Comparison Generalized Item Location Indices for Polytomous Items: A Monte Carlo Simulation Study

Year 2025, Volume: 58 Issue: 3, 1197 - 1228, 15.12.2025

Emrah Gül

https://doi.org/10.30964/auebfd.1675814

Abstract

Generalized Item Location Indices (GILI) is a method that deals with the process of developing or selecting polytomous items based on a single value. This method converts multiple location indices obtained for polytomous items into a single indices. The purpose of this research is to examine the performance of GILI under different simulation conditions. For the study, how three different GILI (LImean -LImedian-LIIRF) change according to the number of categories (3, 5 and 7), location parameter (-2, -1, 0, 1 and 2) and sample size (200, 500 and 1000) were compared with a monte carlo simulation. According to the results, the LImedian was estimated with the highest error in all conditions. On the other hand, LImean and LIIRF produce similar error amounts for all conditions. Although LImean and LIIRF produce similar results at -1, 0 and +1 location levels, LImean makes more accurate predictions at -2 and +2 location levels. It was concluded that as the number of categories increases, the amount of error calculated in small samples increases. LImean -LImedian-LIIRF values, which are matched with the individual's ability in tests developed for different purposes and CAT applications, can be a good parameter for determining which item to choose next during the administration of the test. As a result, the fact that the proposed method is easier and faster will facilitate the practitioners in the item selection process.

Keywords

generalized item location indices , simulation , selecting items , polytomous item

Ethical Statement

There is no need for an ethical declaration

Çok Kategorili Maddeler İçin Genelleştirilmiş Madde Konum İndekslerinin Karşılaştırılması: Monte Carlo Simülasyon Çalışması

Abstract

Genelleştirilmiş madde yer indeksleri (GILI), çok kategorili öğeleri tek bir değere göre geliştirme veya seçme sürecini ele alan bir yöntemdir. Bu yöntem, çok kategorili öğeler için elde edilen birden fazla konum endeksini tek bir endekse dönüştürür. Bu araştırmanın amacı, GILI'nin farklı simülasyon koşulları altında performansını incelemektir. Çalışmada, üç farklı GILI'nin (LImean-LImedian-LIIRF) kategori sayısına (3, 5 ve 7), konum parametresine (-2, -1, 0, 1 ve 2) ve örneklem büyüklüğüne (200, 500 ve 1000) göre nasıl değiştiği Monte Carlo simülasyonuyla karşılaştırılmıştır. Sonuçlara göre, LImedian tüm koşullarda en yüksek hata ile tahmin edilmiştir. Öte yandan, LImean ve LIIRF tüm koşullar için benzer hata miktarları üretmektedir. LImean ve LIIRF -1, 0 ve +1 konum düzeylerinde benzer sonuçlar üretmesine rağmen, LImean -2 ve +2 konum düzeylerinde daha doğru tahminler yapmaktadır. Kategori sayısı arttıkça küçük örneklemlerde hesaplanan hata miktarının arttığı sonucuna varılmıştır. Farklı amaçlar için geliştirilen testlerde ve CAT uygulamalarında bireyin yeteneği ile eşleştirilen LImean -LImedian-LIIRF değerleri, testin uygulanması sırasında hangi maddenin seçileceğini belirlemede iyi bir parametre olabilir. Sonuç olarak önerilen yöntemin daha kolay ve hızlı olması uygulayıcılara madde seçme sürecinde kolaylık sağlayacaktır.

Keywords

genelleştirilmiş madde yer indeksleri , simülasyon , madde seçimi , çok kategorili madde

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