Document Type : Research Paper
Authors
1 Allameh Tabataba'i University
2 Allameh Tabataba'i University
Abstract
A study compared the accuracy of nonparametric equating methods (Bayesian and item-response) with parametric methods (classical and item-response). The study considered the impact of sample size, test length, and heterogeneity in ability distribution between the two forms. The researchers conducted simulations using R software with various parameters, including sample sizes of 500 and 2000, test lengths of 30 and 60 questions, and different levels of heterogeneity. The study used a faster method for nonparametric Bayesian analysis, relying on probabilistic approaches and Karabatsos codes (2009) instead of Markov chain Monte Carlo (MCMC) algorithms. The findings showed that regardless of simulation conditions, the linear equating method had the lowest weighted standard error (mean error of 0.56). Following that, the kernel method had a mean standard error of 0.67, the percentile method had a mean standard error of 0.70, and the actual score item-response method had a mean standard error of 0.64, while the observed score item-response method had a mean standard error of 0.65. Finally, the kernel item-response method had a mean standard error of 0.88, and the nonparametric Bayesian method had a mean standard error of 0.001. Moreover, the actual and observed score item-response methods showed the highest absolute weight bias (3.11 and 3.14, respectively), while the nonparametric Bayesian method showed the lowest absolute weight bias (0.73). However, under homogeneous distribution conditions, the linear equating method had the lowest weight bias, and the Bayesian nonparametric method had the highest bias. The highest value for the square root of the average squared weighting error belonged to the observed score item-response method (3.41), followed by the actual score item-response method (3.39), and the lowest value belonged to the nonparametric Bayesian method (1.35).
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