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

Abstract

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., rij ≥ .65). However, MMR appears to be the better strategy when reliabilities or sample size are low.

Personnel Selection: Looking Toward the Future--Remembering the Past

“…Other Meta-Analyses Meta-analysis of the Five Factor Model validities in U.S. studies from 1992 through 1997 produced results similar to past U.S. metaanalyses (Anderson & Viswesvaran 1998), but meta-analyses involving only European samples produced somewhat different results (Salgado 1997a(Salgado , 1998. Both conscientiousness and emotional stability correlated positively with job performance across occupational groups, and both contributed incremental variance beyond general mental ability in predicting overall job performance.…”

“…Error variance in the independent variables affects differential prediction (Terris 1997), and errors-in-variables regression addresses this problem. Errors-invariables regression detected differential prediction more accurately than moderated multiple regression when reliability coefficients were Ͼ0.65 and sample sizes were Ͼ250 (Anderson et al 1996).…”

Profit‐sharing plans and affective commitment: Does the context matter?

“…EIV regression also avoids some of the difficulties, such as convergence problems and offending estimates, that may arise when SEM techniques are used with complex models involving a large number of parameters (McDonald et al, 2005). Anderson, Stone-Romero, and Tisak (1996) showed that when interaction effects are tested, the estimates obtained using EIV were superior to those obtained employing ordinary least squares when both the sample size and the reliabilities of the predictors are high (above 250 and .65, respectively). Following standard procedure, we entered control variables and main effects in the first step and the interactive terms in the second.…”

Analyzing the Effects of Market and Resource Orientations on Innovative Outcomes in Times of Turbulence*

“…Recent research has questioned the validity of moderated or hierarchical multiple regression for interaction effects (Anderson, Stone-Romero, and Tisak, 1996;Jaccard and Wan, 1995). One of the most commonly cited problems associated with its use is that no moderating effects are often found.…”