Comparison of Bayesian and Frequentist Approaches in Nominal Item Response Theory Modelling

Abstract

The research utilized a non-linear regression model to quantify unobserved characteristics of candidates in examinations and their outcomes [1]. Performances of Bayesian over Frequentist approaches in estimating nominal item response theory model parameters P(y_ij=k│a_i,b_i,θ_j ) (exp⁡{a_ik (θ_j-b_ik)})/(=∑_(h=1)^4▒〖exp⁡{a_ih (θ_j-b_ih)}〗) □(, θ_j~ N(0,1)) [2]. Priors a_(ik )~ dnorm(m.a,pr.a)I(0,0), b_ik~dnorm(m.b,pr.b), m.a ~dnorm(0,0.1), m.b~dnorm(0,0.1) pr.a ~digamma(10,1) and pr.b~digamma(10,1) were used to determine the posterior densities and Brooks-Gelman-Rubin Convergence Diagnostic Statistic suggested 10000 updates to have valid estimates of the intended parameters in accordance to [4]. Findings revealed that Bayesian technique gave positives, and interpretable item discriminating parameters with relatively low standard errors, and more confined credible intervals for the parameters’ estimates in line with the principle of item response theory modelling [5].