The HPLMIXED Procedure

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

Bates, D. M., Lindstrom, M. J., Wahba, G., and Yandell, B. S. (1987), “GCVPACK-Routines for Generalized Cross Validation,” Communications in Statistics—Simulation and Computation, 16, 263–297.

Burdick, R. K. and Graybill, F. A. (1992), Confidence Intervals on Variance Components, New York: Marcel Dekker.

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

Carlin, B. P. and Louis, T. A. (1996), Bayes and Empirical Bayes Methods for Data Analysis, London: Chapman & Hall.

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.

Fuller, W. A. (1976), Introduction to Statistical Time Series, New York: John Wiley & Sons.

Hartley, H. O. and Rao, J. N. K. (1967), “Maximum-Likelihood Estimation for the Mixed Analysis of Variance Model,” Biometrika, 54, 93–108.

Harville, D. A. (1977), “Maximum Likelihood Approaches to Variance Component Estimation and to Related Problems,” Journal of the American Statistical Association, 72, 320–338.

Harville, D. A. (1988), “Mixed-Model Methodology: Theoretical Justifications and Future Directions,” in Proceedings of the Statistical Computing Section, 41–49, Alexandria, VA: American Statistical Association.

Harville, D. A. (1990), “BLUP (Best Linear Unbiased Prediction), and Beyond,” in D. Gianola and K. Hammond, eds., Advances in Statistical Methods for Genetic Improvement of Livestock, volume 18 of Advanced Series in Agricultural Sciences, 239–276, Berlin: Springer-Verlag.

Henderson, C. R. (1984), Applications of Linear Models in Animal Breeding, Guelph, ON: University of Guelph.

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.

Huynh, H. and Feldt, L. S. (1970), “Conditions Under Which Mean Square Ratios in Repeated Measurements Designs Have Exact F-Distributions,” Journal of the American Statistical Association, 65, 1582–1589.

Jennrich, R. I. and Schluchter, M. D. (1986), “Unbalanced Repeated-Measures Models with Structured Covariance Matrices,” Biometrics, 42, 805–820.

Kenward, M. G. (1987), “A Method for Comparing Profiles of Repeated Measurements,” Applied Statistics, 36, 296–308.

Laird, N. M., Lange, N. T., and Stram, D. O. (1987), “Maximum Likelihood Computations with Repeated Measures: Application of the EM Algorithm,” Journal of the American Statistical Association, 82, 97–105.

Laird, N. M. and Ware, J. H. (1982), “Random-Effects Models for Longitudinal Data,” Biometrics, 38, 963–974.

Lindstrom, M. J. and Bates, D. M. (1988), “Newton-Raphson and EM Algorithms for Linear Mixed-Effects Models for Repeated-Measures Data,” Journal of the American Statistical Association, 83, 1014–1022.

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.

Little, R. J. A. (1995), “Modeling the Drop-Out Mechanism in Repeated-Measures Studies,” Journal of the American Statistical Association, 90, 1112–1121.

Macchiavelli, R. E. and Arnold, S. F. (1994), “Variable Order Ante-dependence Models,” Communications in Statistics—Theory and Methods, 23, 2683–2699.

McLean, R. A. and Sanders, W. L. (1988), “Approximating Degrees of Freedom for Standard Errors in Mixed Linear Models,” in Proceedings of the Statistical Computing Section, 50–59, Alexandria, VA: American Statistical Association.

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

Milliken, G. A. and Johnson, D. E. (1992), Designed Experiments, volume 1 of Analysis of Messy Data, New York: Chapman & Hall.

Patel, H. I. (1991), “Analysis of Incomplete Data from a Clinical Trial with Repeated Measurements,” Biometrika, 78, 609–619.

Patterson, H. D. and Thompson, R. (1971), “Recovery of Inter-block Information When Block Sizes Are Unequal,” Biometrika, 58, 545–554.

Robinson, G. K. (1991), “That BLUP Is a Good Thing: The Estimation of Random Effects,” Statistical Science, 6, 15–51.

Rubin, D. B. (1976), “Inference and Missing Data,” Biometrika, 63, 581–592.

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

Searle, S. R. (1971), Linear Models, New York: John Wiley & Sons.

Searle, S. R. (1982), Matrix Algebra Useful for Statisticians, New York: John Wiley & Sons.

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

Serfling, R. J. (1980), Approximation Theorems of Mathematical Statistics, New York: John Wiley & Sons.

Snedecor, G. W. and Cochran, W. G. (1980), Statistical Methods, 7th Edition, Ames: Iowa State University Press.

Steel, R. G. D., Torrie, J. H., and Dickey, D. A. (1997), Principles and Procedures of Statistics: A Biometrical Approach, 3rd Edition, New York: McGraw-Hill.

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. (1996), “Heterogeneous Variance-Covariance Structures for Repeated Measures,” Journal of Agricultural, Biological, and Environmental Statistics, 1, 205–230.

Wolfinger, R. D., Tobias, R. D., and Sall, J. (1994), “Computing Gaussian Likelihoods and Their Derivatives for General Linear Mixed Models,” SIAM Journal on Scientific Computing, 15, 1294–1310.