References

Akaike, H. (1974), “A New Look at Statistical Model Identification,” IEEE Transactions on Automatic Control, 19, 716–723.

Bozdogan, H. (1987), “Model Selection and Akaike’s Information Criterion (AIC): The General Theory and Its Analytical Extensions,” Psychometrika, 52, 345–370.

Brown, H. and Prescott, R. (1999), Applied Mixed Models in Medicine, New York: John Wiley & Sons.

Burnham, K. P. and Anderson, D. R. (1998), Model Selection and Inference: A Practical Information-Theoretic Approach, New York: Springer-Verlag.

Churchill, G. A. (2002), “Fundamentals of Experimental Design for cDNA Microarray,” Nature Genetics, 32, 490–495.

Dempster, A. P., Laird, N. M., and Rubin, D. B. (1977), “Maximum Likelihood from Incomplete Data via the EM Algorithm,” Journal of the Royal Statistical Society, Series B, 39, 1–38.

George, J. A. and Liu, J. W. (1981), Computer Solutions of Large Sparse Positive Definite Systems, Englewood Cliffs, NJ: Prentice-Hall.

Gibson, G. and Wolfinger, R. D. (2004), “Gene Expression Profiling Using Mixed Models,” in A. M. Saxton, ed., Genetic Analysis of Complex Traits Using SAS, 251–278, Cary, NC: SAS Publishing.

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.

Hannan, E. J. and Quinn, B. G. (1979), “The Determination of the Order of an Autoregression,” Journal of the Royal Statistical Society, Series B, 41, 190–195.

Henderson, C. R. (1990), “Statistical Method in Animal Improvement: Historical Overview,” in Advances in Statistical Methods for Genetic Improvement of Livestock, 1–14, New York: Springer-Verlag.

Hurvich, C. M. and Tsai, C.-L. (1989), “Regression and Time Series Model Selection in Small Samples,” Biometrika, 76, 297–307.

Johnson, D. L. and Thompson, R. (1995), “Restricted Maximum Likelihood Estimation of Variance Components for Univariate Animal Models Using Sparse Matrix Techniques and Average Information,” Journal of Dairy Science, 78, 449–456.

Kerr, M. K., Martin, M., and Churchill, G. A. (2000), “Analysis of Variance for Gene Expression Microarray Data,” Journal of Computational Biology, 7, 819–837.

Littell, R. C., Milliken, G. A., Stroup, W. W., and Wolfinger, R. D. (1996), SAS System for Mixed Models, Cary, NC: SAS Institute Inc.

Littell, R. C., Milliken, G. A., Stroup, W. W., Wolfinger, R. D., and Schabenberger, O. (2006), SAS for Mixed Models, Second Edition, Cary, NC: SAS Press.

McLean, R. A., Sanders, W. L., and Stroup, W. W. (1991), “A Unified Approach to Mixed Linear Models,” The American Statistician, 45, 54–64.

Schwarz, G. (1978), “Estimating the Dimension of a Model,” Annals of Statistics, 6, 461–464.

Searle, S. R., Casella, G., and McCulloch, C. E. (1992), Variance Components, New York: John Wiley & Sons.

Shewchuk, J. R. (1994), An Introduction to the Conjugate Gradient Method without the Agonizing Pain, Technical report, Carnegie Mellon University, Pittsburgh, PA.

Tsuruta, S., Misztal, I., and Stranden, I. (2001), “Use of the Preconditioned Conjugate Gradient Algorithm as a Generic Solver for Mixed-Model Equations in Animal Breeding Apllications,” Journal of Animal Science, 79, 1166–1172.

Verbeke, G. and Molenberghs, G., eds. (1997), Linear Mixed Models in Practice: A SAS-Oriented Approach, New York: Springer.

Verbeke, G. and Molenberghs, G. (2000), Linear Mixed Models for Longitudinal Data, New York: Springer.

Wolfinger, R. D., Gibson, G., Wolfinger, E., Bennett, L., Hamadeh, H., Bushel, P., Afshari, C., and Paules, R. S. (2001), “Assessing Gene Significance from cDNA Microarray Expression Data via Mixed Models,” Journal of Computational Biology, 8, 625–637.