Modeling Multivariate Correlated Binary Data
American Journal of Theoretical and Applied Statistics
Volume 5, Issue 4, July 2016, Pages: 225-233
Received: Jun. 13, 2016;
Accepted: Jun. 22, 2016;
Published: Jul. 13, 2016
Views 4769 Downloads 224
Ahmed Mohamed Mohamed El-Sayed, High Institute for Specific Studies, Department of Management Information Systems, Nazlet Al-Batran, Giza, Egypt
Follow on us
This paper provides the model, estimation and test procedures for the measures of association in the correlated binary data associated with covariates in multivariate case. The generalized linear model (GLM) which satisfies the Markov properties for serial dependence, and the alternative quadratic exponential form (AQEF) are employed for multivariate Bernoulli outcome variables. The log-odds ratios as measures of association have been estimated, and the appropriate test procedures are suggested. The over-dispersion measure is investigated for the multivariate correlated binary outcomes. The scaled deviance is used as a goodness of fit of the model. For comparison, we have used the data on the respiratory disorder. In such situation, we indicate that the vectorized generalized linear models (VGLM) and AQEF procedures have the same estimates of regression parameters in the bivariate case.
Multivariate Bernoulli Distribution, Generalized Linear Model, Scaled Deviance Test, Likelihood Ratio Test, Maximum Likelihood Estimators, Alternative Quadratic Exponential Form
To cite this article
Ahmed Mohamed Mohamed El-Sayed,
Modeling Multivariate Correlated Binary Data, American Journal of Theoretical and Applied Statistics.
Vol. 5, No. 4,
2016, pp. 225-233.
Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Agresti A. Categorical data analysis (second edition). New Jersey, United States: John Wiley & Sons; 2002.
El-Sayed A M. M. Modeling trivariate binary data. Al-Azhar University, Journal of College of Science 2016; Accepted.
El-Sayed A M M, Islam M A, Alzaid A A. Estimation and test of measures of association for correlated binary data. Bulletin of the Malaysian Mathematical Sciences Society 2013; 2, 36, 4: 985-1008.
Chambers J M, Hastie TJ. Statistical Models in Solomon. New York: Chapman and Hall; 1993.
Christensen R. Log-linear Models and Logistic Regression (second edition). New York, United States: Springer-Verlag; 1997.
Cox D R. The analysis of multivariate binary data. Journal of the Royal Statistical Society, Series C (Applied Statistics) 1972; 21: 113-120.
Heagerty P J. Marginalized transition models and likelihood inference for longitudinal categorical data. Biometrics 2002; 58: 342-351.
Heagerty P J and Zeger S L. Marginalized multi-level models and likelihood inference (with discussion). Statistical Science 2002; 15: 1-26.
Islam M A, Chowdhury R I, Briollais L. A bivariate binary model for testing dependence in outcomes. Bulletin of the Malaysian Mathematical Sciences Society 2012; 2, 35, 4: 845-858.
Lovison G. A matrix-valued Bernoulli distribution. Journal of Multivariate Analysis 2006; 97: 1573-1585.
McCullagh P, Nelder J A. Generalized linear models (second edition). London, United Kingdom: Chapman & Hall; 1989.
Teugels J L. Some representations of the multivariate Bernoulli and Binomial distributions. Journal of multivariate analysis 1990; 32: 256-268.
Varadhan R, Gilbert P D. BB: An R package for solving a large system of nonlinear equations and for optimizing a high-dimensional nonlinear objective function. Journal of Statistical Software 2009; 32, 4: 1-26.
Yee T W. The VGAM package, R News 2008; 8, 2: 28-39.
Yee T W, Wild C J. Vector generalized additive models. Journal of the Royal Statistical Society, Series B, Methodological 1996; 58: 481-493.
Zhao L P, Prentice R L. Correlated binary regression using a generalized quadratic model. Biometrika 1990; 77: 642-648.