Order selection tests with multiply imputed data

Nonparametric tests for the null hypothesis that a function has a prescribed form are developed and applied to data sets with missing observations. Omnibus nonparametric tests such as the order selection tests, do not need to specify a particular alternative parametric form, and have power against a large range of alternatives. More specifically, likelihood-based order selection tests are defined that can be used for multiply-imputed data when the data are missing at random. A simulation study and data analysis illustrate the performance of the tests. In addition, an Akaike information criterion for model selection is presented that can be used with multiply imputed datasets.