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Quantile regression in linear mixed models: a stochastic approximation EM approach.

ABSTRACT: This paper develops a likelihood-based approach to analyze quantile regression (QR) models for continuous longitudinal data via the asymmetric Laplace distribution (ALD). Compared to the conventional mean regression approach, QR can characterize the entire conditional distribution of the outcome variable and is more robust to the presence of outliers and misspecification of the error distribution. Exploiting the nice hierarchical representation of the ALD, our classical approach follows a Stochastic Approximation of the EM (SAEM) algorithm in deriving exact maximum likelihood estimates of the fixed-effects and variance components. We evaluate the finite sample performance of the algorithm and the asymptotic properties of the ML estimates through empirical experiments and applications to two real life datasets. Our empirical results clearly indicate that the SAEM estimates outperforms the estimates obtained via the combination of Gaussian quadrature and non-smooth optimization routines of the Geraci and Bottai (2014) approach in terms of standard errors and mean square error. The proposed SAEM algorithm is implemented in the R package qrLMM().

SUBMITTER: Galarza CE

PROVIDER: S-EPMC5667718 | biostudies-literature | 2017

REPOSITORIES: biostudies-literature

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Quantile regression in linear mixed models: a stochastic approximation EM approach.

Galarza Christian E CE Lachos Victor H VH Bandyopadhyay Dipankar D

Statistics and its interface 20170101 3

This paper develops a likelihood-based approach to analyze quantile regression (QR) models for continuous longitudinal data via the asymmetric Laplace distribution (ALD). Compared to the conventional mean regression approach, QR can characterize the entire conditional distribution of the outcome variable and is more robust to the presence of outliers and misspecification of the error distribution. Exploiting the nice hierarchical representation of the ALD, our classical approach follows a Stocha ...[more]

PMID: 29104713

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Project description:BackgroundIt has been a long-standing biological challenge to understand the molecular regulatory mechanisms behind mammalian ageing. Harnessing the availability of many ageing microarray datasets, a number of studies have shown that it is possible to identify genes that have age-dependent differential expression (DE) or differential variability (DV) patterns. The majority of the studies identify "interesting" genes using a linear regression approach, which is known to perform poorly in the presence of outliers or if the underlying age-dependent pattern is non-linear. Clearly a more robust and flexible approach is needed to identify genes with various age-dependent gene expression patterns.ResultsHere we present a novel model selection approach to discover genes with linear or non-linear age-dependent gene expression patterns from microarray data. To identify DE genes, our method fits three quantile regression models (constant, linear and piecewise linear models) to the expression profile of each gene, and selects the least complex model that best fits the available data. Similarly, DV genes are identified by fitting and comparing two quantile regression models (non-DV and the DV models) to the expression profile of each gene. We show that our approach is much more robust than the standard linear regression approach in discovering age-dependent patterns. We also applied our approach to analyze two human brain ageing datasets and found many biologically interesting gene expression patterns, including some very interesting DV patterns, that have been overlooked in the original studies. Furthermore, we propose that our model selection approach can be extended to discover DE and DV genes from microarray datasets with discrete class labels, by considering different quantile regression models.ConclusionIn this paper, we present a novel application of quantile regression models to identify genes that have interesting linear or non-linear age-dependent expression patterns. One important contribution of this paper is to introduce a model selection approach to DE and DV gene identification, which is most commonly tackled by null hypothesis testing approaches. We show that our approach is robust in analyzing real and simulated datasets. We believe that our approach is applicable in many ageing or time-series data analysis tasks.

Dataset Information

Quantile regression in linear mixed models: a stochastic approximation EM approach.

Publications

Quantile regression in linear mixed models: a stochastic approximation EM approach.

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