Journal of Sciences, Islamic Republic of Iran

Modelling of Correlated Ordinal Responses, by Using Multivariate Skew Probit with Different Types of Variance Covariance Structures

Document Type : Original Paper

Authors

1 Statistics dept., Mathematical Sciences and computer college, shahid Chamran university of Ahvaz, Ahvaz, Iran

2 Statistics Dept. Mathematical Sciences and Computer college, Shahid Chamran university of Ahvaz, Ahvaz, Iran

Abstract

In this paper, a multivariate fundamental skew probit (MFSP) model is used to model correlated ordinal responses which are constructed from the multivariate fundamental skew normal (MFSN) distribution originate to the greater flexibility of MFSN. To achieve an appropriate VC structure for reaching reliable statistical inferences, many types of variance covariance (VC) structures are considered to model MFSN. Simulation methods are used to find the properties of the parameters estimate. The Schizophrenia Collaborative Study data invokes the proposed MFSN model. The results confirm that the first-order autoregressive (AR(1)) structure substantially enhances the estimation of the parameters. Furthermore, over time the drugs effect the schizophrenia treatment, noticeably. 

Keywords

Main Subjects

  1. Li Y. and Schafer D.W. Likelihood analysis of the multivariate ordinal probit regression model for repeated ordinal responses. Comput. Stat. Data Anal. 52: 3474-3492 (2008).
  2. Xu H. and Craig B.A. Likelihood analysis of multivariate probit models using a parameter expanded MCEM algorithm. Technometrics 52 (2): 340-348 (2010).
  3. Kim J.S. and Ratchford B.T. A Bayesian multivariate probit for ordinal data with semiparametric random-effects. Comput. Stat. Data Anal. 64: 192-208 (2013).
  4. Varin C and Czado C. A mixed autoregressive probit model for ordinal longitudinal data. Biostatistics 111 (1): 127-138 (2010).
  5. Adugna  M., Ketema M., Goshu D. and Debebe S. Market outlet choice decision and its effect on income and productivity of smallholder vegetable producers in lake Tana Basin, Ethiopia. RAAE, 22 (1): 83-90 (2019).
  6. Chib S. and Greenberg E. Analysis of multivariate probit models. Biometrika, 85: 347-361 (1998).
  7. Coppellari L. and Jenkins S.P. Multivariate probit regression using simulated maximum likelihood. Stata J. 3 (3): 278-294 (2003).
  8. Yano Y., Kato E., Ohe Y. and Blandford D. Examining the opinions of potential consumers about plan-derived cosmetics: an application combining word association, co-occurrence network and multivatiate probit. J. Sens. Stud. e12484: 1–9 (2018).
  9. Li C., Poskitt D.S. and Zhao X. The bivariate probit model, maximum likelihood estimator, pseudo true parameters and partial identification. J. Econ. 209 (1): 94-113 (2019).
  10. Azzalini A. and Dalla-Valle A. The multivariate skew-normal distribution, Biometrika 83: 715–726 (1996).
  11. Sahu S.K. and Dey D.K. and Branco, M.D. A new class of multivariate skew distributions with applications to Bayesian regression models, Can. J. Stat. 31: 129–150 (2003).
  12. Azzalini A. The skew normal distribution and related multivariate families. Scand. J. Stat. 32:159-188 (2005).
  13. Genton M.G. and Loperfido N. Generalized skew-elliptical distributions and their quadratic forms. Ann. Inst. Statist. Math. 57 (2): 380-401 (2005).
  14. Arellano-Valle R.B. and Genton M.G. On fundamental skew distribution. J. Multivariate Ana. 96: 93-116 (2005).
  15. Mullahy J. Marginal effect in multivariate probit models. Empir. Econ. 32 (2): 447-461 (2017).

  16.  
    Gibbons R. and Wilcox-Gok V. Health service utilization and insurance coverage: A multivariate probit analysis. J. Am. Stat. Asso. 93: 63-72 (1998).
  1. Song X. and Lee S. A multivariate probit latent variable model for analyzing dichotomous responses. Stat. Sinica, 15: 645-664 (2005).
  2. Fortin M., Daigle G. and Ung C.H. A variance-covariance structure to take into account repeated measurements and heteroscedasticity in growth modeling. Eur. J. For. Res. 126: 573-585 (2007).
  3. Stingo F.C., Stanghellini E. and Capobianco R. On the estimation of a binary response model in a selected population. J. Stat. plan. Infer. 141 (10): 3293-3393 (2012).
  4. Azzalini A. and Capitanio A. Some properties of the multivariate skew-normal distribution. J. Royal Stat. Soc.: Ser. B 61: 579-602 (1999).
  5. Hedeker D. Generalized linear mixed models. In Encyclopedia of Statistics in Behavioral Sciences, Edited by Everitt D. and Howell, 2: 729-738 (2005).
  6. Hedeker D. and Gibbons R.D. A random-effects ordinal regression model for multilevel analysis, Biometrics 50 (4): 933-944 (1994).
Journal of Sciences, Islamic Republic of Iran
Volume 30, Issue 4
November 2019
Pages 363-369