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Hierarchical Generalized Linear Models For Multiple Quantitative Trait Locus Mapping

Nengjun Yi, Samprit Banerjee

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Abstract We develop hierarchical generalized linear models and computationally efficient algorithms for genomewide analysis of quantitative trait loci (QTL) for various types of phenotypes in experimental crosses. The proposed models can fit a large number of effects, including covariates, main effects of numerous loci, and gene–gene (epistasis) and gene–environment (G × E) interactions. The key to the approach is the use of continuous prior distribution on coefficients that favors sparseness in the fitted model and facilitates computation. We develop a fast expectation-maximization (EM) algorithm to fit models by estimating posterior modes of coefficients. We incorporate our algorithm into the iteratively weighted least squares for classical generalized linear models as implemented in the package R. We propose a model search strategy to build a parsimonious model. Our method takes advantage of the special correlation structure in QTL data. Simulation studies demonstrate reasonable power to detect true effects, while controlling the rate of false positives. We illustrate with three real data sets and compare our method to existing methods for multiple-QTL mapping. Our method has been implemented in our freely available package R/qtlbim (www.qtlbim.org), providing a valuable addition to our previous Markov chain Monte Carlo (MCMC) approach.