TY - GEN
T1 - Properties of second-order exponential models as multidimensional response models
AU - Anderson, Carolyn Jane
AU - Yu, Hsiu Ting
PY - 2017
Y1 - 2017
N2 - 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.
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.
KW - Bi-variate exponential
KW - Composite indicators
KW - Dutch Identity
KW - Formative models
KW - Log-multiplicative association models
KW - Reflective models
KW - Skew normal
UR - http://www.scopus.com/inward/record.url?scp=85020863216&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85020863216&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-56294-0_2
DO - 10.1007/978-3-319-56294-0_2
M3 - Conference contribution
AN - SCOPUS:85020863216
SN - 9783319562933
T3 - Springer Proceedings in Mathematics and Statistics
SP - 9
EP - 19
BT - Quantitative Psychology - 81st Annual Meeting of the Psychometric Society, 2016
A2 - Wang, Wen-Chung
A2 - Wiberg, Marie
A2 - Culpepper, Steven A.
A2 - Douglas, Jeffrey A.
A2 - van der Ark, L. Andries
PB - Springer
T2 - 81st annual meeting of the Psychometric Society, 2016
Y2 - 11 July 2016 through 15 July 2016
ER -