Statistical Analysis of Ordinal Response Variable: A Comparative Study-

Section: Research Paper
Published
Jun 25, 2025
Pages
56-67

Abstract

Response variables in biological phenomena vary between three types: numerical response variables, ordinal categorical response variables, and nominal categorical response variables. In statistical studies, handling ordinal variables varies in accordance with the perspective of the statistical approach to the response variable. Ordinal variables can be adopted as nominal categorical variables, which neglect the ordinal property of the categories. Ordinal variables can also be treated.as an ordinal categorical variable (discrete variable), in which case the ranking information can be utilized in establishing the predicted models. In this study, the most important statistical methods that can be used to analyze data with an ordinal response variable have been investigated. Among these methods are the Multiple Regression Method, and The Ordinal Logistic Regression Method. The mechanism of building models and parameter estimations were theoretically exhibited, as well as reading the statistical significance of the regression coefficients in all the models in the study. The application was carried out on a real sample of patients with osteoporosis. Where multiple models were built to determine the most important factors affecting the likelihood of developing the disease. The best model was diagnosed according to the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC). The results of the statistical analysis demonstrated the superiority of the ordinal logistic regression model over the multiple linear regression model in its explanation of the relationship between the response variable and the covariates.

References

  1. Agresti, A. (2003). Categorical data analysis. John Wiley & Sons.
  2. Ananth, C. V., & Kleinbaum, D. G. (1997). Regression models for ordinal responses: a review of methods and applications. International journal of epidemiology, 26(6), 1323-1333.
  3. Armstrong, B. G., & Sloan, M. (1989). Ordinal regression models for epidemiologic data. American Journal of Epidemiology, 129(1), 191-204.
  4. Forthofer, R. N., Lee, E. S., & Hernandez, M. (2006). Biostatistics: a guide to design, analysis and discovery. Elsevier.
  5. IBM Corp. Released 2019. IBM SPSS Statistics for Windows, Version 26.0. Armonk, NY: IBM Corp.
  6. Krger, H., Tuppurainen, M., Honkanen, R., Alhava, E., & Saarikoski, S. (1994). Bone mineral density and risk factors for osteoporosisa population-based study of 1600 perimenopausal women. Calcified Tissue International, 55(1), 1-7.
  7. Kutner, M. H., Nachtsheim, C. J., Neter, J., & Wasserman, W. (2004). Applied linear regression models. New York: McGraw-Hill/Irwin.
  8. Lall, R. (2004). The application of ordinal regression models in quality of life scales used in gerontology (Doctoral dissertation, University of Sheffield).
  9. R Core Team (2022). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/.
  10. Scott, S. C., Goldberg, M. S., & Mayo, N. E. (1997). Statistical assessment of ordinal outcomes in comparative studies. Journal of clinical epidemiology, 50(1), 45-55.
  11. Siegel S, Castellan N. Non-parametric Statistics for the Behavioral Sciences. Second Edition. McGraw-Hill International Editions, 1988.
  12. Strang, G., (1993). Introduction to linear algebra (Vol. 3). Wellesley, MA: Wellesley-Cambridge Press.
  13. Strmberg, U. (1996). Collapsing ordered outcome categories: a note of concern. American journal of epidemiology, 144(4), 421-424.

Identifiers

Download this PDF file

Statistics

How to Cite

Yaseen Alhamdany, L., لقاء, Tarik Al-Khaledi, Z., & زيد. (2025). Statistical Analysis of Ordinal Response Variable: A Comparative Study-. IRAQI JOURNAL OF STATISTICAL SCIENCES, 19(2), 56–67. Retrieved from https://rjps.uomosul.edu.iq/index.php/stats/article/view/20899