Likelihood Ratio Tests for Multiply Imputed Datasets: Introducing milrtest

Through the use of user-written programs, primarily mim (Carlin, Galati, and Royston, 2008), Stata users can analyze multiply imputed (MI) datasets. Among other capabilities, mim allows the user to estimate a range of regression models and to perform a multi-parameter hypothesis tests after model estimation using a Wald test. The program presented here allows the user to perform likelihood ratio tests on models using multiply imputed datasets after mim. This provides an additional means of testing nested models after estimation using MI data. The process used to perform the likelihood ratio tests is described in Meng and Rubin (1992). The test statistic is calculated based on two sets of likelihood ratio tests. The first involves calculating the likelihood ratio for the null versus alternative hypothesis in each of the m imputed datasets. The second involves calculating the likelihood for the null and alternative hypotheses in each of the m datasets, constraining the parameters to be the estimates based on combining coefficient estimates from the m datasets (i.e. the average of the parameter estimates across the m imputed datasets). The current version allows testing for a limited number of regression commands (i.e. regression, logit, and ologit), but subsequent versions may include compatibility with additional commands.