이항 회귀모형의 연결함수 오지정 문제에서 확률화된 분위수 잔차 사용에 대한 연구

Abstract

Logistic regression model is usually used when the response is Bernoulli or binomial to predict the probability of event of interest. Specifically, the logistic model is a generalized linear model(GLM) where the assumed link function is the inverse CDF of the logistic distribution. The link misspecification often occurs when the true link is not the logistic link function. In addition, residuals in the binomial GLM model are of less practical use for diagnostics because the response is not continuous. Randomized quantile residuals are an alternative option because they are defined to follow the standard normal distribution. In this study, we investigated the usage of the randomized quantile residual to diagnose the link misspecification. When the logistic regression is fitted to the data where the true data generating process is irrelevant to the logistic link function, we consider the normality test on the randomized quantile residuals from the misspecified logistic regression model and explore whether the link misspecification can be detected or not via extensive simulation studies. We have found that the randomized quantile residual is far from the normality especially when the fitted logistic link function fails to approximate the true link function so that their gap is big.