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 Genetic Analysis of Complex Traits Using SAS, edited by A. M. Saxton, 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 ed. 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 ed. 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.