A Comparison of Bias and Mean Squared Error in Parameter Estimates of Interaction Effects: Moderated Multiple Regression versus Error-in-Variables Regression

The results of moderated multiple regression (MMR) are highly affected by the unreliability of the predictor variables (regressors). Errors-in-variables regression (EIVR) may remedy this problem as it corrects for measurement error in the regressors, and thus provides less biased parameter estimates. However, little is known about the properties of the EIVR estimators in the moderator variable context. The present study used simulation methods to compare the moderator variable detection capabilities of MMR and EIVR. Specifically, the study examined the bias and mean squared error of the MMR and EIVR estimates under varying conditions of sample size, reliability of the predictor variables, and intercorrelations among the predictor variables. Findings showed that EIVR estimates are superior to MMR estimates when sample size is high (i.e., at least 250) and the reliabilities of the predictors are high (i.e., r(ii) greater than or equal to .65). However, MMR appears to be the better strategy when reliabilities or sample size are low.