Bias Correction in Risk Assessment When Logistic Regression is used with An Unevenly Proportioned Sample between Risk and Non-Risk Groups

Abstract

Linear Logistic Regression is a simple but a very powerful tool to assess the likelihood of being in one "category" for an observation with specific independent characteristic values, i.e., when the response variable is dichotomous and the data is replicated, the conditional probability, that an observation belongs to one of the two categories given independent characteristic values, can easily be estimated through Logistic Regression. For various reasons, stratified sampling, sometimes, causes a different sample proportion between the two groups from the population. Many statistical packages allow their users to adjust weights to fix this bias problem as an option in using the Logistic Procedure. The users, however, would experience more computing cost by using the option. In many cases, the purpose of the biased sampling is for computational economy and if the computing cost stays the same, using the biased sample with adjusted weights is not advantageous.
In this study, simple bias correction without using adjusted weights is explained using simulated bankruptcy data. Since the method can be used for any software without adjusting weights, computational economy can be achieved with unbiased results.