HosmerLemeshow

The Hosmer-Lemeshow test is a statistical goodness-of-fit test that assesses how well a logistic regression model predicts a binary outcome. It is particularly useful for evaluating models where the outcome variable is dichotomous, meaning it can take on only two values, such as yes/no, presence/absence, or success/failure.

The test works by dividing the observed data into groups based on predicted probabilities. Typically, ten groups are formed. Within each group, the observed number of events (cases where the outcome is present) is compared to the expected number of events, which is calculated from the logistic regression model. A chi-squared statistic is then computed to quantify the difference between observed and expected values across all groups.

A low p-value (typically less than 0.05) from the Hosmer-Lemeshow test indicates that there is a statistically significant difference between the observed and predicted outcomes, suggesting that the logistic regression model does not fit the data well. Conversely, a high p-value implies that the model's predictions are reasonably consistent with the observed data, and the model is considered a good fit.

It is important to note that the Hosmer-Lemeshow test is sensitive to the number of groups chosen. While ten groups are commonly used, this can be adjusted. The test's effectiveness can also depend on the sample size and the distribution of predicted probabilities. A well-fitting model should have a high p-value in this test.