Estimation of Latent Regression Item Response Theory Models Using a Second-Order Laplace Approximation

Autor/inn/en	Andersson, Björn; Xin, Tao
Titel	Estimation of Latent Regression Item Response Theory Models Using a Second-Order Laplace Approximation
Quelle	In: Journal of Educational and Behavioral Statistics, 46 (2021) 2, S.244-265 (22 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Andersson, Björn)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	1076-9986
DOI	10.3102/1076998620945199
Schlagwörter	Item Response Theory; Computation; Regression (Statistics); Statistical Bias; Sample Size; Accuracy; Test Items + Suchen Sie Ihr Suchwort? Item-Response-Theorie; Regression; Regressionsanalyse; Test content; Testaufgabe
Abstract	The estimation of high-dimensional latent regression item response theory (IRT) models is difficult because of the need to approximate integrals in the likelihood function. Proposed solutions in the literature include using stochastic approximations, adaptive quadrature, and Laplace approximations. We propose using a second-order Laplace approximation of the likelihood to estimate IRT latent regression models with categorical observed variables and fixed covariates where all parameters are estimated simultaneously. The method applies when the IRT model has a simple structure, meaning that each observed variable loads on only one latent variable. Through simulations using a latent regression model with binary and ordinal observed variables, we show that the proposed method is a substantial improvement over the first-order Laplace approximation with respect to the bias. In addition, the approach is equally or more precise to alternative methods for estimation of multidimensional IRT models when the number of items per dimension is moderately high. Simultaneously, the method is highly computationally efficient in the high-dimensional settings investigated. The results imply that estimation of simple-structure IRT models with very high dimensions is feasible in practice and that the direct estimation of high-dimensional latent regression IRT models is tractable even with large sample sizes and large numbers of items. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01