A Method to Increase the Power of Monte Carlo Method: Increasing the Number of Iteration

Duygu Koçak

doi:10.29333/pr/6258

Abstract

Iteration number in Monte Carlo simulation method used commonly in educational research has an effect on Item Response Theory test and item parameters. The related studies show that the number of iteration is at the discretion of the researcher. Similarly, there is no specific number suggested for the number of iteration in the related literature. The present study investigates the changes in test and item parameters resulting from the changes in MC simulation studies based on Item Response Theory. In this respect, the required number of iterations is determined through IRT three-parameter logistics model test and item parameters under different conditions regarding sample size, item number, and parameter restrictions. The results indicate that estimate error can be lowered to a specific point and the test information increases as the number of iterations is increased and that the required number of iterations decreases as the sample size gets larger. However, it is also observed that the required number of iterations increases when intervals that would restrict parameters during data generation process are defined. It is concluded that the number of iterations has a significant impact on estimate results in MC studies and that the required number of iterations depends on the number of conditions and their levels. The more complex and featured the conditions are, the higher number of iterations will be required to achieve estimates without errors.

Highlights

Simulation studies in education, psychology, econometry, engineering, and statistics have been increasing in line with the advancements in technology
The effectiveness of Monte Carlo method depends on acquiring the data sets that pose the determined qualities; variance value should be minimized by increasing iteration number (Sobol, 1971; Yaşa, 1996)
It is thought that adding qualities and applying limitations to the data to be generated in Monte Carlo simulation studies will affect the performance of the simulation

Summary

Introduction

Simulation studies in education, psychology, econometry, engineering, and statistics have been increasing in line with the advancements in technology. When a case is analyzed using artificial data that display the qualities of the real data which is imitated are called simulation, Model sampling or Monte Carlo (Rubinstein, 1981). Monte Carlo technique is comprised of the phases to identify the conditions that define a situation and to develop a model to reflect this specific situation In this method, to obtain the data for the determined conditions of the situation that can reflect it, each independent variable is seperately repeated NN times to generate NN different sample groups. To obtain the data for the determined conditions of the situation that can reflect it, each independent variable is seperately repeated NN times to generate NN different sample groups Because of this aspect, Monte Carlo method is called statistical trial method. The average value of the NN number samples taken from a population with average μμ and σσ variance will display normal distribution with average μμ and σσ2/NN variance

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