Correction for Attenuation of the Multiple Correlation Coefficient Given Non-Independent Error Scores

Abstract

The multiple correlation coefficient measures the linear relationship between two or more independent variables and a single dependent variable. Like other correlations, the multiple correlation value relies upon observed scores. Researchers attempting to consider the relationship between true scores have relied upon standard corrections for attenuation. However, these standard estimates for the multiple correlation coefficient corrected for attenuation ignore any potentially correlated error in the observed data. In this work we propose a new estimator for the multiple correlation coefficient that accounts for the error in observed data where this error is allowed to covary. We explore properties of the estimator via simulation and illustrate its effectiveness with a real-world data application.