Markov chain generated profile likelihood inference under generalized proportional to size non-ignorable non-response

We apply two non-ignorable non-response models to the data of the Norwegian Labour Force Survey, the Fertility Survey and the Alveolar Bone Loss Survey. Both models focus on the marginal effect which the object variable of interest has on the non-response, where we assume the probability of non-response to be generalized proportional to the size of the object variable. We draw the inference of the parameter of interest based on the first-order theory of the profile likelihood. We adapt the Markov chain sampling techniques to efficiently generate the profile likelihood inference. We explain and demonstrate why the resampling approach is more flexible for the likelihood inference than under the Beyesian framework.