Vertical Equating Accuracy Using Kernel Method

Abstract

This study aims to reveal: (1) the methods that provide more accurate results on vertical equating with the classical approach (linear and equipercentile) with the kernel method; (2) the methods that provide more accurate results on the vertical equating of the IRT approach with the kernel method. This research is simulation research using the Markov Chain Monte Carlo (MCMC) method. The experiment used a factorial design 3 factorial (treatment) and 40 repetitions. The three controlled factors are: 1) ability parameters (th = 0.314; 0.431; and 0.451); 2) the number of samples (500, 1000, and 5000) and 3) the length of the test (10, 20 and 30). The data were generated using the WinGen3 application with one parameter logistic model (1PL / Rasch Model). The analysis was carried out by comparing the mean of standard error equating (MSE). The results of this study are as follows. (1) The vertical equating method using the Item Response Theory (IRT) approach, especially the Haebara and Stocking-Lord methods, is more accurate than the classical method (equipercentile and linear). (2) The non-kernelled IRT approach method is more accurate than the kernelled IRT method (smoothing with the Gaussian kernel).