Joint Variable Selection for Fixed and Random Effects in Linear Mixed‐Effects Models

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.     

Estimating the distribution of selection coefficients from phylogenetic data with applications to mitochondrial and viral DNA

The distribution of selection coefficients of new mutations is of key interest in population genetics. In this paper we explore how codon-based likelihood models can be used to estimate the distribution of selection coefficients of new amino acid replacement mutations from phylogenetic data. To obtain such estimates we assume that all mutations at the same site have the same selection coefficient. We first estimate the distribution of selection coefficients from two large viral data sets under the assumption that the viral population size is the same along all lineages of the phylogeny and that the selection coefficients vary among sites. We then implement several new models in which the lineages of the phylogeny may have different population sizes. We apply the new models to a data set consisting of the coding regions from eight primate mitochondrial genomes. The results suggest that there might be little power to determine the exact shape of the distribution of selection coefficient but that the normal and gamma distributions fit the data significantly better than the exponential distribution.     

A gene selection algorithm based on the gene regulation probability using maximal likelihood estimation

A novel gene selection algorithm based on the gene regulation probability is proposed. In this algorithm, a probabilistic model is established to estimate gene regulation probabilities using the maximum likelihood estimation method and then these probabilities are used to select key genes related by class distinction. The application on the leukemia data-set suggests that the defined gene regulation probability can identify the key genes to the acute lymphoblastic leukemia (ALL)/acute myeloid leukemia (AML) class distinction and the result of our proposed algorithm is competitive to those of the previous algorithms.