Checking the adequacy of a general linear model with responses missing at random

In this paper, we consider model checking problem for a general linear model with response missing at random. First, two completed data sets are constructed by imputation and inverse probability weighting methods. Then two score-type and two empirical process based test statistics are proposed by using the constructed data sets. The large sample properties of the test statistics under the null and local alternative hypotheses are investigated. It is shown that both score-type tests are consistent and can detect the local alternatives close to the null ones at the rate n-rn-r with 0≤r≤12, and the empirical process based tests can detect the local alternatives close to the null ones at the rate n-1/2n-1/2. The power and the choice of the weighting function of the proposed tests are discussed. Simulation studies show that the tests perform well and outperform the existing results.