Inference for clustered data using the independence loglikelihood

We use the properties of independence estimating equations to adjust the 'independence' loglikelihood function in the presence of clustering. The proposed adjustment relies on the robust sandwich estimator of the parameter covariance matrix, which is easily calculated. The methodology competes favourably with established techniques based on independence estimating equations; we provide some insight as to why this is so. The adjustment is applied to examples relating to the modelling of wind speed in Europe and annual maximum temperatures in the U.K. Copyright 2007, Oxford University Press.

[1]  M. Pepe,et al.  A cautionary note on inference for marginal regression models with longitudinal data and general correlated response data , 1994 .

[2]  Janet E. Heffernan,et al.  Dependence Measures for Extreme Value Analyses , 1999 .

[3]  A. Qu,et al.  Assessing robustness of generalised estimating equations and quadratic inference functions , 2004 .

[4]  S. Zeger,et al.  Longitudinal data analysis using generalized linear models , 1986 .

[5]  Martin Crowder,et al.  On the use of a working correlation matrix in using generalised linear models for repeated measures , 1995 .

[6]  Steven Mark Bate,et al.  Generalized linear models for large dependent data sets , 2004 .

[7]  R. Carroll,et al.  A Note on the Efficiency of Sandwich Covariance Matrix Estimation , 2001 .

[8]  P. Diggle,et al.  Analysis of Longitudinal Data. , 1997 .

[9]  James E. Stafford.  A robust adjustment of the profile likelihood , 1996 .

[10]  R. Royall,et al.  Interpreting statistical evidence by using imperfect models: robust adjusted likelihood functions , 2003 .

[11]  H. Goldstein.  Multilevel Statistical Models , 2006 .

[12]  A. Bowman,et al.  Applied smoothing techniques for data analysis : the kernel approach with S-plus illustrations , 1999 .

[13]  Roel Bosker,et al.  Multilevel analysis : an introduction to basic and advanced multilevel modeling , 1999 .

[14]  P. Diggle,et al.  Analysis of Longitudinal Data , 2003 .

[15]  D. Cox,et al.  A note on pseudolikelihood constructed from marginal densities , 2004 .

[16]  Jonathan A. Tawn,et al.  A conditional approach for multivariate extreme values (with discussion) , 2004 .

[17]  William H. Press,et al.  Numerical Recipes in Fortran 77: The Art of Scientific Computing 2nd Editionn - Volume 1 of Fortran Numerical Recipes , 1992 .

[18]  David J. Nott,et al.  A pairwise likelihood approach to analyzing correlated binary data , 2000 .

[19]  H. Joe.  Multivariate models and dependence concepts , 1998 .

[20]  Richard E. Chandler,et al.  On the use of generalized linear models for interpreting climate variability , 2005 .

[21]  T. Derouen,et al.  A Covariance Estimator for GEE with Improved Small‐Sample Properties , 2001, Biometrics.

[22]  Geoffrey S. Watson,et al.  The inefficiency of least squares , 1975 .

[23]  J. Kent.  Robust properties of likelihood ratio tests , 1982 .

[24]  Kalyan Das,et al.  Miscellanea. On the efficiency of regression estimators in generalised linear models for longitudinal data , 1999 .

[25]  W. Pan.  Akaike's Information Criterion in Generalized Estimating Equations , 2001, Biometrics.

[26]  V. Isham,et al.  An Analysis of Daily Maximum Wind Speed in Northwestern Europe Using Generalized Linear Models , 2002 .

[27]  R. Henderson,et al.  A serially correlated gamma frailty model for longitudinal count data , 2003 .

[28]  Andrew Harvey,et al.  Forecasting, Structural Time Series Models and the Kalman Filter. , 1991 .

[29]  Yongdai Kim,et al.  Analysis of longitudinal data in case-control studies , 2004 .

[30]  Space-Time Modelling of Rainfall for Continuous Simulation , 2007 .

[31]  N. Jewell,et al.  Hypothesis testing of regression parameters in semiparametric generalized linear models for cluster correlated data , 1990 .

[32]  G. S. Watson.  Prediction and the efficiency of least squares , 1972 .

[33]  C. Varin.  On composite marginal likelihoods , 2008 .

[34]  G. Fitzmaurice,et al.  A caveat concerning independence estimating equations with multivariate binary data. , 1995, Biometrics.

[35]  Barry McDonald,et al.  Estimating Logistic Regression Parameters for Bivariate Binary Data , 1993 .

[36]  A. Davison,et al.  Generalized additive modelling of sample extremes , 2005 .

[37]  M. Kendall.  Theoretical Statistics , 1956, Nature.

[38]  J. Besag.  On the Statistical Analysis of Dirty Pictures , 1986 .

[39]  M. Fay,et al.  Small‐Sample Adjustments for Wald‐Type Tests Using Sandwich Estimators , 2001, Biometrics.