TY - JOUR
T1 - Evaluating EIV, OLS, and SEM Estimators of Group Slope Differences in the Presence of Measurement Error
T2 - The Single-Indicator Case
AU - Culpepper, Steven Andrew
PY - 2012/7
Y1 - 2012/7
N2 - Measurement error significantly biases interaction effects and distorts researchers' inferences regarding interactive hypotheses. This article focuses on the single-indicator case and shows how to accurately estimate group slope differences by disattenuating interaction effects with errors-in-variables (EIV) regression. New analytic findings were presented along with simulation results to compare the relative bias, power, and Type I error rates of EIV, ordinary least squares (OLS), and sparse (i.e., single indicator) multigroup structural equation model (SEM) estimators of interaction effects in the presence of measurement error. The results suggest that EIV was less biased than were OLS and sparse SEM. Furthermore, OLS and sparse SEM were unable to control the Type I error rate for tests of slope differences in circumstances where groups differ in predictor reliability. Additional derivations examined the impact of using Cronbach's alpha, which is typically a lower bound for reliability, with EIV. The results provided evidence that using alpha does result in overcorrected EIV estimates and the bias in EIV estimates associated with using Cronbach's alpha increases with variability in item loadings and bias decreases as either test length or the average loading increases. The bias in EIV estimates when using alpha is not larger than the bias produced by using OLS or sparse SEM. In summary, the results provide compelling evidence that researchers should use EIV instead of OLS and sparse SEM to estimate group slope differences in the presence of measurement error.
AB - Measurement error significantly biases interaction effects and distorts researchers' inferences regarding interactive hypotheses. This article focuses on the single-indicator case and shows how to accurately estimate group slope differences by disattenuating interaction effects with errors-in-variables (EIV) regression. New analytic findings were presented along with simulation results to compare the relative bias, power, and Type I error rates of EIV, ordinary least squares (OLS), and sparse (i.e., single indicator) multigroup structural equation model (SEM) estimators of interaction effects in the presence of measurement error. The results suggest that EIV was less biased than were OLS and sparse SEM. Furthermore, OLS and sparse SEM were unable to control the Type I error rate for tests of slope differences in circumstances where groups differ in predictor reliability. Additional derivations examined the impact of using Cronbach's alpha, which is typically a lower bound for reliability, with EIV. The results provided evidence that using alpha does result in overcorrected EIV estimates and the bias in EIV estimates associated with using Cronbach's alpha increases with variability in item loadings and bias decreases as either test length or the average loading increases. The bias in EIV estimates when using alpha is not larger than the bias produced by using OLS or sparse SEM. In summary, the results provide compelling evidence that researchers should use EIV instead of OLS and sparse SEM to estimate group slope differences in the presence of measurement error.
KW - bias
KW - Interactions
KW - reliability
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U2 - 10.1177/0146621612446806
DO - 10.1177/0146621612446806
M3 - Article
AN - SCOPUS:84862633692
SN - 0146-6216
VL - 36
SP - 349
EP - 374
JO - Applied Psychological Measurement
JF - Applied Psychological Measurement
IS - 5
ER -