Structural Equation Modeling Approaches to Estimating Score Dependability Within Generalizability Theory-Based Univariate, Multivariate, and Bifactor Designs

Walter P. Vispoel (), Hyeryung Lee and Tingting Chen
Additional contact information
Walter P. Vispoel: Department of Psychological and Quantitative Foundations, University of Iowa, Iowa City, IA 52242, USA
Hyeryung Lee: Department of Psychological and Quantitative Foundations, University of Iowa, Iowa City, IA 52242, USA
Tingting Chen: Department of Psychological and Quantitative Foundations, University of Iowa, Iowa City, IA 52242, USA

Mathematics, 2025, vol. 13, issue 6, 1-51

Abstract: Generalizability theory (GT) provides an all-encompassing framework for estimating accuracy of scores and effects of multiple sources of measurement error when using measures intended for either norm- or criterion-referencing purposes. Structural equation models (SEMs) can replicate results from GT-based ANOVA procedures while extending those analyses to account for scale coarseness, generate Monte Carlo-based confidence intervals for key parameters, partition universe score variance into general and group factor effects, and assess subscale score viability. We apply these techniques in R to univariate, multivariate, and bifactor designs using a novel indicator-mean approach to estimate absolute error. When representing responses to items from the shortened form of the Music Self-Perception Inventory (MUSPI-S) using 2-, 4-, and 8-point response metrics over two occasions, SEMs reproduced results from the ANOVA-based mGENOVA package for univariate and multivariate designs with score accuracy and subscale viability indices within bifactor designs comparable to those from corresponding multivariate designs. Adjusting for scale coarseness improved the accuracy of scores across all response metrics, with dichotomous observed scores least approximating truly continuous scales. Although general-factor effects were dominant, subscale viability was supported in all cases, with transient measurement error leading to the greatest reductions in score accuracy. Key implications are discussed.

Keywords: structural equation models; generalizability theory; multivariate analysis; bifactor models; R programming; reliability; validity; subscale viability; Music Self-Perception Inventory; mGENOVA (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/6/1001/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/6/1001/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:6:p:1001-:d:1615948

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().