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A semiparametric approach for item response function estimation to detect item misfit. / Köhler, Carmen; Robitzsch, Alexander; Fährmann, Katharina; von Davier, Matthias; Hartig, Johannes.

In: British Journal of Mathematical and Statistical Psychology, Vol. 74, No. S1, 07.2021, p. 157-175.

Research output: Contribution to journalJournal articleResearchpeer-review

Harvard

Köhler, C, Robitzsch, A, Fährmann, K, von Davier, M & Hartig, J 2021, 'A semiparametric approach for item response function estimation to detect item misfit', British Journal of Mathematical and Statistical Psychology, vol. 74, no. S1, pp. 157-175. https://doi.org/10.1111/bmsp.12224

APA

Köhler, C., Robitzsch, A., Fährmann, K., von Davier, M., & Hartig, J. (2021). A semiparametric approach for item response function estimation to detect item misfit. British Journal of Mathematical and Statistical Psychology, 74(S1), 157-175. https://doi.org/10.1111/bmsp.12224

Vancouver

Köhler C, Robitzsch A, Fährmann K, von Davier M, Hartig J. A semiparametric approach for item response function estimation to detect item misfit. British Journal of Mathematical and Statistical Psychology. 2021 Jul;74(S1):157-175. https://doi.org/10.1111/bmsp.12224

Author

Köhler, Carmen ; Robitzsch, Alexander ; Fährmann, Katharina ; von Davier, Matthias ; Hartig, Johannes. / A semiparametric approach for item response function estimation to detect item misfit. In: British Journal of Mathematical and Statistical Psychology. 2021 ; Vol. 74, No. S1. pp. 157-175.

BibTeX

@article{c80089aa83a04a49a1b0c365ba4c88eb,
title = "A semiparametric approach for item response function estimation to detect item misfit",
abstract = "When scaling data using item response theory, valid statements based on the measurement model are only permissible if the model fits the data. Most item fit statistics used to assess the fit between observed item responses and the item responses predicted by the measurement model show significant weaknesses, such as the dependence of fit statistics on sample size and number of items. In order to assess the size of misfit and to thus use the fit statistic as an effect size, dependencies on properties of the data set are undesirable. The present study describes a new approach and empirically tests it for consistency. We developed an estimator of the distance between the predicted item response functions (IRFs) and the true IRFs by semiparametric adaptation of IRFs. For the semiparametric adaptation, the approach of extended basis functions due to Ramsay and Silverman (2005) is used. The IRF is defined as the sum of a linear term and a more flexible term constructed via basis function expansions. The group lasso method is applied as a regularization of the flexible term, and determines whether all parameters of the basis functions are fixed at zero or freely estimated. Thus, the method serves as a selection criterion for items that should be adjusted semiparametrically. The distance between the predicted and semiparametrically adjusted IRF of misfitting items can then be determined by describing the fitting items by the parametric form of the IRF and the misfitting items by the semiparametric approach. In a simulation study, we demonstrated that the proposed method delivers satisfactory results in large samples (i.e., N ≥ 1,000).",
keywords = "Methodological research and development, item fit, item response theory, semiparametric estimation, group lasso",
author = "Carmen K{\"o}hler and Alexander Robitzsch and Katharina F{\"a}hrmann and {von Davier}, Matthias and Johannes Hartig",
year = "2021",
month = jul,
doi = "10.1111/bmsp.12224",
language = "English",
volume = "74",
pages = "157--175",
journal = "British Journal of Mathematical and Statistical Psychology",
issn = "0007-1102",
publisher = "Wiley-Blackwell",
number = "S1",

}

RIS

TY - JOUR

T1 - A semiparametric approach for item response function estimation to detect item misfit

AU - Köhler, Carmen

AU - Robitzsch, Alexander

AU - Fährmann, Katharina

AU - von Davier, Matthias

AU - Hartig, Johannes

PY - 2021/7

Y1 - 2021/7

N2 - When scaling data using item response theory, valid statements based on the measurement model are only permissible if the model fits the data. Most item fit statistics used to assess the fit between observed item responses and the item responses predicted by the measurement model show significant weaknesses, such as the dependence of fit statistics on sample size and number of items. In order to assess the size of misfit and to thus use the fit statistic as an effect size, dependencies on properties of the data set are undesirable. The present study describes a new approach and empirically tests it for consistency. We developed an estimator of the distance between the predicted item response functions (IRFs) and the true IRFs by semiparametric adaptation of IRFs. For the semiparametric adaptation, the approach of extended basis functions due to Ramsay and Silverman (2005) is used. The IRF is defined as the sum of a linear term and a more flexible term constructed via basis function expansions. The group lasso method is applied as a regularization of the flexible term, and determines whether all parameters of the basis functions are fixed at zero or freely estimated. Thus, the method serves as a selection criterion for items that should be adjusted semiparametrically. The distance between the predicted and semiparametrically adjusted IRF of misfitting items can then be determined by describing the fitting items by the parametric form of the IRF and the misfitting items by the semiparametric approach. In a simulation study, we demonstrated that the proposed method delivers satisfactory results in large samples (i.e., N ≥ 1,000).

AB - When scaling data using item response theory, valid statements based on the measurement model are only permissible if the model fits the data. Most item fit statistics used to assess the fit between observed item responses and the item responses predicted by the measurement model show significant weaknesses, such as the dependence of fit statistics on sample size and number of items. In order to assess the size of misfit and to thus use the fit statistic as an effect size, dependencies on properties of the data set are undesirable. The present study describes a new approach and empirically tests it for consistency. We developed an estimator of the distance between the predicted item response functions (IRFs) and the true IRFs by semiparametric adaptation of IRFs. For the semiparametric adaptation, the approach of extended basis functions due to Ramsay and Silverman (2005) is used. The IRF is defined as the sum of a linear term and a more flexible term constructed via basis function expansions. The group lasso method is applied as a regularization of the flexible term, and determines whether all parameters of the basis functions are fixed at zero or freely estimated. Thus, the method serves as a selection criterion for items that should be adjusted semiparametrically. The distance between the predicted and semiparametrically adjusted IRF of misfitting items can then be determined by describing the fitting items by the parametric form of the IRF and the misfitting items by the semiparametric approach. In a simulation study, we demonstrated that the proposed method delivers satisfactory results in large samples (i.e., N ≥ 1,000).

KW - Methodological research and development

KW - item fit

KW - item response theory

KW - semiparametric estimation

KW - group lasso

U2 - 10.1111/bmsp.12224

DO - 10.1111/bmsp.12224

M3 - Journal article

VL - 74

SP - 157

EP - 175

JO - British Journal of Mathematical and Statistical Psychology

JF - British Journal of Mathematical and Statistical Psychology

SN - 0007-1102

IS - S1

ER -

ID: 1518494