Abstract
In this paper, a new two-parameter logistic testlet response theory model for dichotomous items is proposed by introducing testlet discrimination parameters to model the local dependence among items within a common testlet. In addition, a highly effective Bayesian sampling algorithm based on auxiliary variables is proposed to estimate the testlet effect models. The new algorithm not only avoids the Metropolis-Hastings algorithm boring adjustment the turning parameters to achieve an appropriate acceptance probability, but also overcomes the dependence of the Gibbs sampling algorithm on the conjugate prior distribution. Compared with the traditional Bayesian estimation methods, the advantages of the new algorithm are analyzed from the various types of prior distributions. Based on the Markov chain Monte Carlo (MCMC) output, two Bayesian model assessment methods are investigated concerning the goodness of fit between models. Finally, three simulation studies and an empirical example analysis are given to further illustrate the advantages of the new testlet effect model and Bayesian sampling algorithm.
Highlights
In education and psychological tests, a testlet is defined as that a bundle of items share a common stimulus (Wainer and Kiely, 1987)
We find that the average Bias and mean squared error (MSE) for item parameters are relatively unchanged under the three different prior distributions
To explore the relations between items with dependent structure, this current study proposes a N2PLTM and presents a effective Bayesian sampling algorithm
Summary
In education and psychological tests, a testlet is defined as that a bundle of items share a common stimulus (a reading comprehension passage or a figure) (Wainer and Kiely, 1987). The Bayesian method, including MetropolisHastings algorithm (Metropolis et al, 1953; Hastings, 1970; Tierney, 1994; Chib and Greenberg, 1995; Chen et al, 2000) and Gibbs algorithm (Geman and Geman, 1984; Tanner and Wong, 1987; Albert, 1992), has some significant advantages over classical statistical analysis It allows meaningful assessments in confidence regions, incorporates prior knowledge into the analysis, yields more precise estimators (provided the prior knowledge is accurate), and follows the likelihood and sufficiency principles. In this current study, an effective slice-Gibbs sampling algorithm (Lu et al, 2018) in the framework of Bayesian is used to estimate the model parameters.
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