Bayesian Item Response Modeling in R with brms and Stan
Dublin Core
Title
Bayesian Item Response Modeling in R with brms and Stan
Subject
: item response theory, Bayesian statistics, R, Stan, brms.
Description
Item response theory (IRT) is widely applied in the human sciences to model persons’
responses on a set of items measuring one or more latent constructs. While several
R packages have been developed that implement IRT models, they tend to be restricted to
respective pre-specified classes of models. Further, most implementations are frequentist
while the availability of Bayesian methods remains comparably limited. I demonstrate
how to use the R package brms together with the probabilistic programming language
Stan to specify and fit a wide range of Bayesian IRT models using flexible and intuitive
multilevel formula syntax. Further, item and person parameters can be related in both a
linear or non-linear manner. Various distributions for categorical, ordinal, and continuous
responses are supported. Users may even define their own custom response distribution
for use in the presented framework. Common IRT model classes that can be specified
natively in the presented framework include 1PL and 2PL logistic models optionally also
containing guessing parameters, graded response and partial credit ordinal models, as
well as drift diffusion models of response times coupled with binary decisions. Posterior
distributions of item and person parameters can be conveniently extracted and postprocessed. Model fit can be evaluated and compared using Bayes factors and efficient
cross-validation procedures.
responses on a set of items measuring one or more latent constructs. While several
R packages have been developed that implement IRT models, they tend to be restricted to
respective pre-specified classes of models. Further, most implementations are frequentist
while the availability of Bayesian methods remains comparably limited. I demonstrate
how to use the R package brms together with the probabilistic programming language
Stan to specify and fit a wide range of Bayesian IRT models using flexible and intuitive
multilevel formula syntax. Further, item and person parameters can be related in both a
linear or non-linear manner. Various distributions for categorical, ordinal, and continuous
responses are supported. Users may even define their own custom response distribution
for use in the presented framework. Common IRT model classes that can be specified
natively in the presented framework include 1PL and 2PL logistic models optionally also
containing guessing parameters, graded response and partial credit ordinal models, as
well as drift diffusion models of response times coupled with binary decisions. Posterior
distributions of item and person parameters can be conveniently extracted and postprocessed. Model fit can be evaluated and compared using Bayes factors and efficient
cross-validation procedures.
Creator
Paul-Christian Bürkner
Source
https://www.jstatsoft.org/article/view/v100i05
Publisher
University of Stuttgart
Date
November 2021
Contributor
Fajar bagus W
Format
PDF
Language
English
Type
Text
Files
Collection
Citation
Paul-Christian Bürkner, “Bayesian Item Response Modeling in R with brms and Stan,” Repository Horizon University Indonesia, accessed March 13, 2025, https://repository.horizon.ac.id/items/show/8218.