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The situation of nonrandomly missing data has theoretically different implications for item parameter estimation depending on whether joint maximum likelihood or marginal maximum likelihood methods are used in the estimation. The objective of this paper is to illustrate what potentially can happen, under these estimation procedures, when there is an association between ability and the absence of response. In this example, a simulation using the one-parameter logistic item response model, data are missing because some students, particularly low-ability students, did not complete the test. (Contains 2 tables, 2 figures, and 16 references.) (SLD) Reproductions supplied by EDRS are the best that can be made from the original document