@article{bondell_krishna_ghosh_2010, title={Joint Variable Selection for Fixed and Random Effects in Linear Mixed-Effects Models}, volume={66}, ISSN={["1541-0420"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-78650073483&partnerID=MN8TOARS}, DOI={10.1111/j.1541-0420.2010.01391.x}, abstractNote={Summary It is of great practical interest to simultaneously identify the important predictors that correspond to both the fixed and random effects components in a linear mixed‐effects (LME) model. Typical approaches perform selection separately on each of the fixed and random effect components. However, changing the structure of one set of effects can lead to different choices of variables for the other set of effects. We propose simultaneous selection of the fixed and random factors in an LME model using a modified Cholesky decomposition. Our method is based on a penalized joint log likelihood with an adaptive penalty for the selection and estimation of both the fixed and random effects. It performs model selection by allowing fixed effects or standard deviations of random effects to be exactly zero. A constrained expectation–maximization algorithm is then used to obtain the final estimates. It is further shown that the proposed penalized estimator enjoys the Oracle property, in that, asymptotically it performs as well as if the true model was known beforehand. We demonstrate the performance of our method based on a simulation study and a real data example.}, number={4}, journal={BIOMETRICS}, author={Bondell, Howard D. and Krishna, Arun and Ghosh, Sujit K.}, year={2010}, month={Dec}, pages={1069–1077} }
 @article{krishna_bondell_ghosh_2009, title={Bayesian variable selection using an adaptive powered correlation prior}, volume={139}, ISSN={["1873-1171"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-67349268430&partnerID=MN8TOARS}, DOI={10.1016/j.jspi.2008.12.004}, abstractNote={The problem of selecting the correct subset of predictors within a linear model has received much attention in recent literature. Within the Bayesian framework, a popular choice of prior has been Zellner's g-prior which is based on the inverse of empirical covariance matrix of the predictors. An extension of the Zellner's prior is proposed in this article which allow for a power parameter on the empirical covariance of the predictors. The power parameter helps control the degree to which correlated predictors are smoothed towards or away from one another. In addition, the empirical covariance of the predictors is used to obtain suitable priors over model space. In this manner, the power parameter also helps to determine whether models containing highly collinear predictors are preferred or avoided. The proposed power parameter can be chosen via an empirical Bayes method which leads to a data adaptive choice of prior. Simulation studies and a real data example are presented to show how the power parameter is well determined from the degree of cross-correlation within predictors. The proposed modification compares favorably to the standard use of Zellner's prior and an intrinsic prior in these examples.}, number={8}, journal={JOURNAL OF STATISTICAL PLANNING AND INFERENCE}, author={Krishna, Arun and Bondell, Howard D. and Ghosh, Sujit K.}, year={2009}, month={Aug}, pages={2665–2674} }