AM  Vol.3 No.11 A , November 2012
Parameter Estimation in Logistic Regression for Transition, Reverse Transition and Repeated Transition from Repeated Outcomes
ABSTRACT
Covariate dependent Markov models dealing with estimation of transition probabilities for higher orders appear to be restricted because of over-parameterization. An improvement of the previous methods for handling runs of events by expressing the conditional probabilities in terms of the transition probabilities generated from Markovian assumptions was proposed using Chapman-Kolmogorov equations. Parameter estimation of that model needs extensive pre-processing and computations to prepare data before using available statistical softwares. A computer program developed using SAS/IML to estimate parameters of the model are demonstrated, with application to Health and Retirement Survey (HRS) data from USA.

Cite this paper
R. Chowdhury, M. Islam, S. Huda and L. Briollais, "Parameter Estimation in Logistic Regression for Transition, Reverse Transition and Repeated Transition from Repeated Outcomes," Applied Mathematics, Vol. 3 No. 11, 2012, pp. 1739-1749. doi: 10.4236/am.2012.331240.
References
[1]   L. R. Muenz and L. V. Rubinstein, “Markov Models for Covariate Dependence of Binary Sequences,” Biometrics, Vol. 41, No. 1, 1985, pp. 91-101. doi:10.2307/2530646

[2]   M. A. Islam and R. I. Chowdhury, “A Higher-Order Markov Model for Analyzing Covariate Dependence,” Applied Mathematical Modelling, Vol. 30, No. 6, 2006, pp. 477-488. doi:10.1016/j.apm.2005.05.006

[3]   M. A. Islam, R. I. Chowdhury and S. Huda, “A Multistate Transition Model for Analyzing Longitudinal Depression Data,” Bulletin of the Malaysian Mathematical Sciences Society, 2012. http://www.emis.de/journals/BMMSS/accepted_papers.htm

[4]   SAS/IML 9.1, “User’s Guide,” SAS Institute Inc., Cary, 2004.

[5]   M. A. Islam, R. I. Chowdhury and S. Huda, “Markov Models with Covariate Dependence for Repeated Measures, Chapter 9,” Nova Science, New York, 2009.

[6]   M. A. Islam, R. I. Chowdhury and S. Huda, “A Multistage Model for Analyzing Repeated Observations on Depression in Elderly,” Festschrift in Honor of Distinguished Professor Mir Masoom Ali, 18-19 May 2007, pp. 44-54.

[7]   D. W. Hosmer and S. Lemeshow, “Applied Logistic Regression,” Wiley, New York, 1989, p. 136.

[8]   Public Use Dataset, “Health and Retirement Study,” University of Michigan, Ann Arbor, 1992-2004.

[9]   M. A. Islam, “Multistate Survival Models for Transitions and Reverse Transitions: An Application to Contraceptive Use Data,” Journal of Royal Statistical Society A, Vol. 157, No. 3, 1994, pp. 441-455.

[10]   M. A. Islam, R. I. Chowdhury, N. Chakraborty and W. Bari, “A Multistage Model for Maternal Morbidity during Antenatal, Delivery and Postpartum Periods,” Statistics in Medicine, Vol. 23, No. 1, 2004, pp. 137-158. doi:10.1002/sim.1594

 
 
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