Bürkner 2021 - Bayesian IRT with brms and Stan
Routing Summary
Full capture of Bürkner (JSS 2021): IRT models (Rasch/1PL, 2PL, 3PL, GRM, PCM, response-time and diffusion models) as multilevel distributional regressions in brms/Stan, with hierarchical priors, identification, covariates, DIF and LOO comparison. 8 notes.
- Need paper summary and source map? → Bürkner 2021 - Bayesian IRT with brms Overview
- Need response families (Bernoulli, cumulative, adjacent-category, Wiener…)? → Bürkner 2021 - Response Families and Distributional IRT
- Need 1PL/2PL/3PL definitions and identification? → Bürkner 2021 - IRT Model Classes 1PL 2PL and Extensions
- Need covariates and DIF? → Bürkner 2021 - Covariates and Differential Item Functioning
- Need priors, partial pooling, identification? → Bürkner 2021 - Priors Hierarchical Pooling and Identification
- Need brms syntax, Stan code, post-processing? → Bürkner 2021 - brms Specification Stan Code and Post-Processing
- Need VerbAgg results? → Bürkner 2021 - Worked Examples Binary Models VerbAgg
- Need ordinal, response-time, package comparison? → Bürkner 2021 - Worked Examples Ordinal and Response-Time Models
Concept Map
| Concept | Note | Type | Depends On | Key Result |
|---|---|---|---|---|
| Response families | Bürkner 2021 - Response Families and Distributional IRT | definition | Overview | each family gives an IRT model |
| Rasch, 2PL, 3PL | Bürkner 2021 - IRT Model Classes 1PL 2PL and Extensions | definition | families | 2PL scale non-identifiable |
| Explanatory IRT, DIF | Bürkner 2021 - Covariates and Differential Item Functioning | definition | 1PL | DIF = person x item interaction |
| IRT priors, identification | Bürkner 2021 - Priors Hierarchical Pooling and Identification | theorem | 2PL | fix |
| brms workflow | Bürkner 2021 - brms Specification Stan Code and Post-Processing | concept | priors | non-centered Stan code |
| VerbAgg | Bürkner 2021 - Worked Examples Binary Models VerbAgg | example | all above | 2PL adds nothing; DIF b=-0.94 |
| Ordinal and RT | Bürkner 2021 - Worked Examples Ordinal and Response-Time Models | example | VerbAgg | PCM category-specific effects |
Notes
- Bürkner 2021 - Bayesian IRT with brms Overview — CONTAINS: summary, source map, E116 link.
- Bürkner 2021 - Response Families and Distributional IRT — CONTAINS: Sec. 2.1 table.
- Bürkner 2021 - IRT Model Classes 1PL 2PL and Extensions — CONTAINS: Rasch, 2PL, 3PL, identification theorem, Python, PyMC.
- Bürkner 2021 - Covariates and Differential Item Functioning — CONTAINS: Sec. 2.3-2.4.
- Bürkner 2021 - Priors Hierarchical Pooling and Identification — CONTAINS: Sec. 2.5-2.6.
- Bürkner 2021 - brms Specification Stan Code and Post-Processing — CONTAINS: Sec. 3-4.
- Bürkner 2021 - Worked Examples Binary Models VerbAgg — CONTAINS: Sec. 5.1 tables.
- Bürkner 2021 - Worked Examples Ordinal and Response-Time Models — CONTAINS: Sec. 5.2-5.3, 6, 7.
Sources
Burkner 2021 - Bayesian Item Response Modeling in R with brms and Stan