A Generalized Linear Transformation and Its Effects on Logistic Regression

Abstract

Linear transformations such as min–max normalization and z-score standardization are commonly used in logistic regression for the purpose of scaling. However, the work in the literature on linear transformations in logistic regression has two major limitations. First, most work focuses on improving the fit of the regression model. Second, the effects of transformations are rarely discussed. In this paper, we first generalized a linear transformation for a single variable to multiple variables by matrix multiplication. We then studied various effects of a generalized linear transformation in logistic regression. We showed that an invertible generalized linear transformation has no effects on predictions, multicollinearity, pseudo-complete separation and complete separation. We also showed that multiple linear transformations do not have effects on the variance inflation factor (VIF). Numeric examples with a real data were presented to validate our results. Our results of no effects justify the rationality of linear transformations in logistic regression.

Keywords

• logistic regression
• linear transformations
• predictions
• ordinary least squares estimator
• maximum likelihood estimator