A Flexible Skewed Link Model for Ordinal Outcomes: An Application to Infertility


  • Mohammad Chehrazi Department of Biostatistics and Epidemiology, School of Public Health, Babol University of Medical Sciences, Babol, Iran
  • Seyed Hassan Saadat Behavioral Sciences Research Center, Lifestyle Institute, Baqiyatallah University of Medical Sciences, Tehran, Iran
  • Mahmoud Hajiahmadi Department of Biostatistics and Epidemiology, School of Public Health, Babol University of Medical Sciences, Babol, Iran
  • Mirko Spiroski Scientific Foundation SPIROSKI, Skopje, Republic of Macedonia




Latent variable, cumulative regression, Markov chain Monte Carlo, ordinal data, skewed link function


BACKGROUND: An important issue in modeling categorical response data is the choice of the links. The commonly used complementary log-log link is inclined to link misspecification due to its positive and fixed skewness parameter.

AIM: The objective of this paper is to introduce a flexible skewed link function for modeling ordinal data with some covariates.

METHODS: We introduce a flexible skewed link model for the cumulative ordinal regression model based on Chen model.

RESULTS: The main advantage suggested by the proposed links is the skewed link provide much more identifiable than the existing skewed links. The propriety of posterior distributions under proper and improper priors is explored in detail. An efficient Markov chain Monte Carlo algorithm is developed for sampling from the posterior distribution.

CONCLUSION: The proposed methodology is motivated and illustrated by ovary hyperstimulation syndrome data.


Download data is not yet available.


Metrics Loading ...

Plum Analytics Artifact Widget Block


McCullagh P, Nelder JA. Generalized Linear Models. Boca Raton, Florida: CRC Press; 1989.

Chen MH, Dey DK, Shao QM. A new skewed link model for dichotomous quantal response data. J Am Stat Assoc. 1999;94:1172-86.

Czado C, Santner TJ. The effect of link misspecification on binary regression inference. J Stat Plann Inference. 1992;33:213-31. https://doi.org/10.1016/0378-3758(92)90069-5

Jiang X, Dey DK, Prunier R, Wilson AM, Holsinger KE. A new class of flexible link functions with application to species co-occurrence in cape floristic region. Ann Appl Stat. 2013;7:2180-204. https://doi.org/10.1214/13-aoas663

Stukel TA. Generalized logistic models. J Am Stat Assoc. 1988;83:426-31.

Kim S, Chen MH, Dey DK. Flexible generalized t-link models for binary response data. Biometrika. 2008;95:93-106. https://doi. org/10.1093/biomet/asm079

Aranda-Ordaz FJ. On two families of transformations to additivity for binary response data. Biometrika. 1981;68:357-63. https://doi.org/10.1093/biomet/68.2.357

Guerrero VM, Johnson RA. Use of the box-cox transformation with binary response models. Biometrika. 1982;69:309-14. https://doi.org/10.1093/biomet/69.2.309

Jones M. Families of distributions arising from distributions of order statistics. Test. 2004;13:1-43. https://doi.org/10.1007/ bf02602999

Albert JH, Chib S. Bayesian analysis of binary and polychotomous response data. J Am Stat Assoc. 1993;88:669-79.

Wang X, Dey D. A Flexible Skewed Link Function for Binary Response Data. University of Connecticut, Department of Statistics, Technical Report; 2008.

Tehraninejad ES, Hafezi M, Arabipoor A, Aziminekoo E, Chehrazi M, Bahmanabadi A. Comparison of cabergoline and intravenous albumin in the prevention of ovarian hyperstimulation syndrome: A randomized clinical trial. J Assist Reprod Genet. 2012;29:259-64. https://doi.org/10.1007/s10815-011-9708-4

Spiegelhalter DJ, Best NG, Carlin BP, Van Der Linde A. Bayesian measures of model complexity and fit. J R Stat Soc. 2002;64:583-639. https://doi.org/10.1111/1467-9868.00353

Cowles MK, Carlin BP. Markov chain Monte Carlo convergence diagnostics: A comparative review. J Am Stat Assoc. 1996;91(434):883-904. https://doi.org/10.1080/01621459.1996.1 0476956

Newton MA, Czado C, Chappell R. Bayesian inference for semiparametric binary regression. J Am Stat Assoc. 1996;91:142- 53. https://doi.org/10.1080/01621459.1996.10476671

Basu S, Mukhopadhyay S. Binary response regression with normal scale mixture links. Biostat Basel. 2000;5:231-42.




How to Cite

Chehrazi M, Saadat SH, Hajiahmadi M, Spiroski M. A Flexible Skewed Link Model for Ordinal Outcomes: An Application to Infertility. Open Access Maced J Med Sci [Internet]. 2020 Apr. 5 [cited 2021 Jul. 31];8(A):119-24. Available from: https://oamjms.eu/index.php/mjms/article/view/4386

Most read articles by the same author(s)

1 2 > >>