Pseudolikelihood ratio test with biased observations

This paper explores testing procedures with response-related incomplete data, with particular attention centered to pseudolikelihood ratio tests. We construct pseudolikelihood functions with the biased observations supplemented by auxiliary information, without specifying the association between the primary variables and the auxiliary variables. The asymptotic distributions of the test statistics under the null hypothesis are derived and finite-sample properties of the testing procedures are examined via simulation. The methodology is illustrated with an example involving evaluation of kindergarten readiness skills in children with sickle cell disease.