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Introduction

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Dynamic Mixed Models for Familial Longitudinal Data

Part of the book series: Springer Series in Statistics ((SSS))

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Abstract

Discrete data analysis such as count or binary clustered data analysis has been an important research topic over the last three decades. In general, two types of clusters are frequently encountered. First, a cluster may be formed with the responses along with associated covariates from the members of a group/family. These clustered responses are supposed to be correlated as the members of the cluster share a common random group/family effect. In this book, we refer to this type of correlation among the responses of members of same family as the familial correlation. Second, a cluster may be formed with the repeated responses along with associated covariates collected from an individual. These repeated responses from the same individual are also supposed to be correlated as there may be a dynamic relationship between the present and past responses. In this book, we refer to these correlations among the repeated responses collected from the same individual as the longitudinal correlations. It is of interest to fit a suitable parametric or semi-parametric familial and/or longitudinal correlation model primarily to analyze the means and variances of the data. Note that the familial and longitudinal correlations, however, play an important role in a respective setup to analyze the means and variances of the data efficiently.

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References

  1. Armitage, P. (1971). Statistical Methods in Medical Research. Oxford: Blackwell.

    Google Scholar 

  2. Berkson, J. (1944). Application of the logistic function to bio-assay. J. Am. Statist. Assoc., 39, 357−365.

    Article  Google Scholar 

  3. Berkson, J. (1951). Why I prefer logits to probits. Biometrics, 7, 327−339.

    Article  Google Scholar 

  4. Breslow, N, E. & Clayton, D. G. (1993). Approximate inference in generalized linear mixed models. . J. Amer. Stat. Assoc., 88, 9−25.

    Google Scholar 

  5. Breslow, N. E. & Lin, X. (1995). Bias correction in generalized linear models with a single component of dispersion. Biometrika, 82, 81−92.

    Article  MATH  MathSciNet  Google Scholar 

  6. Chowdhury, M. R. I. & Sutradhar, B. C. (2009). Generalized quasilikelihood versus hierarchial likelihood inferences in generalized linear mixed models for count data. Sankhya B: Indian J. Stat., 71, 55−78.

    MATH  MathSciNet  Google Scholar 

  7. Crowder, M. (1995). On the use of a working correlation matrix in using generalized linear models for repeated measures. Biometrika, 82, 407−410.

    Article  MATH  Google Scholar 

  8. Diggle, P. J., Heagety, P., Liang, K.-Y., & Zeger, S. L. (2002). Analysis of Longitudinal Data. Oxford Science. Oxford: Clarendon Press.

    Google Scholar 

  9. Diggle, P. J., Liang, K.-Y., & Zeger, S. L. (1994). Analysis of Longitudinal Data. Oxford Science. Oxford: Clarendon Press.

    Google Scholar 

  10. Dyke, G. V. & Patterson, H. D. (1952). Analysis of factorial arrangements when data are proportion. Biometrics, 8, 1−12.

    Article  Google Scholar 

  11. Fitzmaurice, G. M., Laird, N. M., & Rotnitzky, A. G. (1993). Regression models for discrete longitudinal responses. Statist. Sci., 8, 284−309.

    Article  MATH  MathSciNet  Google Scholar 

  12. Haberman, S. J. (1974). Log-linear models for frequency tables with ordered classifications. Biometrics, 36, 589−600.

    Article  MathSciNet  Google Scholar 

  13. Hall, D. B., & Severini, T. A. (1998). Extended generalized estimating equations for clustered data. J. Amer. Statist. Assoc., 93, 1365−75.

    Article  MATH  MathSciNet  Google Scholar 

  14. Heagerty, P. J. (1999). Marginally specified logistic-normal models for longitudinal binary data. Biometrics, 55, 688−98.

    Article  MATH  Google Scholar 

  15. Henderson, C. R. (1963). Selection index and expected genetic advance. In Statistical Genetics and Plant Breeding, National Research Council Publication No. 892, pp. 141−63. National Academy of Sciences.

    Google Scholar 

  16. Jiang, J. (1998). Consistent estimators in generalized linear mixed models. J. Amer. Statist. Assoc., 93, 720−729.

    Article  MATH  MathSciNet  Google Scholar 

  17. Jiang, J. & Zhang, W. (2001). Robust estimation in generalized linear mixed models. Biometrika, 88, 753−765.

    Article  MATH  MathSciNet  Google Scholar 

  18. Jowaheer, V., Sutradhar, B. C. & Sneddon, G. (2009). On familial Poisson mixed models with multi-dimensional random effects. J. Statist. Comp. Simul., 79, 1043−1062.

    Article  MATH  Google Scholar 

  19. Jowaheer, V. & Sutradhar, B. C. (2002). Analysing longitudinal count data with overdispersion. Biometrika, 89, 389−399.

    Article  MATH  MathSciNet  Google Scholar 

  20. Kuk, A. Y. C. (1995). Asymptotically unbised estimation in generalized linear models with random effects. J. R. Stastist. Soc. B, 58, 619−678.

    Google Scholar 

  21. Lee, Y. & Nelder, J.A. (1996). Hierarchical generalized linear models. J. R. Statist. Soc. B,, 58, 619−678.

    MATH  MathSciNet  Google Scholar 

  22. Lee, Y. & Nelder, J.A. (2001). Hierarchical generalized linear models: A synthesis of generalized linear models, random-effect models and structured dispersions. Biometrika,, 88, 987−1006.

    Article  MATH  MathSciNet  Google Scholar 

  23. Liang, K. Y. & Zeger, S. L. (1986). Longitudinal data analysis using generalized linear models. Biometrika, 73, 13−22.

    Article  MATH  MathSciNet  Google Scholar 

  24. Lin, X. & N. E. Breslow (1996). Bias correction in generalized linear mixed models with multiple components of dispersion. J. Am. Statist. Assoc., 91, 1007−1016.

    Article  MATH  MathSciNet  Google Scholar 

  25. McCullagh, P. & J. A. Nelder (1983, 1989). Generalized Linear Models. Chapman and Hall, London.

    Google Scholar 

  26. Molenberghs, G. & Verbeke, G. (2005). Models for Discrete Longitudinal Data. Springer, New York.

    Google Scholar 

  27. Nelder, J. A. (1974). Log-linear models for contingency tables: A generalization of classical least squares. Appl. Statist., 23, 323−329.

    Article  MathSciNet  Google Scholar 

  28. Neuhaus, J. M. (1993). Estimation efficiency and tests of covariate effects with clustered binary data. Biometrics, 49, 989−996.

    Article  Google Scholar 

  29. Pearson, J. D., Morrell, C. H., Landis, P. K., Carter, H. B., & Brant, L. J. (1994). Mixedeffects regression models for studying the natural history of prostate disease. Statist. Med., 13, 587−601.

    Article  Google Scholar 

  30. Plackett, R. L. (1981). The Analysis of Categorical Data. Griffin, London.

    Google Scholar 

  31. Prentice, R. L. & Zhao, L.P. (1991). Estimating equations for parameters in means and covariances of multivariate discrete and continuous responses. Biometrics, 47, 825−39.

    Article  MATH  MathSciNet  Google Scholar 

  32. Schall, R. (1991). Estimation in generalized linear models with random effects. Biometrika, 78, 719−27.

    Article  MATH  Google Scholar 

  33. Sneddon, G. & Sutradhar, B. C. (2004). On semi-parametric familial-longitudinal models. Statist. Probab. Lett., 69, 369−379.

    Article  MATH  MathSciNet  Google Scholar 

  34. Sutradhar, B. C. (2003). An overview on regression models for discrete longitudinal responses. Statist. Sci., 18, 377−93.

    Article  MATH  MathSciNet  Google Scholar 

  35. Sutradhar, B.C. (2004). On exact quasilikelihood inference in generalized linear mixed models. Sankhyā: Indian J. Statist., 66, 261−289.

    MathSciNet  Google Scholar 

  36. Sutradhar, B. C. (2010). Inferences in generalized linear longitudinal mixed models. Canad. J. of Statist., 38, 174−196.

    Article  MATH  MathSciNet  Google Scholar 

  37. Sutradhar, B. C. & Das, K. (1999). On the efficiency of regression estimators in generalized linear models for longitudinal data. Biometrika, 86, 459−65.

    Article  MATH  MathSciNet  Google Scholar 

  38. Sutradhar, B. C. & Kumar, P. (2001). On the efficiency of extended generalized estimating equation approaches. Statist. Probab. Lett., 55, 53−61.

    Article  MATH  MathSciNet  Google Scholar 

  39. Sutradhar, B. C. & Mukerjee, R. (2005). On likelihood inference in binary mixed model with an application to COPD data. Comput. Statist. Data Anal., 48, 345−361.

    Article  MATH  MathSciNet  Google Scholar 

  40. Sutradhar, B. C. & Z. Qu (1998). On approximate likelihood inference in Poisson mixed model. Canad. J. Statist., 26, 169−186.

    Article  MATH  MathSciNet  Google Scholar 

  41. Sutradhar, B. C. & Rao, R. P. (2003). On quasi-likelihood inference in generalized linear mixed models with two components of dispersion. Canad. J. Statist., 31, 415−435.

    Article  MATH  MathSciNet  Google Scholar 

  42. Thall, P. F. & Vail, S. C. (1990). Some covariance models for longitudinal count data with overdispersion. Biometrics, 46, 657−71.

    Article  MATH  MathSciNet  Google Scholar 

  43. Verbeke, G. & Lesaffre, E. (1999). The effect of drop-out on the efficiency of longitudinal experiments. Appl. Statist., 48, 363−375.

    MATH  Google Scholar 

  44. Verbeke, G. & Molenberghs, G. (2000). Linear Mixed Models for Longitudinal Data. Springer, New York.

    Google Scholar 

  45. Waclawiw, M. A. & K.-Y. Liang (1993). Prediction of random effects in the generalized linear model. J. Am. Statist. Assoc., 88, 171−178.

    Article  MATH  Google Scholar 

  46. Wedderburn, R. (1974). Quasilikelihood functions, generalized linear models and the Gauss-Newton method. Biometrika, 61, 439−447.

    MATH  MathSciNet  Google Scholar 

  47. Zhao, L. P. & Prentice, R. L. (1990). Correlated binary regression using a quadratic exponential model. Biometrika, 77, 642−48.

    Article  MathSciNet  Google Scholar 

  48. Zhao, L. P., Prentice, R. L. & Self, S. G. (1992). Multivariate mean parameter estimation by using a partly exponential model. J. Roy. Statist. Soc. Ser. B, 54, 805−811.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Memorial University, A1C 5S7, Saint John’s, Newfoundland and Labrador, Canada

    Brajendra C. Sutradhar

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  1. Brajendra C. Sutradhar
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Correspondence to Brajendra C. Sutradhar .

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Sutradhar, B.C. (2011). Introduction. In: Dynamic Mixed Models for Familial Longitudinal Data. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8342-8_1

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