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A marginalized multilevel model for bivariate longitudinal binary data

Author

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  • Gul Inan

    (Middle East Technical University)

  • Ozlem Ilk

    (Middle East Technical University)

Abstract

This study considers analysis of bivariate longitudinal binary data. We propose a model based on marginalized multilevel model framework. The proposed model consists of two levels such that the first level associates the marginal mean of responses with covariates through a logistic regression model and the second level includes subject/time specific random intercepts within a probit regression model. The covariance matrix of multiple correlated time-specific random intercepts for each subject is assumed to represent the within-subject association. The subject-specific random effects covariance matrix is further decomposed into its dependence and variance components through modified Cholesky decomposition method and then the unconstrained version of resulting parameters are modelled in terms of covariates with low-dimensional regression parameters. This provides better explanations related to dependence and variance parameters and a reduction in the number of parameters to be estimated in random effects covariance matrix to avoid possible identifiability problems. Marginal correlations between responses of subjects and within the responses of a subject are derived through a Taylor series-based approximation. Data cloning computational algorithm is used to compute the maximum likelihood estimates and standard errors of the parameters in the proposed model. The validity of the proposed model is assessed through a Monte Carlo simulation study, and results are observed to be at acceptable level. Lastly, the proposed model is illustrated through Mother’s Stress and Children’s Morbidity study data, where both population-averaged and subject-specific interpretations are drawn through Emprical Bayes estimation of random effects.

Suggested Citation

  • Gul Inan & Ozlem Ilk, 2019. "A marginalized multilevel model for bivariate longitudinal binary data," Statistical Papers, Springer, vol. 60(3), pages 601-628, June.
    • Handle: RePEc:spr:stpapr:v:60:y:2019:i:3:d:10.1007_s00362-016-0840-1
    DOI: 10.1007/s00362-016-0840-1
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    References listed on IDEAS

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    1. Lee, Keunbaik & Lee, JungBok & Hagan, Joseph & Yoo, Jae Keun, 2012. "Modeling the random effects covariance matrix for generalized linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1545-1551.
    2. Harvey Goldstein & Jon Rasbash, 1996. "Improved Approximations for Multilevel Models with Binary Responses," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 159(3), pages 505-513, May.
    3. Tony Vangeneugden & Geert Molenberghs & Geert Verbeke & Clarice G.B. Dem�trio, 2011. "Marginal correlation from an extended random-effects model for repeated and overdispersed counts," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(2), pages 215-232, September.
    4. Li, Erning & Pourahmadi, Mohsen, 2013. "An alternative REML estimation of covariance matrices in linear mixed models," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1071-1077.
    5. Yoonsang Kim & Young-Ku Choi & Sherry Emery, 2013. "Logistic Regression With Multiple Random Effects: A Simulation Study of Estimation Methods and Statistical Packages," The American Statistician, Taylor & Francis Journals, vol. 67(3), pages 171-182, August.
    6. Lele, Subhash R. & Nadeem, Khurram & Schmuland, Byron, 2010. "Estimability and Likelihood Inference for Generalized Linear Mixed Models Using Data Cloning," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1617-1625.
    7. Torabi, Mahmoud, 2013. "Likelihood inference in generalized linear mixed measurement error models," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 549-557.
    8. Patrick J. Heagerty, 2002. "Marginalized Transition Models and Likelihood Inference for Longitudinal Categorical Data," Biometrics, The International Biometric Society, vol. 58(2), pages 342-351, June.
    9. Patrick J. Heagerty, 1999. "Marginally Specified Logistic-Normal Models for Longitudinal Binary Data," Biometrics, The International Biometric Society, vol. 55(3), pages 688-698, September.
    10. Samuel Iddi & Geert Molenberghs, 2012. "A joint marginalized multilevel model for longitudinal outcomes," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(11), pages 2413-2430, July.
    11. Özgür Asar & Ozlem Ilk, 2016. "First-order marginalised transition random effects models with probit link function," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(5), pages 925-942, April.
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