Table 1.

Person-Fit Indices.

Person-fit index	Description
Nonparametric
Personal point-biserial correlation ( $r_{\mathrm{pbis}}$ ; Donlon & Fischer, 1968)	It is the correlation between the individual’s score and the item proportion-correct score.
Caution statistic ( $C$ ; Sato, 1975)	It is the complement of the two covariances ratio that measures to what extent an individual’s response deviates from a perfect response pattern.
Modified caution statistic ( $C^{*}$ ; Harnisch & Linn, 1981)	It is the modified version of the caution statistic, which ranges from zero to one.
Number of Guttman errors ( $G$ ; Meijer, 1994)	Guttman error occurs when an easy item is answered incorrectly and a hard item is answered correctly.
Normalized Guttman errors ( $G^{*}$ ; van der Flier, 1977)	It is the normalized version of the Guttman error which ranges from zero to one.
Agreement statistic ( $A$ ; Kane & Brennan, 1980)	It is the agreement between an individual’s responses $(x_i)$ on an item and proportion-correct score $(p_i)$ on that item. $A=\sum _i{x}_i{p}_i$
Disagreement statistic ( $D$ ; Kane & Brennan, 1980)	$D=A(\max )-A$
Dependability statistic ( $E$ ; Kane & Brennan, 1980)	$E=A/A(\max )$
$U3$ statistic ( $U3$ ; van der Flier, 1980)	It is a global fit index that assumes invariant item ordering based on the proportion-correct score on items.
Standardized normal $U3$ ( $\mathrm{ZU}3$ ; van der Flier, 1982)	It is the standardized normal version of $U3$ .
Norm conformity index ( $\mathrm{NCI}$ ; Tatsuoka & Tatsuoka, 1982, 1983)	It is the conformity of an individual’s response pattern in comparison with a criterion order such as item difficulty order.
$H^T$ statistic ( $H^T$ ; Sijtsma, 1986; Sijtsma & Meijer, 1992)	When an individual’s response is compared with the rest of the respondents, the $H^T$ measures the extent to which data complies with the Guttman model.
Parametric
Standardized normal loglikelihood ( $l_z$ ; Drasgow et al., 1985)	It measures the standardized normal loglikelihood fit of an individual’s response based on an IRT model.
Corrected $l_z$ ( $l_z^{*}$ ; Snijders, 2001)	It is the corrected form of $l_z$ .