Applying Bayesian Item Response Theory for Small-Scale Datasets: An Example Workflow for Measuring Multidimensional Mathematics Teachers' Belief about Equity

This paper demonstrates the application of Bayesian Item Response Theory (IRT) for constructing and validating instruments measuring mathematics teachers' beliefs about equity with small sample sizes. While IRT provides valuable item-level analysis for measuring latent constructs, traditional frequentist approaches require large samples, especially for complex multidimensional models. Using data from Chinese secondary mathematics teachers (n=155), I illustrate how Bayesian methods effectively address these limitations through a transparent workflow that integrates theoretical frameworks with statistical modeling. I compare competing theoretical models—unidimensional, correlated-traits, and bi-factor structures—to identify the optimal representation of teachers' equity beliefs across mathematics, learner, and pedagogy dimensions. Through systematic model iterations involving different response scale structures and link functions, the results support a bi-factor structure, revealing that mathematics teachers' beliefs about equity form a complex system where both general inclusive beliefs and dimension-specific beliefs coexist. The findings also indicate differential functioning by gender and school district, with female teachers and those from higher socioeconomic districts demonstrating stronger inclusive beliefs.