Several person-fit statistics (PFSs) are offered. These statistics allow assessing whether individual response patterns to tests or questionnaires are (im)plausible given the other respondents in the sample or given a specified item response theory model. Some PFSs apply to dichotomous data, such as the likelihood-based PFSs ($l_z$, $l_z^*$) and the group-based PFSs (personal biserial correlation, caution index, (normed) number of Guttman errors, agreement/disagreement/dependability statistics, $U3$, $ZU3$, $NCI$, $H^t$). PFSs suitable to polytomous data include extensions of $l_z$, $U3$, and (normed) number of Guttman errors.
