A Gaussian pseudolikelihood approach for quantile regression with repeated measurements

To enhance the efficiency of regression parameter estimation by modeling the correlation structure of correlated binary error terms in quantile regression with repeated measurements, we propose a Gaussian pseudolikelihood approach for estimating correlation parameters and selecting the most appropriate working correlation matrix simultaneously. The induced smoothing method is applied to estimate the covariance of the regression parameter estimates, which can bypass density estimation of the errors. Extensive numerical studies indicate that the proposed method performs well in selecting an accurate correlation structure and improving regression parameter estimation efficiency. The proposed method is further illustrated by analyzing a dental dataset.

[1]  Martin Crowder,et al.  Gaussian Estimation for Correlated Binomial Data , 1985 .

[2]  Pablo Kurlat.  Asset Markets With Heterogeneous Information , 2016 .

[3]  Zhongyi Zhu,et al.  Empirical likelihood for quantile regression models with longitudinal data , 2011 .

[4]  Liya Fu,et al.  Quantile regression for longitudinal data with a working correlation model , 2012, Comput. Stat. Data Anal..

[5]  R. Potthoff,et al.  A generalized multivariate analysis of variance model useful especially for growth curve problems , 1964 .

[6]  You‐Gan Wang,et al.  A Modified Pseudolikelihood Approach for Analysis of Longitudinal Data , 2007, Biometrics.

[7]  Jianwen Cai,et al.  Quantile Regression Models with Multivariate Failure Time Data , 2005, Biometrics.

[8]  R. Koenker.  Quantile regression for longitudinal data , 2004 .

[9]  Criterion for the simultaneous selection of a working correlation structure and either generalized estimating equations or the quadratic inference function approach , 2014, Biometrical journal. Biometrische Zeitschrift.

[10]  Modified Gaussian estimation for correlated binary data , 2013, Biometrical journal. Biometrische Zeitschrift.

[11]  Min Zhu,et al.  Efficient parameter estimation in longitudinal data analysis using a hybrid GEE method. , 2009, Biostatistics.

[12]  You-Gan Wang,et al.  Working covariance model selection for generalized estimating equations , 2011, Statistics in medicine.

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

[14]  Martin Crowder,et al.  On repeated measures analysis with misspecified covariance structure , 2001 .

[15]  Lee-Jen Wei,et al.  Quantile Regression for Correlated Observations , 2004 .

[16]  R. Koenker,et al.  Robust Tests for Heteroscedasticity Based on Regression Quantiles , 1982 .

[17]  R. Koenker,et al.  Computing regression quantiles , 1987 .

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

[19]  B. M. Brown,et al.  Standard errors and covariance matrices for smoothed rank estimators , 2005 .

[20]  Weiping Zhang,et al.  Smoothing combined estimating equations in quantile regression for longitudinal data , 2014, Stat. Comput..

[21]  Sin-Ho Jung.  Quasi-Likelihood for Median Regression Models , 1996 .

[22]  Chenlei Leng,et al.  Empirical likelihood and quantile regression in longitudinal data analysis , 2011 .