Using the Stan Program for Bayesian Item Response Theory

Abstract

Stan is a new Bayesian statistical software program that implements the powerful and efficient Hamiltonian Monte Carlo (HMC) algorithm. To date there is not a source that systematically provides Stan code for various item response theory (IRT) models. This article provides Stan code for three representative IRT models, including the three-parameter logistic IRT model, the graded response model, and the nominal response model. We demonstrate how IRT model comparison can be conducted with Stan and how the provided Stan code for simple IRT models can be easily extended to their multidimensional and multilevel cases.

Analysing Standard Progressive Matrices (SPM-LS) with Bayesian Item Response Models

“…There are a lot of IRT specific software packages available, in particular in the programming language R (R Core Team, 2019), for example, mirt (Chalmers, 2012), sirt (Robitzsch, 2019), or TAM (Robitzsch et al, 2019; see Bürkner, 2019 for a detailed comparison). In addition to these more specialized packages, general purpose probabilistic programming languages can be used to specify and fit Bayesian IRT models, for example, BUGS (Lunn, Spiegelhalter, Thomas, & Best, 2009; see also Curtis & others, 2010), JAGS (Plummer, 2013; see also Depaoli, Clifton, & Cobb, 2016;Zhan, Jiao, Man, & Wang, 2019), or Stan (Carpenter et al, 2017; see also Ames & Au, 2018;Luo & Jiao, 2018). In this paper, I will use the brms package (Bürkner, 2017(Bürkner, , 2018, a higher level interface to Stan, which is not focussed specifically on IRT models but more generally on (Bayesian) regression models.…”

Longitudinal item response modeling and posterior predictive checking in {R} and {Stan}

“…In the field of Bayesian estimation, Stan (Stan Development Team, 2017) is a very powerful implementation of a Hamiltonian Monte Carlo algorithm (Betancourt, 2017;Gelman et al, 2014) that allows the fast and efficient exploration of posterior distributions even in higher dimensions. There is a number of articles giving tutorials on Stan (e.g., Luo & Jiao, 2018;Jiang & Carter, 2018;Sorensen, Hohenstein, & Vasishth, 2016). These are extended to multidimensional longitudinal IRT modeling in this article and an account of posterior predictive checking in Stan and R is given.…”

Using Hamiltonian Monte Carlo to estimate the log-linear cognitive diagnosis model via Stan

“…Follow the article structure of Luo and Jiao (2017) and Jiang and Skorupski (2017), this paragraph introduces the components of a Stan program via R. The R code consists of two parts: (1) .stan file specification and (2) syntax for executing R. The .stan file is made of six Stan code blocks, as can be seen in Table 2; of these blocks, data, parameters, and model are mandatory, whereas the remaining blocks are needbased. There are a few general rules being applied to each code block of the .stan file: (1) the symbol // is used to place comment, (2) the data type needs to be specified for both the data records and model variables (including those before transformations), (3) the value range constraint can be placed to meet the requirement of permissible sampling numerical space, and (4) the symbol ; should be put at the end of each code line but before the symbol //.…”

“…HMC is the default choice in Stan software program, which has been introduced to psychometric modeling; for example, Luo and Jiao (2017) provide a tutorial on how to apply Stan for item response models (IRT). In yet another tutorial, Annis, Miller, and Palmeri (2017) delineate the steps of specifying customized distributions in Stan via linear ballistic accumulator models.…”