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Abstract:
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Generalized linear models (GLMs) are commonly used in studying the relationship between a binary response variable and a number of explanatory variables. When the explanatory variables form a large number of unique values, the asymptotic requirement for the Pearson chi-squared test is violated, and instead the Hosmer-Lemeshow (HL) test is commonly used to assess the overall goodness-of-fit (GoF) of the fitted model. Our study shows that when overdispersion presents, the HL test tends to be too sensitive in the practical sense that it rejects models that are good except for the variance estimate. This is particularly an important issue in modeling a large amount of data, when overdispersion is common and yet not always material. We found that the residual sum of squares (RSS) test, or unweighted sum of squares (USS) test, is more robust in this sense for GLMs with logit, probit and cloglog links. We use a case study on the probability of default (PD) of consumer financial transactions to illustrate the idea.
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