Toward Optimal Estimation in Psychometrics
What Is the Best Way to Estimate?
Central Question
Given a psychometric model, what is the best way to estimate its parameters — and how do we know?
Overview
This research program investigates the statistical foundations of estimation in psychometric models. The work spans multiple models, examines different statistical properties, and develops computational procedures — forming a cross-cutting framework for understanding optimal estimation.
Three Aspects
Models
The psychometric models under investigation:
| Model | Context |
|---|---|
| Item Response Theory (IRT) | Ability estimation from item responses |
| Ordinal SEM | Structural models with ordinal indicators |
| Polychoric correlation | Latent correlations from ordinal data |
| Item Factor Analysis (IFA) | Factor structure of ordinal items |
Properties
The statistical properties examined for each model:
| Property | Question |
|---|---|
| Identifiability | Can the parameters be uniquely determined? |
| Existence & uniqueness of MLE | Does the estimate exist for all response patterns? |
| Bias | How far is the estimate from the true value on average? |
| Efficiency | How close to the theoretical optimum (Cramér–Rao bound)? |
| RMSE | What is the actual estimation error in finite samples? |
Procedures
Computational methods developed or applied:
| Procedure | Purpose |
|---|---|
| Parametric bootstrap | Exact finite-sample inference for the 2PL model |
| Fisher information | Quantifying estimator precision and deriving efficiency bounds |
| Cramér–Rao lower bound | Universal efficiency criterion for biased and unbiased estimators |
Model × Property Matrix
Each cell represents a research contribution at the intersection of a model and a property:
| Identifiability | Existence & Uniqueness | Bias | Efficiency | RMSE | |
|---|---|---|---|---|---|
| IRT | MLE existence, uniqueness, finiteness | Exact bias curves | Universal Cramér–Rao bound | Exact RMSE curves | |
| Ordinal SEM | Identifiability conditions | ||||
| Polychoric | N&S conditions (elliptical distributions) | Existence & uniqueness of correlation | |||
| IFA | Identifiability conditions |
Selected Publications
Journal Articles
Cheng, C., Yang, H.-H., & Hsu, Y.-F. (2025). Identifiability of polychoric models with latent elliptical distributions. Psychometrika, 90(2), 757–778. https://doi.org/10.1017/psy.2024.25 Professor Chao-ming Cheng Memorial Scholarship
Conference Presentations
Cheng, C., Yang, H.-H., & Hsu, Y.-F. (2025, October 18–19). The universal Cram\'{e}r-Rao lower bound: A genuine efficiency criterion for both biased and unbiased estimators [Oral presentation]. The 64th Annual Convention of the Taiwanese Psychology Association, Tainan, Taiwan.
Cheng, C., Yang, H.-H., & Hsu, Y.-F. (2025, August 29–September 1). When the test information curve misleads [Oral presentation]. The 53rd Annual Meeting of the Behaviormetric Society, Kanagawa, Japan. https://conference.wdc-jp.com/bms/2025/index.html/
Cheng, C. (2025, December 4–6). Identifiability of ordinal SEM and item factor analysis [Invited talk]. The 13th Conference of the IASC-ARS, Ho Chi Minh City, Vietnam. https://viasm.edu.vn/en/hdkh/iasc-ars-2025
Cheng, C., Yang, H.-H., & Hsu, Y.-F. (2024, July 16–19). On the existence, uniqueness, and finiteness of MLE of the ability in IRT [Poster presentation]. International Meeting of the Psychometric Society 2024, Prague, Czech Republic. https://www.psychometricsociety.org/annual-meeting/
Cheng, C., Yang, H.-H., & Hsu, Y.-F. (2024, September 6–8). On the existence and uniqueness of polychoric correlations [Poster presentation]. The 88th Annual Convention of the Japanese Psychological Association, Kumamoto, Japan. https://pub.confit.atlas.jp/ja/event/jpa2024/
Cheng, C., Yang, H.-H., & Hsu, Y.-F. (2023, August 25–28). Identifiability of polychoric models with latent elliptical distributions [Oral presentation]. International Meeting of the Psychometric Society 2023, College Park, Maryland, United States. https://www.psychometricsociety.org/annual-meeting/
Yang, H.-H., Cheng, C., & Hsu, Y.-F. (2023, August 25–28). Estimates of standard errors and confidence intervals for the ability parameter in the 2PL model with fast and exact parametric bootstrap [Poster presentation]. International Meeting of the Psychometric Society 2023, College Park, Maryland, United States. https://www.psychometricsociety.org/annual-meeting/
Journal manuscripts in preparation.