Investigating the power of goodness-of-fit tests for multinomial logistic regression

Goodness-of-fit tests are important to assess if the model fits the data. In this paper we investigate the Type I error and power of two goodness-of-fit tests for multinomial logistic regression via a simulation study. The GoF test using partitioning strategy (clustering) in the covariate space, was compared with another test, Cg which was based on grouping of predicted probabilities. The power of both tests was investigated when the quadratic term or an interaction term were omitted from the model. The proposed test shows good Type I error and ample power except for models with highly skewed covariate distribution. The proposed test also has good power in detecting omission of continuous interaction term.The application on a real dataset was performed to illustrate the use of goodness-of-fit test for multinomial logistic regression in practice using R.