Bayesian Analysis of Markov Based Logistic Model

Authors

  • Soma Chowdhury Biswas Department of Statistics, University of Chittagong, Chittagong, Bangladesh
  • Janardan Mahanta Department of Statistics, University of Chittagong, Chittagong, Bangladesh
  • Manindra Kumar Roy Ranada Prasad Shaha University, Narayanganj, Bangladesh

DOI:

https://doi.org/10.6000/1929-6029.2018.07.02.4

Keywords:

Bayesian approach, Bayes Factor (BF), Linear exponential (LINEX), Longitudinal data, Markov model, Modified linear exponential (MLINEX).

Abstract

In analyzing longitudinal data the correlations between responses obtained from same individual need to be taken into account. Various models can be used to handle such correlations. This article focuses on the application of transition modeling using Bayesian approach for analyzing longitudinal binary data. For Bayesian estimation asymmetric loss functions, such as, linear exponential (LINEX) and modified linear exponential (MLINEX) loss function and Tierney and Kadnae (T.K.) approximation has been used. Comparison is made using Bayes factor and Bayesian approach under LINEX loss function can be suggested to estimate the parameters of transition model.

References

Korn EL, Whittemore AS. Methods of Analyzing Panel Studies of Acute Health Effects of Air Pollution. Biometrics 1979; 35: 795-802. https://doi.org/10.2307/2530111 DOI: https://doi.org/10.2307/2530111

Regier MH. A Two State Markov Model for Behavior Change. Journal of American Statistical Association 1968; 63: 993-999. DOI: https://doi.org/10.1080/01621459.1968.11009325

Kalbfleisch JD, Lawless JF. The analysis of panel data under a Markov assumption. Journal of American Statistical Association 2005; 88: 863-871. DOI: https://doi.org/10.1080/01621459.1985.10478195

Azzalini A. Logistic Regression for Autocorrelated data with Application to Repeated Measure. Biometrika 1994; 81(4): 767-775. https://doi.org/10.1093/biomet/81.4.767 DOI: https://doi.org/10.1093/biomet/81.4.767

Muenz KR, Rubinstein LV. Markov chain for covariance dependence of binary sequences. Biometrics 1985; 41: 91-101. https://doi.org/10.2307/2530646 DOI: https://doi.org/10.2307/2530646

Liu T. Application of Markov Chains to Analyze and Predict the Time Series. Modern Applied Science 2010; 4 (5): 162-166. https://doi.org/10.5539/mas.v4n5p162 DOI: https://doi.org/10.5539/mas.v4n5p162

Islam MA, Chowdhury RI, Singh KP. A Markov Model for Analyzing Polytomous Outcome Data. Pakistan Journal of Statistics and Operation Research 2012; 8 (3): 593-603. https://doi.org/10.18187/pjsor.v8i3.530 DOI: https://doi.org/10.18187/pjsor.v8i3.530

Sirdari MZ, Islam MA, Awang N. A stationarity test on Markov chain models based on marginal distribution. Statistical Methodology 2013; 11: 68-76. https://doi.org/10.1016/j.stamet.2012.10.001 DOI: https://doi.org/10.1016/j.stamet.2012.10.001

Dey R, Islam MA. A conditional count model for repeated count data and its application to GEE approach. (504, Ed.) Statistical Papers 2017; 58 (2): 485. https://doi.org/10.1007/s00362-015-0708-9 DOI: https://doi.org/10.1007/s00362-015-0708-9

Sirdari MZ, Islam MA. Goodness of fit test for higher order binary Markov chain models. Cogent Mathematics & Statistics 2018; 5: 1-15. DOI: https://doi.org/10.1080/23311835.2017.1421003

Islam MA, Chowdhury RI. A Three State Markov Model for Analyzing Covariate Dependence. International Journal of Statistical Sciences 2004; 3: 241-249.

Islam MA, Chowdhury RI. A higher order Markov model for analyzing covariate dependence. Applied Mathematical Modelling 2006; 30: 477-488. https://doi.org/10.1016/j.apm.2005.05.006 DOI: https://doi.org/10.1016/j.apm.2005.05.006

Islam MA, Chowdhury RI, Briollais L. A bivariate binary model for testing dependence in outcomes. Bulletin of the Malaysian Mathematical Sciences Society 2012; 35(4): 845-858.

Islam MA, Chowdhury RI, Singh KP. Covariate Dependent Markov Models for Analysis of Repeated Binary Outcomes. Journal of Modern Applied Statistical Methods 2008; 6 (2): 561-572. https://doi.org/10.22237/jmasm/1193890800 DOI: https://doi.org/10.22237/jmasm/1193890800

Chowdhury RI, Islam MA, Shah MA, Enezi NA. A computer program to estimate the parameters of covariate dependent higher order Markov model. Computer Methods and Programs in Biomedicine 2005; 77: 175-181. https://doi.org/10.1016/j.cmpb.2004.10.003 DOI: https://doi.org/10.1016/j.cmpb.2004.10.003

Hanson TE, Branscum AJ, Johnson WO. Informative g-Prior for logistic regression. International Society for Bayesian Analysis 2004; 9: 597-612. https://doi.org/10.1214/14-BA868 DOI: https://doi.org/10.1214/14-BA868

Noorian S, Ganjali M. Bayesian Analysis of Transition Model for Longitudinal Ordinal Response Data: Application to Insomnia Data. International Journal of Statistics in Medical Research 2012; 1: 148-161. DOI: https://doi.org/10.6000/1929-6029.2012.01.02.08

Acquah HD. Bayesian Logistic Regression Modeling via Markov Chain Monte Carlo Algorithm. Journal of Social and Development Sciences 2013; 4 (4): 193-197. DOI: https://doi.org/10.22610/jsds.v4i4.751

Mahanta J, Biswas, SC, Roy MK, Islam MA. A Comparison of Bayesian and Classical Approach for Estimating Markov Based Logistic Model. American Journal of Mathematics and Statistics 2015; 5 (4): 178-183.

Mahanta J, Biswas SC. Comparison of Bayesian approach and classical approach for estimating the parameter of Markov model. Journal of reliability and statistical studies 2016; 9 (2): 81-90.

Zellner A. Bayesian Estimation and Prediction using asymmetric loss functions. Journal of American Statistical Association 1986; 81: 446-451. https://doi.org/10.1080/01621459.1986.10478289 DOI: https://doi.org/10.1080/01621459.1986.10478289

Tierney L, Kadane JB. Accurate Approximation for Posterior Moments and Marginal Densiies. Journal of American Statistical Association 1986; 81 (393): 82-86. https://doi.org/10.1080/01621459.1986.10478240 DOI: https://doi.org/10.1080/01621459.1986.10478240

Wahed ASF, Uddin B. Bayes estimation under asymmetric loss function. Dhaka University Journal of Science 1998; 46 (6): 355-361.

Kass, Raftery AE. Bayes Factor. Journal of American Statistical Association 1995; 90: 773-795. https://doi.org/10.1080/01621459.1995.10476572 DOI: https://doi.org/10.1080/01621459.1995.10476572

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Published

2018-05-08

How to Cite

Biswas, S. C., Mahanta, J., & Roy, M. K. (2018). Bayesian Analysis of Markov Based Logistic Model. International Journal of Statistics in Medical Research, 7(2), 57–65. https://doi.org/10.6000/1929-6029.2018.07.02.4

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General Articles