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Logistic Regression Procedure Using Penalized Maximum Likelihood Estimation for Differential Item Functioning
Author(s) -
Lee Sunbok
Publication year - 2019
Publication title -
journal of educational measurement
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.917
H-Index - 47
eISSN - 1745-3984
pISSN - 0022-0655
DOI - 10.1111/jedm.12253
Subject(s) - statistics , estimation , differential item functioning , logistic regression , mathematics , wald test , type i and type ii errors , sample size determination , statistical power , regression , sample (material) , statistical hypothesis testing , nominal level , variance (accounting) , event (particle physics) , regression analysis , econometrics , confidence interval , item response theory , psychometrics , chemistry , management , physics , chromatography , quantum mechanics , economics , business , accounting
In the logistic regression (LR) procedure for differential item functioning (DIF), the parameters of LR have often been estimated using maximum likelihood (ML) estimation. However, ML estimation suffers from the finite‐sample bias. Furthermore, ML estimation for LR can be substantially biased in the presence of rare event data. The bias of ML estimation due to small samples and rare event data can degrade the performance of the LR procedure, especially when testing the DIF of difficult items in small samples. Penalized ML (PML) estimation was originally developed to reduce the finite‐sample bias of conventional ML estimation and also was known to reduce the bias in the estimation of LR for the rare events data. The goal of this study is to compare the performances of the LR procedures based on the ML and PML estimation in terms of the statistical power and Type I error. In a simulation study, Swaminathan and Rogers's Wald test based on PML estimation (PSR) showed the highest statistical power in most of the simulation conditions, and LRT based on conventional PML estimation (PLRT) showed the most robust and stable Type I error. The discussion about the trade‐off between bias and variance is presented in the discussion section.