Here is what I refer to in PROC HPLOGISTIC documentation.
LACKFIT< (DFREDUCE=r NGROUPS=G) >
performs the Hosmer and Lemeshow goodness-of-fit test (Hosmer and Lemeshow 2000) for binary
response models.
The subjects are divided into at most G groups of roughly the same size, based on the percentiles of
the estimated probabilities. You can specify G as any integer greater than or equal to 5; by default,
G=10. Let the actual number of groups created be g. The discrepancies between the observed and
expected number of observations in these g groups are summarized by the Pearson chi-square statistic,
which is then compared to a chi-square distribution with g–r degrees of freedom. You can specify a
nonnegative integer r that satisfies g–r 1; by default, r=2.
A small p-value suggests that the fitted model is not an adequate model. For more information, see the
section “The Hosmer-Lemeshow Goodness-of-Fit Test” on page 4274.
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