Investigating bias in squared regression structure coefficients

Kim F. Nimon, Linda R. Zientek, Bruce Thompson

The importance of structure coefficients and analogs of regression weights for analysis within the general linear model (GLM) has been well-documented. The purpose of this study was to investigate bias in squared structure coefficients in the context of multiple regression and to determine if a formula that had been shown to correct for bias in squared Pearson correlation coefficients and coefficients of determination could be used to correct for bias in squared regression structure coefficients. Using data from a Monte Carlo simulation, this study found that squared regression structure coefficients corrected with Pratt's formula produced less biased estimates and might be more accurate and stable estimates of population squared regression structure coefficients than estimates with no such corrections. While our findings are in line with prior literature that identified multicollinearity as a predictor of bias in squared regression structure coefficients but not coefficients of determination, the findings from this study are unique in that the level of predictive power, number of predictors, and sample size were also observed to contribute bias in squared regression structure coefficients.