Assessment of Person Fit for Mixed-Format Tests

Person-fit assessment may help the researcher to obtain additional information regarding the answering behavior of persons. Although several researchers examined person fit, there is a lack of research on person-fit assessment for mixed-format tests. In this article, the l z statistic and the ζ 2 statistic, both of which have been used for tests with only dichotomous items or with only polytomous items, were modified for use with mixed-format tests. In a detailed simulation, the l z and ζ 2 statistics are found to be conservative under a (frequentist) asymptotic normal approximation. However, the use of the statistics along with the (Bayesian) posterior predictive model checking method leads to a larger power. The suggested approaches are applied to an operational data set. The approaches appear to be satisfactory tools for assessing person fit for mixed-format tests.