Estimating Multiplicative Regression Terms in the Presence of Measurement Error

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Abstract
Measurement error is a continuing concern for sociologists. A particularly nagging problem has been estimating regression coefficients of multiplicative effects when the component variables contain measurement error. Recently, Heise (1986) presented a corrected estimator for multiplicative terms containing measurement error. The research presented here extends Heise's work, and examines the use of an alternate corrected/constrained estimator proposed by Fuller (1980, 1987). The results of a Monte Carlo simulating give some support for Heise's findings, while providing further explanation for the behavior of estimators. The simulation focuses on small samples (n = 60 and n = 90), and examines the impact of different levels of measurement reliability on error correction procedures. Estimators are compared on the basis of bias, variance, root mean squared error, and singlesample inference accuracy. OLS is included as a benchmark. Results indicated only modest improvements over OLS in estimation using the corrected/constrained estimator, and some hazards in using the simpler corrected estimator in small samples. OLS is judged to be fairly robust and predictable in its inaccuracy.

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