Polytomous Differential Item Functioning and Violations of Ordering of the Expected Latent Trait by the Raw Score

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The graded response (GR) and generalized partial credit (GPC) models do not imply that examinees ordered by raw observed score will necessarily be ordered on the expected value of the latent trait (OEL). Factors were manipulated to assess whether increased violations of OEL also produced increased Type I error rates in differential item functioning (DIF) procedures conditioned on the raw score. Shorter tests and greater variance in item slope parameters increased OEL violations for the GR data but not for the GPC data. These same factors, combined with group mean differences between the reference and focal groups, increased the Type I error rate for the observed raw score DIF methods for both the GR and GPC data. A procedure condi-tioned on the classical test theory latent score estimate instead of the observed score helped reduce the Type I error in some of the conditions but not for the shortest tests.