Simultaneous variable selection and estimation for multivariate multilevel longitudinal data with both continuous and binary responses

Complex structured data settings are studied where outcomes are multivariate and multilevel and are collected longitudinally. Multivariate outcomes include both continuous and discrete responses. In addition, the data contain a large number of covariates but only some of them are important in explaining the dynamic features of the responses. To delineate the complex association structures of the responses, a model with correlated random effects is proposed. To handle the large dimensionality of covariates, a simultaneous variable selection and parameter estimation method is developed. To implement the method, a computationally feasible algorithm is described. The proposed method is evaluated empirically by simulation studies and illustrated by analyzing the data arising from the Waterloo Smoking Prevention Project.

[1]  Geert Verbeke,et al.  High dimensional multivariate mixed models for binary questionnaire data , 2006 .

[2]  D. Bates,et al.  Newton-Raphson and EM Algorithms for Linear Mixed-Effects Models for Repeated-Measures Data , 1988 .

[3]  Samuel Müller,et al.  Joint Selection in Mixed Models using Regularized PQL , 2017 .

[4]  Nicholas T. Longford.  Logistic regression with random coefficients , 1994 .

[5]  Gerhard Tutz,et al.  Variable selection for generalized linear mixed models by L1-penalized estimation , 2012, Statistics and Computing.

[6]  Samuel Mueller,et al.  Hierarchical selection of fixed and random effects in generalized linear mixed models , 2017 .

[7]  A. Azzalini,et al.  Statistical applications of the multivariate skew normal distribution , 2009, 0911.2093.

[8]  N. Breslow,et al.  Approximate inference in generalized linear mixed models , 1993 .

[9]  D. Hedeker,et al.  Random effects probit and logistic regression models for three-level data. , 1997, Biometrics.

[10]  Henrik Holmberg,et al.  Generalized linear models with clustered data: Fixed and random effects models , 2011, Comput. Stat. Data Anal..

[11]  D. Rubin,et al.  The ECME algorithm: A simple extension of EM and ECM with faster monotone convergence , 1994 .

[12]  Harvey Goldstein,et al.  Improved Approximations for Multilevel Models with Binary Responses , 1996 .

[13]  R. Wolfinger,et al.  Generalized linear mixed models a pseudo-likelihood approach , 1993 .

[14]  N. Goldman,et al.  Improved estimation procedures for multilevel models with binary response: a case‐study , 2001 .

[15]  J. Ibrahim,et al.  Fixed and Random Effects Selection in Mixed Effects Models , 2011, Biometrics.

[16]  Chao Huang,et al.  Random effects selection in generalized linear mixed models via shrinkage penalty function , 2013, Statistics and Computing.

[17]  M. Genton,et al.  Robust Likelihood Methods Based on the Skew‐t and Related Distributions , 2008 .

[18]  H. Bondell,et al.  Joint Variable Selection for Fixed and Random Effects in Linear Mixed‐Effects Models , 2010, Biometrics.

[19]  Jianqing Fan,et al.  Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties , 2001 .

[20]  K. Brown,et al.  Effectiveness of a social influences smoking prevention program as a function of provider type, training method, and school risk. , 1999, American journal of public health.

[21]  A. Agresti,et al.  A Correlated Probit Model for Joint Modeling of Clustered Binary and Continuous Responses , 2001 .

[22]  P. Phillips,et al.  Model Selection in the Presence of Incidental Parameters , 2013 .

[23]  H. Zou.  The Adaptive Lasso and Its Oracle Properties , 2006 .

[24]  Geert Verbeke,et al.  Pairwise Fitting of Mixed Models for the Joint Modeling of Multivariate Longitudinal Profiles , 2006, Biometrics.

[25]  Raymond J Carroll,et al.  Methods to assess an exercise intervention trial based on 3-level functional data. , 2015, Biostatistics.

[26]  Grace Y. Yi,et al.  A pairwise likelihood approach for longitudinal data with missing observations in both response and covariates , 2013, Comput. Stat. Data Anal..