Algebraic relationships between Hosmer–Lemeshow (HL), Pigeon–Heyse (J2), and Tsiatis (T) goodness-of-fit statistics for binary logistic regression models with continuous covariates were investigated, and their distributional properties and performances studied using simulations. Groups were formed under deciles-of-risk (DOR) and partition-covariate-space (PCS) methods. Under DOR, HL and T followed reported null distributions, while J2 did not. Under PCS, only T followed its reported null distribution, with HL and J2 dependent on model covariate number and partitioning. Generally, all had similar power. Of the three, T performed best, maintaining Type-I error rates and having a distribution invariant to covariate characteristics, number, and partitioning.
|Number of pages||24|
|Journal||COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION|
|Early online date||2017|
|Publication status||Published - 16 Mar 2017|
- Binary logistic regression
- Partition the covariate space