Assessing the Dimensionality and Model Fit of the 2015 NECOMathematics Multiple-Choice Items in Nigeria Using the Four-Parameter Logistic Model for Achieving SDG 4
DOI:
https://doi.org/10.71291/6rtdfq13Keywords:
Item Response Theory (IRT), Four-Parameter Logistic Model (4PL), Model fit, Dimensionality, Sustainable Development Goal 4 (SDG 4)Abstract
Evidence on the psychometric quality of large-scale examinations remains essential for ensuring valid educational decisions and monitoring learning outcomes. This study examined the dimensionality and model fit of the 2015 National Examinations Council (NECO) Mathematics items in Nigeria using Four-Parameter Logistic (4PL) item response theory model. An ex-post-facto research design was adopted. The population comprised 24,718 candidates who wrote the 2015 NECO Senior School Certificate Mathematics III Examination in Osun State, Nigeria. Using a multistage sampling procedure, responses from 3,000 examinees were selected for analysis. Data were analysed using the MIRT package in R, with item parameters estimated through marginal maximum likelihood estimation and the expectation-maximisation algorithm. Dimensionality was assessed using factor analytic procedures, while model-fit was evaluated using Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Sample-Size Adjusted Bayesian Information Criterion (SABIC), and Hannan-Quinn Information Criterion (HQ). Results indicated that the unidimensional model provided a superior fit to the data compared with multidimensional alternatives, yielding lower information criterion values (AIC=1,142,691; SABIC=1,144,092; HQ=1,145,043; BIC=1,145,043). Item parameter estimates further indicated that most items demonstrated acceptable discrimination, moderate difficulty, low pseudo-guessing parameters, and minimal upper-asymptote effects. These results indicate that the examination items functioned satisfactorily within the 4PL framework and met the unidimensionality assumption. The study provides empirical evidence for the psychometric soundness of the 2015 NECO Mathematics examination and underscores the importance of rigorous measurement practices to enhance the validity, fairness, and accountability of large-scale educational assessments in support of Sustainable Development Goal 4 (SDG 4).
References
Adediwura, A. A., & Kasali, J. (2022). Conformity of National Examinations Council mathematics multiple choice test items to the assumption of item response theory. Al-Hikmah Journal of Arts and Social Sciences, 4(1), 1-8.
Ajayi, O. A., Salam, R. I., & Saka, O. Y. (2024). Comparing Dimensionality and Local Independence Parameters of Lagos State Unified Mock and West African Senior School Certificate Examinations in Biology. African Journal of Science, Technology and Mathematics Education (AJSTME), 10(5), 763-768.
Andrich, D., & Marais, I. (2019). The Dichotomous Rasch Model—The Simplest Modern Test Theory Model. In A Course in Rasch Measurement Theory: Measuring in the Educational, Social and Health Sciences (pp. 75-87). Springer Nature Singapore. https://doi.org/10.1007/978-981-13-7496-8_6
Asuru, V. (2015). Measurement and evaluation in education and psychology. Port Harcourt: Pearl Publishers International Ltd.
Ayanwale, M. (2017). Efficacy of item response theory in score ranking and concurrent Validity of dichotomous and polytomous response mathematics achievement test in Osun State, Nigeria. Unpublished Ph. D. Thesis, University of Ibadan.
Babtimehin, T., Adamu, D., & Adeoye, O. P. (2021). Comparison of local item independence of WAEC and NECO dichotomously scored chemistry items in Osun State, Nigeria. Nigerian Journal of Educational Research and Evaluation, 20, 194-211.
Baker, F. B., & Kim, S.-H. (2017). The basics of item response theory using R (Vol. 10). Springer.
Barton, M. A., & Lord, F. M. (1981). An upper asymtote for the three-parameter logistic item-response model. ETS Research Report Series, 1981(1), 1-8. https://doi.org/10.1002/j.2333-8504.1981.tb01255.x
Cai, L. (2010). High-dimensional Exploratory Item Factor Analysis by A Metropolis–Hastings Robbins–Monro Algorithm. Psychometrika, 75(1), 33-57. https://doi.org/10.1007/s11336-009-9136-x
Chalmers, R. P. (2012). mirt: A Multidimensional Item Response Theory Package for the R Environment. Journal of Statistical Software, 48(6), 1 - 29. https://doi.org/10.18637/jss.v048.i06
Chen, W.-H., & Thissen, D. (1997). Local Dependence Indexes for Item Pairs Using Item Response Theory. Journal of Educational and Behavioral Statistics, 22(3), 265-289. https://doi.org/10.3102/10769986022003265
Cuhadar, I. (2022). Sample Size Requirements for Parameter Recovery in the 4-Parameter Logistic Model. Measurement: Interdisciplinary Research and Perspectives, 20(2), 57-72. https://doi.org/10.1080/15366367.2021.1934805
DeMars, C. (2010). Item response theory. Oxford University Press.
Embretson, S. E., & Reise, S. P. (2000). Item response theory for psychologists. Mahwah, NJ: Erlbaum. https://doi.org/10.4324/9781410605269
Fuentes-Penna, A., Cárdenas, R. G., & Rascón, A. C. (2025). Quality Education and Inclusive Education. In Machine and Deep Learning Solutions for Achieving the Sustainable Development Goals (pp. 63-78). IGI Global Scientific Publishing.
Goel, N., Deshmukh, K., Patel, B. C., & Chacko, S. (2021). Tools and rubrics for assessment of learning outcomes. In Assessment Tools for Mapping Learning Outcomes with Learning Objectives (pp. 211-254). IGI Global Scientific Publishing.
Gyamfi, A., & Acquaye, R. (2023). Parameters and models of item response theory (IRT): A review of literature. Acta Educationis Generalis, 13(3), 68-78. https://doi.org/10.2478/atd-2023-0022
Hambleton, R. K., Swaminathan, H., & Rogers, H. J. (1991). Fundamentals of item response theory (Vol. 2). Sage.
Hussein, A., & Gasmalla, H. E. E. (2023). Introduction to the Psychometric Analysis. In H. E. E. Gasmalla, A. A. M. Ibrahim, M. M. Wadi, & M. H. Taha (Eds.), Written Assessment in Medical Education (pp. 111-135). Springer International Publishing. https://doi.org/10.1007/978-3-031-11752-7_9
Immekus, J. C., Snyder, K. E., & Ralston, P. A. (2019). Multidimensional Item Response Theory for Factor Structure Assessment in Educational Psychology Research [Methods]. Frontiers in Education, Volume 4 - 2019. https://doi.org/10.3389/feduc.2019.00045
Jimoh, K., Opesemowo, O. A., & Faremi, Y. A. (2022). Psychometric Analysis of Senior Secondary School Certificate Examination (SSCE) 2017 Neco English Language Multiple Choice Test Items in Kwara State Using Item Response Theory. Journal of Applied Research and Multidisciplinary Studies, 3(2), 1-19. https://doi.org/10.32350/jarms.32.01
Kline, R. B. (2015). Principles and practice of structural equation modeling. Guilford publications.
Liao, X., & Bolt, D. M. (2021). Item Characteristic Curve Asymmetry: A Better Way to Accommodate Slips and Guesses Than a Four-Parameter Model? Journal of Educational and Behavioral Statistics, 46(6), 753-775. https://doi.org/10.3102/10769986211003283
Livingston, S. A. (2020). Basic Concepts of Item Response Theory: A Nonmathematical Introduction. Research Memorandum. ETS RM-20-06. Educational Testing Service.
Loken, E., & Rulison, K. L. (2010). Estimation of a four-parameter item response theory model. British Journal of Mathematical and Statistical Psychology, 63(3), 509-525. https://doi.org/10.1348/000711009X474502
Moyo, S., & Nenty, H. (2017). Dimensionality analysis of agricultural examination: Implications. Research Journal of Educational, 5(1), 1-10.
OECD. (2019). PISA 2018 results: What students know and can do. OECD Publishing.
Ogunbanwo, R. A. (2014). Analysis of students' performance in West African senior certificate examinations in boarding and day secondary schools in Kano metropolis, Nigeria (2005-2011)
Ohanyelu, C. N. (2021). Augmentation of Students' Academic Performance in Mathematics Through Classroom Management Practices in Nigeria. Turība University Conference - Artificial Intelligence and Green Thinking, 12, 103-118. https://doi.org/10.37804/1691-6077-2021-12-103-118
Ojerinde, D. (2013). Classical test theory (CTT) vs item response theory (IRT): an evaluation of the comparability of item analysis results. A guest lecture presented at the Institute of Education, University of Ibadan on 23rd May.
Okoye, R. O., & Nduka, S. V. (2022). Application of Item Response Theory in calibrating 2020 NECO Mathematics multiple-choice questions. International Journal of Advanced Education and Research, 7(1), 1-5.
Opesemowo, O. A. G. (2023). Intra and Inter-Local Item Dependence of Mathematics Items. Research in Social Sciences and Technology, 8(4), 37-55. https://doi.org/10.46303/ressat.2023.32
Opesemowo, O. A. G. (2025). Exploring undue advantage of differential item functioning in high-stakes assessments: Implications on sustainable development goal 4. Social Sciences & Humanities Open, 11, 101257. https://doi.org/10.1016/j.ssaho.2024.101257
Reckase, M. D. (2009). Historical background for multidimensional item response theory (MIRT). In Multidimensional item response theory (pp. 57-77). Springer.
Sen, S., & Cohen, A. S. (2023). The Impact of Sample Size and Various Other Factors on Estimation of Dichotomous Mixture IRT Models. Educational and Psychological Measurement, 83(3), 520-555. https://doi.org/10.1177/00131644221094325
Wang, V. (2017). Handbook of research on program development and assessment methodologies in K-20 education. IGI Global.
Downloads
Published
Issue
Section
License
Copyright (c) 2026 Oluwaseyi Aina Gbolade Opesemowo, Kehinde Olufunke Opatunji, Temitope Babatimehin, Titilope Rachael Opesemowo (Author)
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
