Date of Award

6-21-2024

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Education

First Advisor

Ken Fujimoto

Abstract

Response data corresponding to educational and psychological instruments may represent different dimensional structures to account for different patterns of the dependencies in the data. One of the dimensional structures that has been increasingly discussed in the literature is the bifactor structure. This structure can effectively separate different sources that influence the responses, which contributes to score validity and provides theoretical insights about the measured trait. Unfortunately, estimating this structure in practice comes with challenges. One such challenge is an empirical identification issue that is seldom discussed in the literature. This issue occurs when an item’s discriminations on the general and specific dimensions (or within-item discriminations) are similar in strength, making it difficult to obtain accurate estimates for those discriminations. The current evidence regarding the empirical identification issue was shown in only limited situations under full information maximum likelihood (FIML) estimation method. The extent to which the within-item discriminations have to be similar before estimation issues arise and whether the similarity depends on sample size, strength of the item discriminations, and item targetedness (i.e., how well the items’ response categories are targeted to the respondents) are unclear. Also, whether the empirical identification issue occurs under other estimation methods is unknown. This dissertation fills these gaps using three simulation studies. The results suggest that the empirical identification issue of the bifactor model due to the item’s discriminations being similar is moderated by the magnitude of the within-item discriminations. In addition, larger sample sizes can mitigate the estimation inaccuracies caused by within-item discriminations being similar and the discriminations being strong in magnitude. The results also show that Bayesian estimation using adaptive informative priors may produce more accurate discrimination estimates than FIML and Bayesian estimation using less informative priors when the empirical identification issue occurs.

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