| Past research has shown that the results of moderated multiple regression (MMR) are highly affected by the unreliability of the predictor variables. Some researchers (Bohrnstedt & Marwell, 1978; Busemeyer & Jones, 1983) have suggested that errors-in-variables regression (EIVR) (Warren, White, & Fuller, 1974) may be useful for dealing with the problems of measurement error in the search for moderators. The method suggested by these researchers entails obtaining an estimate of the measurement error present in the cross-product term of the regression through a formula developed by Bohrnstedt and Marwell (1978). This estimated error covariance matrix can then be used in the EIVR calculations. This procedure has been advocated by several researchers, and implemented in a number of cases. Yet, little is known about the properties of the EIVR estimators in the context of moderator variable detection. The present study is a simulation designed to compare the parameter estimates of interaction effects under each of these techniques. The dependent variables were the bias and the mean squared error (MSE) of the parameter estimates. MMR and EIVR were compared using these criteria under varying conditions of sample size, reliability of the predictor variables, mean to standard deviation ratios of the predictor variables, and intercorrelations among the predictor variables. Results indicated that the EIVR parameter estimates were consistently less biased than the MMR estimates, however, the MSE of the EIVR estimates was greater than that for the MMR estimates in many cases. Increases in the reliability of the predictor variables led to improved estimates under both techniques. However, the reliability of the predictors had a greater effect on EIVR estimates. Increases in sample size also improved the parameter estimates of both techniques, however, the EIVR estimates were affected to a much greater degree than the MMR estimates. In general, the 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 $geq$.65). However, MMR appears to be the superior strategy under more typical research circumstances. |
