In work with data collected under a responsive design, most analytic approaches may be viewed as extensions of methods developed previously under, respectively, selection models or pattern-mixture models for nonresponse. Under selection models, one approximates the probability of specified responses (or, more generally, the probability of observing certain profiles of paradata) as a function of observable information from frame data, survey data and paradata. Under pattern-mixture models, one views the moment structure of observed survey data as functions of specified response patterns (or, more generally, specified patterns of observed paradata). For the pattern-mixture approach, an especially important issue is the use of constraints on subpopulation moments to ensure that the resulting models are estimable from available data. Following a brief review of these concepts, this paper presents some simulation-based evaluations of the properties of the estimators based on the pattern-mixture approach. Special attention is directed toward evaluation of these properties under moderate deviations from assumed conditions.