Incorporating LASSO effects into a mixed model for quantitative trait loci detection

  • Scott D. Foster
  • Arūnas P. Verbyla
  • Wayne S. Pitchford
Article

Abstract

The identification of quantitative trait loci (QTL) can be viewed as a subset selection problem. In a simulation study the least absolute selection and shrinkage operator (LASSO) is shown to be a useful and powerful tool for QTL identification. LASSO effects are embedded into a mixed model allowing simultaneous modeling of genetic and experimental effects. This provides the flexibility to model the experiment in conjunction with the power of LASSO QTL identification. Estimation is performed using an approximation to the restricted likelihood and modified Gaussian elimination. The extended mixed model is used to analyze a cattle gene mapping dataset.

Key Words

Adjusted scores Partial Laplace approximation Quantitative trial loci Restricted likelihood Subset selection 

References

  1. Afolayan, R. A., Pitchford, W. S., Weatherly, A. W., and Bottema, C. D. K. (2002), “Genetic Variation in Growth and Body Dimensions of Jersey and Limousin Cross Cattle. 1. Pre-Weaning Performance,”, Asian-Australian Journal of Animal Sciences, 15, 1371–1377.Google Scholar
  2. Broman, K. W., and Speed, T. R. (2002), “A Model Selection Approach for the Identification of Quantitative Trait Loci in Experimental Crosses,”, Journal of the Royal Statistical Society, Series B, 64, 641–656.MATHCrossRefMathSciNetGoogle Scholar
  3. Foster, S. D. (2006), “The LASSO Linear Mixed Model for Mapping Quantitative Trait Loci,” unpublished PhD thesis, University of Adelaide.Google Scholar
  4. Foster, S. D., Verbyla, A. P., and Pitchford, W. S. (2007), “A Random Model Approach for the LASSO,” Computational Statistics, accepted.Google Scholar
  5. Gianola, D., Perez-Enciso, M., and Toro, M. A. (2003), “On Marker-Assisted Prediction of Genetic Value: Beyond the Ridge,”, Genetics, 163, 347–365.Google Scholar
  6. Gilmour, A. R., Thompson, R., and Cullis, B. R. (1995), “Average Information REML: An Efficient Algorithm for Variance Parameter Estimation in Linear Mixed Models,”, Biometrics, 51, 1440–1450.MATHCrossRefGoogle Scholar
  7. Haley, C. S., and Knott, S. A. (1992), “A Simple Regression Method for Mapping Quantitative Trail Loci in Line Crosses Using Flanking Markers,”, Heredity, 69, 315–324.Google Scholar
  8. Henderson, C. R. (1950), “Estimation of Genetic Parameters,”, (abstract), Annals of Mathematical Statistics, 21, 309–310.Google Scholar
  9. Jansen, R. C. (1993), “Interval Mapping of Multiple Quantitative Trait Loci,”, Genetics, 135, 205–211.Google Scholar
  10. Kao, C. H. (2000), “On the Differences Between Maximum Likelihood and Regression Interval Mapping in the Analysis of Quantitative Trait Loci,”, Genetics, 156, 855–865.Google Scholar
  11. Kao, C. H., Zeng, Z. B., and Teasdale, R. D. (1999), “Multiple Interval Mapping for Quantitative Trait Loci,”, Genetics, 152, 1203–1216.Google Scholar
  12. Knott, S. A., Elsen, J. M., and Haley, C. S. (1996,”, Methods for Multiple-Marker Mapping of Quantitative Trait Loci in Half-Sib Populations,”, Theoretical and Applied Genetics, 93, 71–80.CrossRefGoogle Scholar
  13. Lander, E. S., and Botstein, D. (1989), “Mapping Mendelian Factors Underlying Quantitative Traits Using RFLP Linkage Maps,”, Genetics, 121, 185–199.Google Scholar
  14. McCullagh, P., and Tibshirani, R. (1990), “A Simple Method for the Adjustment of Profile Likelihoods,”, Journal of the Royal Statistical Society, Series B, 52, 325–344.MATHMathSciNetGoogle Scholar
  15. Miller, A. (2002), Subset Selection in Regression, Vol. 95 of Monographs on Statistics and Applied Probability (2nd ed.), London: Chapman & Hall/CRC.Google Scholar
  16. Morris, C. A., Cullen, N. G., Pitchford, W. S., Hickey, S. M., Hyndman, D. L., Crawford, A. M., and Bottema, C. D. K. (2003), “QTL for Birth Weight in Bos Taurus Cattle,”, in Proceedings of the Association for the Advancement of Animal Breeding and Genetics, Melbourne, vol. 15, pp. 400–403.Google Scholar
  17. Osborne, M. R. (1985), Finite Algorithms in Optimization and Data Analysis, Wiley Series in Probability and Mathematical Statistics, Chichester: Wiley.MATHGoogle Scholar
  18. Osborne, M. R., Presnell, B., and Turlach, B. A. (2000), “On the LASSO and its Dual,”, Journal of Computational and Graphical Statistics, 9, 319–337.CrossRefMathSciNetGoogle Scholar
  19. Patterson, H. D., and Thompson, R. (1971), “Recovery of Interblock Information when Block Sizes are Unequal,” Biometrika, 31, 100–109.MathSciNetGoogle Scholar
  20. Satagopan, J. M., Yandell, Y. S., Newton, M. A., and Osborn, T. C. (1996), “A Bayesian Approach to Detect Quantitative Trait Loci using Markov Chain Monte Carlo,”, Genetics, 144, 805–816.Google Scholar
  21. Seaton, G., Haley, C. S., Knott, S. A., Kearsey, M., and Visscher, P. M. (2002), “QTL Express: Mapping Quantitative Trait Loci in Simple and Complex Pedigrees,”, Bioinformatics, 18, 339–340.CrossRefGoogle Scholar
  22. Sen, S., and Churchill, G. A. (2001), “A Statistical Framework for Quantitative Trait Mapping,”, Genetics, 159, 371–387.Google Scholar
  23. Taylor, J. D., and Verbyla, A. P. (2006), “Asymptotic Likelihood Approximations Using a Partial Laplace Approximation,”, Australian and New Zealand Journal of Statistics, 48, 465–476.MATHCrossRefMathSciNetGoogle Scholar
  24. Tibshirani, R. (1996), “Regression Shrinkage and Selection via the Lasso,”, Journal of the Royal Statistical Society, Series B, 48, 267–288.MathSciNetGoogle Scholar
  25. Verbyla, A. P. (1990), “A Conditional Derivation of Residual Maximum Likelihood,”, Australian Journal of Statistics, 32, 227–230.CrossRefGoogle Scholar
  26. Wang, H., Zhang, Y. M., Li, X. M., Masinde, G. L., Mohan, S., Baylink, D. J., and Xu, S. Z. (2005), “Bayesian Shrinkage Estimation of Quantitative Trait Loci Parameters,”, Genetics, 170, 465–480.CrossRefGoogle Scholar
  27. Whittaker, J. C., Thompson, R., and Denham, M. C. (2000), “Marker-Assisted Selection Using Ridge Regression,”, Genetical Research, 75, 249–252.CrossRefGoogle Scholar
  28. Xu, S. Z. (2003), “Estimating Polygenic Effects Using Markers of the Entire Genome,”, Genetics 163, 789–801.Google Scholar
  29. Yi, N. J., Yandell, B. S., Churchill, G. A., Allison, D. B., Eisen, E. J., and Pomp, D. (2005), “Bayesian Model Selection for Genome-Wide Epistatic Quantitative Trait Loci Analysis,”, Genetics, 170, 1333–1344.CrossRefGoogle Scholar
  30. Zeng, Z. B. (1994), “Precision Mapping of Quantitative Trait Loci,”, Genetics, 136, 1457–1468.Google Scholar

Copyright information

© International Biometric Society 2007

Authors and Affiliations

  • Scott D. Foster
    • 1
  • Arūnas P. Verbyla
    • 1
  • Wayne S. Pitchford
    • 1
  1. 1.School of Agriculture, Food and WineThe University of AdelaideGlen Osmond
  2. 2.CSIRO Mathematical and Information SciencesHobartAustralia

Personalised recommendations