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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi REiD (Research and Evaluation in Education)
Munaya Nikma Rosyada
Universitas Islam Internasional Indonesia
Education Mathematics

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Deep-Rasch as an Alternative to Rasch Modeling under Assumption Violations and Small Sample Sizes Agus Santoso; Farit Mochamad Afendi; Timbul Pardede; Heri Retnawati; Ibnu Rafi; Ezi Apino; Munaya Nikma Rosyada
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i2.36276

Abstract

In certain situations, it may be challenging to fully exploit the advantages of modern test theory, including Rasch modeling and item response theory (IRT), when applied to real data. Although Rasch modeling tends to be more robust than IRT for small sample sizes, it still requires that the assumptions of unidimensionality and local independence be satisfied. In practice, these assumptions are often violated, which can lead to less accurate analyses and reduced validity of the results. Deep-Rasch, which integrates deep learning with Rasch modeling, has been proposed as an alternative measurement framework to overcome these limitations. This study examines the potential of Deep-Rasch as an alternative to Rasch modeling using student response data from 17 final semester examinations at Universitas Terbuka (UT), with sample sizes ranging from 33 to 11,504 students. Most examinations consisted of 30 multiple-choice items. The analyses showed that several datasets violated one or both assumptions of Rasch modeling. Nevertheless, Deep-Rasch performed comparably to conventional Rasch modeling in estimating item difficulty and student ability parameters, as well as in predicting student responses. Remarkably, for the smallest sample size (\emph{n} = 33), Deep-Rasch exhibited slightly better performance than Rasch modeling.
Optimal number of response categories for a Likert-type questionnaire: A simulation study within the frameworks of Classical Test and Item Response Theory Neng Ida Soniawati; Ezi Apino; Heri Retnawati; Farida Agus Setiawati; Ibnu Rafi; Munaya Nikma Rosyada; Rezkilaturahmi Rezkilaturahmi
REID (Research and Evaluation in Education) Vol. 12 No. 1 (2026)
Publisher : Graduate School of Universitas Negeri Yogyakarta & Himpunan Evaluasi Pendidikan Indonesia (HEPI)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21831/reid.v12i1.95846

Abstract

Likert-type questionnaires have been widely used in educational contexts with many types of response categories. The use of many response categories raises the question of the optimal number of response categories for a Likert-type questionnaire. This issue continues to be investigated by researchers, and the current findings present an inconsistent answer. This study aims to find the optimal number of response categories in developing the Likert-type questionnaire based on classical test theory (CTT) and item response theory (IRT) framework. The simulation design used 8 (number of response categories: 3- to 10-point scale) × 3 (number of items: 20, 25, and 30 items) × 5 (sample size: 100, 200, 500, 1000, and 5000) = 120 conditions. We generated a dataset for each condition for 1000 replications using WinGen 3 and randomly took 10 data points from each dataset to estimate its psychometric properties using the CTT and IRT analysis frameworks. The optimal number of response categories was determined based on the highest reliability coefficient, total explained variance, and information function values. Using the CTT analysis framework, the simulation results indicated that the 8-point scale is optimal for Likert-type questionnaires with 20 and 30 items and for all sample size variations. However, for questionnaires with 25 items, the 8-point scale is only optimal for sample sizes of 100 and 5000, while for sample sizes of 200 to 1000, the 10-point scale is more optimal. Using the IRT analysis framework, the simulations reveal that it is necessary to consider the number of items and the sample size to determine the optimal number of response categories. In this context, 8- and 10-point scales are generally more recommended for Likert-type questionnaires. The findings provide researchers with insight into the optimal number of response categories and the analytical model for developing a Likert-type questionnaire.
Co-Authors Agus Santoso Ezi Apino Farida Agus Setiawati Farit Mochamad Afendi Heri Retnawati Ibnu Rafi Ibnu Rafi Neng Ida Soniawati Pardede, Timbul Rezkilaturahmi Rezkilaturahmi