The HPMIXED Procedure

References

  • Akaike, H. (1974), “A New Look at the Statistical Model Identification,” IEEE Transactions on Automatic Control, AC-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 Institute Inc.

  • 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, 2nd Edition, Cary, NC: SAS Institute Inc.

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

  • Ott, E. R. (1967), “Analysis of Means: A Graphical Procedure,” Industrial Quality Control, 24, 101–109, reprinted in Journal of Quality Technology, 15 (1983), 10–18.

  • Pothoff, R. F. and Roy, S. N. (1964), “A Generalized Multivariate Analysis of Variance Model Useful Especially for Growth Curve Problems,” Biometrika, 51, 313–326.

  • Schabenberger, O., Gregoire, T. G., and Kong, F. (2000), “Collections of Simple Effects and Their Relationship to Main Effects and Interactions in Factorials,” American Statistician, 54, 210–214.

  • 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.

  • 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.

  • Winer, B. J. (1971), Statistical Principles in Experimental Design, 2nd Edition, New York: McGraw-Hill.

  • 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.