Estimating the Effect of a Predictor Measured by Two Informants on a Continuous Outcome: A Comparison of Methods

Investigators sometimes use information about a given variable obtained from multiple informants. We focus on estimating the effect of a predictor on a continuous outcome, when that predictor cannot be observed directly but is measured by two informants. We describe various approaches to using information from two informants to estimate a regression or correlation coefficient for the effect of the (true) predictor on the outcome. These approaches include methods we refer to as single informant, simple average, optimal weighted average, principal components analysis, and classical measurement error. Each of these five methods effectively uses a weighted average of the informants' reports as a proxy for the true predictor in calculating the correlation or regression coefficient. We compare the performance of these methods in simulation experiments that assume a rounded congeneric measurement model for the relationship between the informants' reports and a true predictor that is a mixture of zeros and positively-distributed continuous values. We also compare the methods' performance in a real data example -the relationship between vigorous physical activity (the predictor) and body mass index (the continuous outcome). The results of the simulations and the example suggest that the simple average is a reasonable choice when there are only two informants.