The use of the $l_z$ and $l_z^*$ person-fit statistics and problems derived from model misspecification

We extend a recent didactic by Magis, Raîche, and Béland on the use of the $l_z$ and $l_z^*$ person-fit statistics. We discuss a number of possibly confusing details and show that it is important to first investigate item response theory model fit before assessing person fit. Furthermore, it is argued that appropriate distributions are only a first step for practical use of person-fit statistics.

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