Properties of second-order exponential models as multidimensional response models

Carolyn J. Anderson; Hsiu Ting Yu

doi:10.1007/978-3-319-56294-0_2

Properties of second-order exponential models as multidimensional response models

Carolyn J. Anderson, Hsiu Ting Yu

Educational Psychology

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

Second-order exponential (SOE) models have been proposed as item response models (e.g., Anderson et al., J. Educ. Behav. Stat. 35:422–452, 2010; Anderson, J. Classif. 30:276–303, 2013. doi: 10.1007/s00357-00357-013-9131-x; Hessen, Psychometrika 77:693–709, 2012. doi:10.1007/s11336-012-9277-1 Holland, Psychometrika 55:5–18, 1990); however, the philosophical and theoretical underpinnings of the SOE models differ from those of standard item response theory models. Although presented as reexpressions of item response theory models (Holland, Psychometrika 55:5–18, 1990), which are reflective models, the SOE models are formative measurement models. We extend Anderson and Yu (Psychometrika 72:5–23, 2007) who studied unidimensional models for dichotomous items to multidimensional models for dichotomous and polytomous items. The properties of the models for multiple latent variables are studied theoretically and empirically. Even though there are mathematical differences between the second-order exponential models and multidimensional item response theory (MIRT) models, the SOE models behave very much like standard MIRT models and in some cases better than MIRT models.

Original language	English (US)
Title of host publication	Quantitative Psychology - 81st Annual Meeting of the Psychometric Society, 2016
Editors	Wen-Chung Wang, Marie Wiberg, Steven A. Culpepper, Jeffrey A. Douglas, L. Andries van der Ark
Publisher	Springer
Pages	9-19
Number of pages	11
ISBN (Print)	9783319562933
DOIs	https://doi.org/10.1007/978-3-319-56294-0_2
State	Published - 2017
Event	81st annual meeting of the Psychometric Society, 2016 - Asheville, United States Duration: Jul 11 2016 → Jul 15 2016

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	196
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Other

Other	81st annual meeting of the Psychometric Society, 2016
Country/Territory	United States
City	Asheville
Period	7/11/16 → 7/15/16

Keywords

Bi-variate exponential
Composite indicators
Dutch Identity
Formative models
Log-multiplicative association models
Reflective models
Skew normal

ASJC Scopus subject areas

General Mathematics

Online availability

10.1007/978-3-319-56294-0_2

Library availability

Discover UIUC Full Text

Cite this

Anderson, C. J., & Yu, H. T. (2017). Properties of second-order exponential models as multidimensional response models. In W.-C. Wang, M. Wiberg, S. A. Culpepper, J. A. Douglas, & L. A. van der Ark (Eds.), Quantitative Psychology - 81st Annual Meeting of the Psychometric Society, 2016 (pp. 9-19). (Springer Proceedings in Mathematics and Statistics; Vol. 196). Springer. https://doi.org/10.1007/978-3-319-56294-0_2

Properties of second-order exponential models as multidimensional response models. / Anderson, Carolyn J.; Yu, Hsiu Ting.
Quantitative Psychology - 81st Annual Meeting of the Psychometric Society, 2016. ed. / Wen-Chung Wang; Marie Wiberg; Steven A. Culpepper; Jeffrey A. Douglas; L. Andries van der Ark. Springer, 2017. p. 9-19 (Springer Proceedings in Mathematics and Statistics; Vol. 196).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Anderson, CJ & Yu, HT 2017, Properties of second-order exponential models as multidimensional response models. in W-C Wang, M Wiberg, SA Culpepper, JA Douglas & LA van der Ark (eds), Quantitative Psychology - 81st Annual Meeting of the Psychometric Society, 2016. Springer Proceedings in Mathematics and Statistics, vol. 196, Springer, pp. 9-19, 81st annual meeting of the Psychometric Society, 2016, Asheville, United States, 7/11/16. https://doi.org/10.1007/978-3-319-56294-0_2

Anderson, Carolyn J. ; Yu, Hsiu Ting. / Properties of second-order exponential models as multidimensional response models. Quantitative Psychology - 81st Annual Meeting of the Psychometric Society, 2016. editor / Wen-Chung Wang ; Marie Wiberg ; Steven A. Culpepper ; Jeffrey A. Douglas ; L. Andries van der Ark. Springer, 2017. pp. 9-19 (Springer Proceedings in Mathematics and Statistics).

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AB - Second-order exponential (SOE) models have been proposed as item response models (e.g., Anderson et al., J. Educ. Behav. Stat. 35:422–452, 2010; Anderson, J. Classif. 30:276–303, 2013. doi: 10.1007/s00357-00357-013-9131-x; Hessen, Psychometrika 77:693–709, 2012. doi:10.1007/s11336-012-9277-1 Holland, Psychometrika 55:5–18, 1990); however, the philosophical and theoretical underpinnings of the SOE models differ from those of standard item response theory models. Although presented as reexpressions of item response theory models (Holland, Psychometrika 55:5–18, 1990), which are reflective models, the SOE models are formative measurement models. We extend Anderson and Yu (Psychometrika 72:5–23, 2007) who studied unidimensional models for dichotomous items to multidimensional models for dichotomous and polytomous items. The properties of the models for multiple latent variables are studied theoretically and empirically. Even though there are mathematical differences between the second-order exponential models and multidimensional item response theory (MIRT) models, the SOE models behave very much like standard MIRT models and in some cases better than MIRT models.

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ER -

Properties of second-order exponential models as multidimensional response models

Abstract

Publication series

Other

Keywords

ASJC Scopus subject areas

Online availability

Library availability

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Quantitative Psychology: The 81st Annual Meeting of the Psychometric Society, Asheville, North Carolina, 2016

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