Curvilinearity in the Reference Composite and Practical Implications for Measurement
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| Title: | Curvilinearity in the Reference Composite and Practical Implications for Measurement |
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| Language: | English |
| Authors: | Xiangyi Liao (ORCID |
| Source: | Journal of Educational Measurement. 2024 61(3):511-541. |
| Availability: | Wiley. Available from: John Wiley & Sons, Inc. 111 River Street, Hoboken, NJ 07030. Tel: 800-835-6770; e-mail: cs-journals@wiley.com; Web site: https://www.wiley.com/en-us |
| Peer Reviewed: | Y |
| Page Count: | 31 |
| Publication Date: | 2024 |
| Sponsoring Agency: | National Science Foundation (NSF), Division of Research on Learning in Formal and Informal Settings (DRL) |
| Contract Number: | 1749275 |
| Document Type: | Journal Articles Reports - Research |
| Descriptors: | Difficulty Level, Simulation, Multidimensional Scaling, Graphs, Causal Models, Measurement |
| Assessment and Survey Identifiers: | Early Childhood Longitudinal Survey |
| DOI: | 10.1111/jedm.12402 |
| ISSN: | 0022-0655 1745-3984 |
| Abstract: | Item difficulty and dimensionality often correlate, implying that unidimensional IRT approximations to multidimensional data (i.e., reference composites) can take a curvilinear form in the multidimensional space. Although this issue has been previously discussed in the context of vertical scaling applications, we illustrate how such a phenomenon can also easily occur within individual tests. Measures of reading proficiency, for example, often use different task types within a single assessment, a feature that may not only lead to multidimensionality, but also an association between item difficulty and dimensionality. Using a latent regression strategy, we demonstrate through simulations and empirical analysis how associations between dimensionality and difficulty yield a nonlinear reference composite where the weights of the underlying dimensions "change" across the scale continuum according to the difficulties of the items associated with the dimensions. We further show how this form of curvilinearity produces systematic forms of misspecification in traditional unidimensional IRT models (e.g., 2PL) and can be better accommodated by models such as monotone-polynomial or asymmetric IRT models. Simulations and a real-data example from the Early Childhood Longitudinal Study--Kindergarten are provided for demonstration. Some implications for measurement modeling and for understanding the effects of 2PL misspecification on measurement metrics are discussed. |
| Abstractor: | As Provided |
| Entry Date: | 2024 |
| Accession Number: | EJ1449415 |
| Database: | ERIC |
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