A reusable Bayesian IRT workflow for instrument validation: A tutorial with a small-sample case study in teacher belief measurement

Bayesian Item Response Theory (IRT) offers distinct advantages for fitting complex measurement models under sample-size constraints, yet practical guidance on implementing complete Bayesian IRT workflows for applied researchers remains limited. This tutorial presents a reusable workflow for validating multidimensional instruments with limited samples using the R package brms. The workflow guides researchers through five integrated steps: (1) preprocessing decisions for sparse ordinal responses, (2) comparing competing dimensional structures including bi-factor models, (3) using discrimination parameters as diagnostic tools for identifying threshold anomalies and misfitting items, (4) selecting among ordinal link functions using cross-validation and stability diagnostics, and (5) incorporating covariates and differential item functioning analysis. Throughout, we emphasise how the rich diagnostic information provided by Bayesian posterior distributions supports informed qualitative judgment at each decision point. The workflow is illustrated through the validation of a 24-item instrument measuring Chinese secondary mathematics teachers' beliefs about equity (n = 155). The iterative process identified misfitting items, resolved threshold anomalies, and ultimately supported a bi-factor graded response model with a general inclusive belief factor and three domain-specific components. All analysis code and data are available in a companion repository.