Large Sample Confidence Intervals for Item Response Theory Reliability Coefficients
Bibliographic Data
| ID | 20472003 |
|---|---|
| Authors | Björn Andersson (0000-0002-9007-2440, Collaborative Innovation Center of Assessment toward Basic Education Quality, Beijing Normal University, Beijing, China, corresponding author), Tao Xin (0009-0007-8886-1866, Collaborative Innovation Center of Assessment toward Basic Education Quality, Beijing Normal University, Beijing, China) |
| Year | 2017 |
| Volume | 78 |
| Issue | 1 |
| Pages | 32-45 |
| Publication date | 2017-06-22 |
| Open Access | Yes |
| Type | ARTICLE |
| Venue | Educational and Psychological Measurement (JOURNAL) |
| Journal identifiers | ISSN: 0013-1644 • E-ISSN: 1552-3888 |
| Publisher | SAGE Publishing (PUBLISHER • US) |
| DOI | 10.1177/0013164417713570 |
| PMID | 29795945 |
| OpenAlex | W2712118978 |
| Language | EN |
| Citations received | 7 |
| References cited | 23 |
In applications of item response theory (IRT), an estimate of the reliability of the ability estimates or sum scores is often reported. However, analytical expressions for the standard errors of the estimators of the reliability coefficients are not available in the literature and therefore the variability associated with the estimated reliability is typically not reported. In this study, the asymptotic variances of the IRT marginal and test reliability coefficient estimators are derived for dichotomous and polytomous IRT models assuming an underlying asymptotically normally distributed item parameter estimator. The results are used to construct confidence intervals for the reliability coefficients. Simulations are presented which show that the confidence intervals for the test reliability coefficient have good coverage properties in finite samples under a variety of settings with the generalized partial credit model and the three-parameter logistic model. Meanwhile, it is shown that the estimator of the marginal reliability coefficient has finite sample bias resulting in confidence intervals that do not attain the nominal level for small sample sizes but that the bias tends to zero as the sample size increases
Confidence interval · Econometrics · Estimator · Item response theory · Polytomous Rasch model · Psychometrics · Reliability (semiconductor) · Sample (material) · Sample size determination · Standard error · Statistics · Advanced Statistical Modeling Techniques · Grit, Self-Efficacy, and Motivation · Mathematics · Psychometric Methodologies and Testing
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| Citations per year | 1.17 |
|---|---|
| Citation span | 2020 - 2026 (7) |
| Highly cited | No |