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## The Impact of Ignoring Multilevel Data Structure on the Estimation of Dichotomous Item Response Theory Models

#### Hyung Rock Lee [1] , Sunbok Lee [2] , Jaeyun Sung [3]

##### 27 248

Applying single-level statistical models to multilevel data typically produces underestimated standard errors, which may result in misleading conclusions. This study examined the impact of ignoring multilevel data structure on the estimation of item parameters and their standard errors of the Rasch, two-, and three- parameter logistic models in item response theory (IRT) to demonstrate the degree of such underestimation in IRT. Also, the Lord’s chi-square test using the underestimated standard errors was used to test differential item functioning (DIF) to show the impact of such underestimation on the practical applications of IRT. The results of simulation studies showed that, in the most severe case of multilevel data, the standard error estimate from the standard single-level IRT models was about half of the minimal asymptotic standard error, and the type I error rate of the Lord’s chi-square test was inflated up to .35. The results of this study suggest that standard single-level IRT models may seriously mislead our conclusions in the presence of multilevel data, and therefore multilevel IRT models need to be considered as alternatives.
Item Response Theory, Rasch, Multilevel Data, Monte Carlo Simulation
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Primary Language en Education, Scientific Disciplines March Articles Orcid: 0000-0002-7415-9466Author: Hyung Rock Lee (Primary Author)Institution: University of Central ArkansasCountry: United States Orcid: 0000-0020-0924-7056Author: Sunbok LeeInstitution: University of HoustonCountry: United States Orcid: 0000-0001-7461-3123Author: Jaeyun SungInstitution: Lyon CollegeCountry: United States
 Bibtex @research article { ijate523586, journal = {International Journal of Assessment Tools in Education}, issn = {}, eissn = {2148-7456}, address = {İzzet KARA}, year = {2019}, volume = {6}, pages = {92 - 108}, doi = {10.21449/ijate.523586}, title = {The Impact of Ignoring Multilevel Data Structure on the Estimation of Dichotomous Item Response Theory Models}, key = {cite}, author = {Lee, Hyung Rock and Lee, Sunbok and Sung, Jaeyun} } APA Lee, H , Lee, S , Sung, J . (2019). The Impact of Ignoring Multilevel Data Structure on the Estimation of Dichotomous Item Response Theory Models. International Journal of Assessment Tools in Education, 6 (1), 92-108. DOI: 10.21449/ijate.523586 MLA Lee, H , Lee, S , Sung, J . "The Impact of Ignoring Multilevel Data Structure on the Estimation of Dichotomous Item Response Theory Models". International Journal of Assessment Tools in Education 6 (2019): 92-108 Chicago Lee, H , Lee, S , Sung, J . "The Impact of Ignoring Multilevel Data Structure on the Estimation of Dichotomous Item Response Theory Models". International Journal of Assessment Tools in Education 6 (2019): 92-108 RIS TY - JOUR T1 - The Impact of Ignoring Multilevel Data Structure on the Estimation of Dichotomous Item Response Theory Models AU - Hyung Rock Lee , Sunbok Lee , Jaeyun Sung Y1 - 2019 PY - 2019 N1 - doi: 10.21449/ijate.523586 DO - 10.21449/ijate.523586 T2 - International Journal of Assessment Tools in Education JF - Journal JO - JOR SP - 92 EP - 108 VL - 6 IS - 1 SN - -2148-7456 M3 - doi: 10.21449/ijate.523586 UR - https://doi.org/10.21449/ijate.523586 Y2 - 2019 ER - EndNote %0 International Journal of Assessment Tools in Education The Impact of Ignoring Multilevel Data Structure on the Estimation of Dichotomous Item Response Theory Models %A Hyung Rock Lee , Sunbok Lee , Jaeyun Sung %T The Impact of Ignoring Multilevel Data Structure on the Estimation of Dichotomous Item Response Theory Models %D 2019 %J International Journal of Assessment Tools in Education %P -2148-7456 %V 6 %N 1 %R doi: 10.21449/ijate.523586 %U 10.21449/ijate.523586 ISNAD Lee, Hyung Rock , Lee, Sunbok , Sung, Jaeyun . "The Impact of Ignoring Multilevel Data Structure on the Estimation of Dichotomous Item Response Theory Models". International Journal of Assessment Tools in Education 6 / 1 (March 2019): 92-108. https://doi.org/10.21449/ijate.523586