Predictive performance of logistic regression for imbalanced data with categorical covariate

Abstract

Logistic regression is often used for the classification of a binary categorical dependent variable using various types of covariates (continuous or categorical). Imbalanced data will lead to biased parameter estimates and classification performance of the logistic regression model. Imbalanced data occurs when the number of cases in one category of the binary dependent variable is very much smaller than the other category. This simulation study investigates the effect of imbalanced data measured by imbalanced ratio on the parameter estimate of the binary logistic regression with a categorical covariate. Datasets were simulated with controlled different percentages of imbalance ratio (IR), from 1% to 50%, and for various sample sizes. The simulated datasets were then modeled using binary logistic regression. The bias in the estimates was measured using MSE (Mean Square Error). The simulation results provided evidence that the effect of imbalance ratio on the parameter estimate of the covariate decreased as sample size increased. The bias of the estimates depended on sample size whereby for sample size 100, 500, 1000 – 2000 and 2500 – 3500, the estimates were biased for IR below 30%, 10%, 5% and 2% respectively. Results also showed that parameter estimates were all biased at IR 1% for all sample size. An application using a real dataset supported the simulation results.