Hierarchical Generalized Linear Models for Multiple Quantitative Trait Locus Mapping

By Yi, Nengjun; Banerjee, Samprit | Genetics, March 2009 | Go to article overview

Hierarchical Generalized Linear Models for Multiple Quantitative Trait Locus Mapping


Yi, Nengjun, Banerjee, Samprit, Genetics


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.

MOST complex traits are influenced by interacting networks of multiple quantitative trait loci (QTL) and environmental factors (Carlborg and Haley 2004). Mapping QTL is to infer which genomic loci are strongly associated with the complex trait and to estimate genetic effects of these loci, i.e.,main effectsand gene-gene (epistasis) and gene-environment (G × E) interactions. Due to the multilocus nature of complex traits, it is desirable to simultaneously analyze multiple loci rather than one locus (or a few loci) at a time. However, QTL mapping studies usually genotype hundreds or thousands of genomic loci (markers), leading to numerous variables and a huge number of possible models, and the dependence of genotypes on a chromosome results inmanycorrelated variables.Therefore,mapping multiple QTL requires sophisticated methods that can handle problems with high-dimensional correlated variables.

The popular approaches to mapping multiple QTL are some form of variable selection. Such techniques involve identifying a subset of all possible genetic effects (a multiple-QTL model) that best explains the phenotypic variation. Classical variable selection methods use forward or stepwise search procedures and selection criteria such as Bayesian information criteria (BIC) or modified versions to find a multiple-QTL model (Kao et al. 1999; Broman and Speed 2002; Bogdan et al. 2004; Baierl et al. 2006). Bayesian methods proceed by setting up a likelihood function for observed data and prior distributions on unobserved quantities. Two types of prior distributions have been suggested for multiple-QTL mapping. The first assumes a two-component mixture distribution for each genetic effect, typically a normal distribution with known or unknown variance and a point mass at zero. This discrete prior allows each effect to have positive probability of dropping out of the model (Yi 2004; Yiand Shriner 2008). The second formulation takes continuous prior distributions for genetic effects that favor a sparse structure with many of the effects having values close to zero and few with large values (Meuwissen et al. 2001; Xu 2003; Yi and Xu 2008). These Bayesian models are computed using Markov chain Monte Carlo (MCMC) algorithms to sample from the posterior distribution. Due to the recent development of MCMC algorithms and associated computer software, Bayesian methods have become increasingly popular inQTLmapping (Yiet al. 2005, 2007a,b; Yandell et al. 2007; Yi and Shriner 2008). The Bayesian MCMC approaches can provide comprehensive information, but they are computationally intensive in interacting- QTL analysis. …

The rest of this article is only available to active members of Questia

Already a member? Log in now.

Notes for this article

Add a new note
If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
One moment ...
Default project is now your active project.
Project items
Notes
Cite this article

Cited article

Style
Citations are available only to our active members.
Buy instant access to cite pages or passages in MLA 8, MLA 7, APA and Chicago citation styles.

(Einhorn, 1992, p. 25)

(Einhorn 25)

(Einhorn 25)

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

Note: primary sources have slightly different requirements for citation. Please see these guidelines for more information.

Cited article

Hierarchical Generalized Linear Models for Multiple Quantitative Trait Locus Mapping
Settings

Settings

Typeface
Text size Smaller Larger Reset View mode
Search within

Search within this article

Look up

Look up a word

  • Dictionary
  • Thesaurus
Please submit a word or phrase above.
Print this page

Print this page

Why can't I print more than one page at a time?

Help
Full screen
Items saved from this article
  • Highlights & Notes
  • Citations
Some of your highlights are legacy items.

Highlights saved before July 30, 2012 will not be displayed on their respective source pages.

You can easily re-create the highlights by opening the book page or article, selecting the text, and clicking “Highlight.”

matching results for page

    Questia reader help

    How to highlight and cite specific passages

    1. Click or tap the first word you want to select.
    2. Click or tap the last word you want to select, and you’ll see everything in between get selected.
    3. You’ll then get a menu of options like creating a highlight or a citation from that passage of text.

    OK, got it!

    Cited passage

    Style
    Citations are available only to our active members.
    Buy instant access to cite pages or passages in MLA 8, MLA 7, APA and Chicago citation styles.

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn, 1992, p. 25).

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences."1

    1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

    Cited passage

    Thanks for trying Questia!

    Please continue trying out our research tools, but please note, full functionality is available only to our active members.

    Your work will be lost once you leave this Web page.

    Buy instant access to save your work.

    Already a member? Log in now.

    Search by... Author
    Show... All Results Primary Sources Peer-reviewed

    Oops!

    An unknown error has occurred. Please click the button below to reload the page. If the problem persists, please try again in a little while.