Linear quantile mixed models

Dependent data arise in many studies. Frequently adopted sampling designs, such as cluster, multilevel, spatial, and repeated measures, may induce this dependence, which the analysis of the data needs to take into due account. In a previous publication (Geraci and Bottai in Biostatistics 8:140–154,...

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Vydáno v:Statistics and computing Ročník 24; číslo 3; s. 461 - 479
Hlavní autoři: Geraci, Marco, Bottai, Matteo
Médium: Journal Article
Jazyk:angličtina
Vydáno: Boston Springer US 01.05.2014
Témata:
Algorithms
Artificial Intelligence
Computation
Computer simulation
Mathematical models
Mathematics and Statistics
Maximization
Optimization
Probability and Statistics in Computer Science
Quantiles
Regression
Statistical Theory and Methods
Statistics
Statistics and Computing/Statistics Programs
Hierarchical models
Gaussian quadrature
Best linear predictor
Clarke’s derivative
ISSN:0960-3174, 1573-1375
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Shrnutí:Dependent data arise in many studies. Frequently adopted sampling designs, such as cluster, multilevel, spatial, and repeated measures, may induce this dependence, which the analysis of the data needs to take into due account. In a previous publication (Geraci and Bottai in Biostatistics 8:140–154, 2007 ), we proposed a conditional quantile regression model for continuous responses where subject-specific random intercepts were included to account for within-subject dependence in the context of longitudinal data analysis. The approach hinged upon the link existing between the minimization of weighted absolute deviations, typically used in quantile regression, and the maximization of a Laplace likelihood. Here, we consider an extension of those models to more complex dependence structures in the data, which are modeled by including multiple random effects in the linear conditional quantile functions. We also discuss estimation strategies to reduce the computational burden and inefficiency associated with the Monte Carlo EM algorithm we have proposed previously. In particular, the estimation of the fixed regression coefficients and of the random effects’ covariance matrix is based on a combination of Gaussian quadrature approximations and non-smooth optimization algorithms. Finally, a simulation study and a number of applications of our models are presented.
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ISSN:0960-3174
1573-1375
DOI:10.1007/s11222-013-9381-9