Examining The Effect of Sample Size and Test Length on Parameter Estimates in The Multidimensional Item Response Theory Model Using Different Algorithms

OpenAlex · İngilizce

Multidimensional Item Response Theory (MIRT) offers a robust framework for modeling complex latent traits, addressing the limitations of unidimensional models in educational and psychological assessments. This study aims to examine the estimation performance of three widely used algorithms—Expectation-Maximization (EM), Stochastic EM (SEM), and Metropolis-Hastings Robbins-Monro (MH-RM)—under varying test lengths (10, 20, and 40 items) and sample sizes (N = 1000 and 5000). Employing a Monte Carlo simulation design, datasets were generated in R to reflect multidimensional structures. Item and ability parameters were estimated, and estimation accuracy was evaluated using Root Mean Square Error (RMSE) and bias statistics. Findings indicate that under a sample size of 1000, MH-RM performs most effectively for discrimination parameters (a) in longer tests, while SEM is preferable for shorter tests. EM yielded the least biased estimates for difficulty (d) and guessing (c) parameters. At N = 5000, both EM and MH-RM demonstrated lower RMSE values, while SEM showed higher error rates. Overall, increasing sample size and test length led to improved estimation accuracy across all methods. Results corroborate previous findings and highlight the superior performance of MH-RM in high-dimensional estimation, particularly in large-scale testing scenarios. These outcomes provide practical guidance for researchers in selecting suitable estimation techniques under different test conditions. Keywords: Multidimensional Item Response Theory, Expectation Maximization, Metropolis-Hastings Robbins-Monro, Stochastic Expectation Maximization.