Standardized Regression Coefficients: Right or Wrong ?

Lawrence Lessner

For the traditional general linear model, multivariate regression Y_I = b₀ + b₁x_1I + + b_kx_ki + e_i , the regression coefficients b_I are used as a measure of effect in assessing the association between the predictor X_I and the outcome Y. However, the numerical size of the coefficient b_I does depend on the units of measurement X_i . Thus standardizing each of the predictors,

X_i* = ( X_i ­ X_i) / s _i and obtaining the least squares estimates, results in the standardized regression coefficients b_I . These coefficients result from predictors X_I which are uniformly scaled and centered at zero. It is common practice, recommended in many statistical resources to use the standardized b _I as measures of association between Y and X _I and to select that predictor

X_I which is most influential on the predicted value of Y as the X _I having the largest b _I . This presentation presents the work of J. Bring 1994 and S. Greenland 1986 that refutes the use of standardized regression coefficients just described. An alternative to using b _I to obtain the most 'important' predictors to the predicted value of Y is presented.