multiple regression (MMR) reveals that MMR is an appropriate technique when predictors are fixed variables (i.e., values of predictor variables are selected) and the distribution of errors is normal but is not an appropriate technique when predictors are random variables (i.e., values of predictor variables are obtained through random sampling) and the joint distribution of criterion and predictor variables is multivariate normal. The forner situation is characteristic of experimental research, whereas the latter situation is characteristic of observational studies. Thus findings of negligible moderator effects in observational research may be due to inappropriate application of MMR to situations in which predictors should be viewed as random variables.