The purpose of this research was to examine the effects of missing data on person-model fit and person trait estimation in tests with dichotomous items. Under the missing-completely-at-random framework, four missing data treatment techniques were investigated including pairwise deletion, coding missing responses as incorrect, hotdeck imputation, and model-based imputation. Person traits were estimated using the two-parameter item response model. Overall, missing data increased the difficulty in assessing person-model fit for both model-fitting and model-misfitting persons. The higher the proportion of missing data, the larger the number of persons incorrectly diagnosed. Among the four techniques, the pairwise deletion method performed best in recovering person-model fit and person trait level. Treating missing responses as incorrect caused the examinees with missing data to not fit the measurement model, thus invalidating the person trait estimates. (Contains 6 figures.)