Assessing whether the number of predictors affect the power of the Hosmer-Lemeshow test in large data sets
Logistic regression models are popular in public health and biomedical research. When implementing a logistic regression model, it is important to assess the model’s fit, as inferences drawn from the model can be incorrect. The Hosmer-Lemeshow test is a widely used goodness-of-fit test for logistic regression models, which groups subjects based on the estimated probabilities of the outcome. Despite its wide use, no one in the literature has examined whether the power of the Hosmer-Lemeshow test is affected by the number of predictors in the logistic regression model. Using both simulation and analysis from the ALLHAT clinical trial, power was evaluated on the Hosmer-Lemeshow test with the number of predictors. For the simulation, the power changed little with it slightly decreasing as the number of predictors increased from one to five and slightly increasing as the predictors increased from two to five. For the ALLHAT analysis, as the number of predictors in the models increased, the power of the Hosmer-Lemeshow test decreased. Thus, the power of the Hosmer-Lemeshow test may depend on the number of predictors possibly decreasing as the number increases in the logistic regression model.^
Blanchard, Christina Theoktisto, "Assessing whether the number of predictors affect the power of the Hosmer-Lemeshow test in large data sets" (2016). Texas Medical Center Dissertations (via ProQuest). AAI10182174.