Assessing a binary regression model based on ungrouped data is a   commonly encountered but very challenging problem. Although tests, such as   Hosmer–Lemeshow test, have been devised and widely used in applications, they   often have low power in detecting lack of fit and not much theoretical   justification has been made on when they can work well. In this talk, we will   present two new approaches to address the problem.

The first approach is based on a cross-validation (CV) voting   system: The model under examination is compared to a nonparametric method and   a lack of fit is declared when the nonparametric method wins the competition.   Under some mild conditions, the CV comparison leads to both type I and II   error probabilities converging to zero.

The second approach intends to control the probability of type I   error while enhancing the power.  It   directly addresses a core weakness of the popular Hosmer–Lemeshow test: Its   grouping of observations to compare the fitted probabilities and the observed   responses is rigid and not effective. The new methodology, named binary   regression adaptive goodness-of-fit test (BAGofT), is a two-stage solution   where the first stage adaptively selects candidate partitions using   "training" data, and the second stage performs tests based on   "test" data. A proper data splitting ensures that the test has   desirable size and power properties. From our experimental results, BAGofT   performs much better than the Hosmer-Lemeshow test in many situations.

The work is joint with Jie Ding, Chunling Lu and Jiawei Zhang.

基于未分组数据评估二进制回归模型是一个经常遇到但非常具有挑战性的问题。尽管已经设计并广泛使用了诸如Hosmer-Lemeshow检验之类的检验，但它们通常在检验拟合不足的power很低，且何时表现良好还没有足够的理论证明。   他们何时可以正常工作已经有了理论上的证明。 在本次演讲中，我们将介绍两种解决该问题的新方法。

第一种方法基于交叉验证（CV）投票系统：将正在检查的模型与非参数方法进行比较，并且当非参数方法在投票中获胜时就认为拟合不足。 在某些较弱的条件下，CV比较方法会导致I类和II类错误概率均收敛到零。