Properties of second-order exponential models as multidimensional response models

Carolyn J. Anderson, Hsiu Ting Yu

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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 languageEnglish (US)
Title of host publicationQuantitative Psychology - 81st Annual Meeting of the Psychometric Society, 2016
EditorsWen-Chung Wang, Marie Wiberg, Steven A. Culpepper, Jeffrey A. Douglas, L. Andries van der Ark
Number of pages11
ISBN (Print)9783319562933
StatePublished - 2017
Event81st annual meeting of the Psychometric Society, 2016 - Asheville, United States
Duration: Jul 11 2016Jul 15 2016

Publication series

NameSpringer Proceedings in Mathematics and Statistics
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017


Other81st annual meeting of the Psychometric Society, 2016
Country/TerritoryUnited States


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

ASJC Scopus subject areas

  • General Mathematics


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