The GLIMMIX Procedure

References

  • Abramowitz, M. and Stegun, I. A. (1972), Handbook of Mathematical Functions, New York: Dover Publications.

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

  • Bahadur, R. R. (1961), Studies in Item Analysis and Prediction, chapter A Representation of the Joint Distribution of Responses to n Dichotomous Items, Stanford, CA: Stanford University Press.

  • Beale, E. M. L. (1972), “A Derivation of Conjugate Gradients,” in F. A. Lootsma, ed., Numerical Methods for Nonlinear Optimization, London: Academic Press.

  • Bell, R. M. and McCaffrey, D. F. (2002), “Bias Reduction in Standard Errors for Linear Regression with Multi-Stage Samples,” Survey Methodology, 28, 169–181.

  • Bickel, P. J. and Doksum, K. A. (1977), Mathematical Statistics, San Francisco: Holden-Day.

  • Booth, J. G. and Hobert, J. P. (1998), “Standard Errors of Prediction in Generalized Linear Mixed Models,” Journal of the American Statistical Association, 93, 262–272.

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

  • Breslow, N. E. and Clayton, D. G. (1993), “Approximate Inference in Generalized Linear Mixed Models,” Journal of the American Statistical Association, 88, 9–25.

  • Breslow, N. E. and Lin, X. (1995), “Bias Correction in Generalised Linear Mixed Models with a Single Component of Dispersion,” Biometrika, 81, 81–91.

  • Brinkman, N. D. (1981), “Ethanol Fuel—A Single-Cylinder Engine Study of Efficiency and Exhaust Emissions,” Society of Automotive Engineers Transactions, 90, 1410–1424.

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

  • 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.

  • Cameron, A. C. and Trivedi, P. K. (1998), Regression Analysis of Count Data, Cambridge: Cambridge University Press.

  • Clayton, D. and Kaldor, J. (1987), “Empirical Bayes Estimates of Age-Standardized Relative Risks for Use in Disease Mapping,” Biometrics, 43, 671–681.

  • Cleveland, W. S. and Grosse, E. (1991), “Computational Methods for Local Regression,” Statistics and Computing, 1, 47–62.

  • Cockerham, C. C. and Weir, B. S. (1977), “Quadratic Analyses of Reciprocal Crosses,” Biometrics, 33, 187–203.

  • Davis, A. W. (1977), “A Differential Equation Approach to Linear Combinations of Independent Chi-Squares,” Journal of the American Statistical Association, 72, 212–214.

  • de Boor, C. (2001), A Practical Guide to Splines, Revised Edition, New York: Springer-Verlag.

  • Dennis, J. E., Gay, D. M., and Welsch, R. E. (1981), “An Adaptive Nonlinear Least-Squares Algorithm,” ACM Transactions on Mathematical Software, 7, 348–368.

  • Dennis, J. E. and Mei, H. H. W. (1979), “Two New Unconstrained Optimization Algorithms Which Use Function and Gradient Values,” Journal of Optimization Theory Applications, 28, 453–482.

  • Dennis, J. E. and Schnabel, R. B. (1983), Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Englewood, NJ: Prentice-Hall.

  • Diggle, P. J., Liang, K.-Y., and Zeger, S. L. (1994), Analysis of Longitudinal Data, Oxford: Clarendon Press.

  • Dunnett, C. W. (1980), “Pairwise Multiple Comparisons in the Unequal Variance Case,” Journal of the American Statistical Association, 75, 796–800.

  • Edwards, D. and Berry, J. J. (1987), “The Efficiency of Simulation-Based Multiple Comparisons,” Biometrics, 43, 913–928.

  • Eilers, P. H. C. and Marx, B. D. (1996), “Flexible Smoothing with B-Splines and Penalties,” Statistical Science, 11, 89–121, with discussion.

  • Eskow, E. and Schnabel, R. B. (1991), “Algorithm 695: Software for a New Modified Cholesky Factorization,” ACM Transactions on Mathematical Software, 17, 306–312.

  • Evans, G. (1993), Practical Numerical Integration, New York: John Wiley & Sons.

  • Fai, A. H. T. and Cornelius, P. L. (1996), “Approximate F-Tests of Multiple Degree of Freedom Hypotheses in Generalized Least Squares Analyses of Unbalanced Split-Plot Experiments,” Journal of Statistical Computation and Simulation, 54, 363–378.

  • Fay, M. P. and Graubard, B. I. (2001), “Small-Sample Adjustments for Wald-Type Tests Using Sandwich Estimators,” Biometrics, 57, 1198–1206.

  • Ferrari, S. L. P. and Cribari-Neto, F. (2004), “Beta Regression for Modelling Rates and Proportions,” Journal of Applied Statistics, 31, 799–815.

  • Fisher, R. A. (1936), “The Use of Multiple Measurements in Taxonomic Problems,” Annals of Eugenics, 7, 179–188.

  • Fletcher, R. (1987), Practical Methods of Optimization, Second Edition, Chichester, UK: John Wiley & Sons.

  • Friedman, J. H., Bentley, J. L., and Finkel, R. A. (1977), “An Algorithm for Finding Best Matches in Logarithmic Expected Time,” ACM Transactions on Mathematical Software, 3, 209–226.

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

  • Games, P. A. and Howell, J. F. (1976), “Pairwise Multiple Comparison Procedures with Unequal n’s and/or Variances: A Monte Carlo Study,” Journal of Educational Statistics, 1, 113–125.

  • Gay, D. M. (1983), “Subroutines for Unconstrained Minimization,” ACM Transactions on Mathematical Software, 9, 503–524.

  • Giesbrecht, F. G. and Burns, J. C. (1985), “Two-Stage Analysis Based on a Mixed Model: Large-Sample Asymptotic Theory and Small-Sample Simulation Results,” Biometrics, 41, 477–486.

  • Gilliland, D. and Schabenberger, O. (2001), “Limits on Pairwise Association for Equi-Correlated Binary Variables,” Journal of Applied Statistical Sciences, 10, 279–285.

  • Gilmour, A. R., Anderson, R. D., and Rae, A. L. (1987), “Variance Components on an Underlying Scale for Ordered Multiple Threshold Categorical Data Using a Generalized Linear Mixed Model,” Journal of Animal Breeding and Genetics, 104, 149–155.

  • Golub, G. H. and Welsch, J. H. (1969), “Calculation of Gaussian Quadrature Rules,” Mathematical Computing, 23, 221–230.

  • Goodnight, J. H. (1978a), Computing MIVQUE0 Estimates of Variance Components, Technical report, SAS Institute Inc, Cary, NC, SAS Technical Report R-105 Edition.

  • Goodnight, J. H. (1978b), Tests of Hypotheses in Fixed-Effects Linear Models, Technical Report R-101, SAS Institute Inc, Cary, NC.

  • Goodnight, J. H. (1979), “A Tutorial on the Sweep Operator,” The American Statistician, 33, 149–158.

  • Goodnight, J. H. and Hemmerle, W. J. (1979), “A Simplified Algorithm for the W-Transformation in Variance Component Estimation,” Technometrics, 21, 265–268.

  • Gotway, C. A. and Stroup, W. W. (1997), “A Generalized Linear Model Approach to Spatial Data and Prediction,” Journal of Agricultural, Biological, and Environmental Statistics, 2, 157–187.

  • Guirguis, G. and Tobias, R. D. (2004), “On the Computation of the Distribution for the Analysis of Means,” Communications in Statistics: Simulation and Computation, 33, 861–888.

  • Hand, D. J., Daly, F., Lunn, A. D., McConway, K. J., and Ostrowski, E. (1994), A Handbook of Small Data Sets, London: Chapman & Hall.

  • Handcock, M. S. and Stein, M. L. (1993), “A Bayesian Analysis of Kriging,” Technometrics, 35, 403–410.

  • Handcock, M. S. and Wallis, J. R. (1994), “An Approach to Statistical Spatial-Temporal Modeling of Meteorological Fields (with Discussion),” Journal of the American Statistical Association, 89, 368–390.

  • 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.

  • Harville, D. A. and Jeske, D. R. (1992), “Mean Squared Error of Estimation or Prediction under a General Linear Model,” Journal of the American Statistical Association, 87, 724–731.

  • Hastie, T., Tibshirani, R., and Friedman, J. (2001), The Elements of Statistical Learning, New York: Springer-Verlag.

  • Hemmerle, W. J. and Hartley, H. O. (1973), “Computing Maximum Likelihood Estimates for the Mixed AOV Model Using the W-Transformation,” Technometrics, 15, 819–831.

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

  • Hinkley, D. V. (1977), “Jackknifing in Unbalanced Situations,” Technometrics, 19, 285–292.

  • Hirotsu, C. and Srivastava, M. (2000), “Simultaneous Confidence Intervals Based on One-Sided Max t Test,” Statistics and Probability Letters, 49, 25–37.

  • Holm, S. (1979), “A Simple Sequentially Rejective Multiple Test Procedure,” Scandinavian Journal of Statistics, 6, 65–70.

  • Hsu, J. C. (1992), “The Factor Analytic Approach to Simultaneous Inference in the General Linear Model,” Journal of Computational and Graphical Statistics, 1, 151–168.

  • Hsu, J. C. (1996), Multiple Comparisons: Theory and Methods, London: Chapman & Hall.

  • Hsu, J. C. and Peruggia, M. (1994), “Graphical Representation of Tukey’s Multiple Comparison Method,” Journal of Computational and Graphical Statistics, 3, 143–161.

  • Huber, P. J. (1967), “The Behavior of Maximum Likelihood Estimates under Nonstandard Conditions,” Proc. Fifth Berkeley Symp. Math. Statist. Prob., 1, 221–233.

  • 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.

  • Joe, H. and Zhu, R. (2005), “Generalized Poisson Distribution: The Property of Mixture of Poisson and Comparison with Negative Binomial Distribution,” Biometrical Journal, 47, 219–229.

  • Johnson, N. L., Kotz, S., and Balakrishnan, N. (1994), Continuous Univariate Distributions, volume 1, Second Edition, New York: John Wiley & Sons.

  • Kackar, R. N. and Harville, D. A. (1984), “Approximations for Standard Errors of Estimators of Fixed and Random Effects in Mixed Linear Models,” Journal of the American Statistical Association, 79, 853–862.

  • Kahaner, D., Moler, C., and Nash, S. (1989), Numerical Methods and Software, Englewood Cliffs: Prentice-Hall.

  • Karim, M. Z. and Zeger, S. L. (1992), “Generalized Linear Models with Random Effects; Salamander Mating Revisited,” Biometrics, 48, 631–644.

  • Kass, R. E. and Steffey, D. (1989), “Approximate Bayesian Inference in Conditionally Independent Hierarchical Models (Parametric Empirical Bayes Models),” Journal of the American Statistical Association, 84, 717–726.

  • Kauermann, G. and Carroll, R. J. (2001), “A Note on the Efficiency of Sandwich Covariance Estimation,” Journal of the American Statistical Association, 96, 1387–1396.

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

  • Kenward, M. G. and Roger, J. H. (1997), “Small Sample Inference for Fixed Effects from Restricted Maximum Likelihood,” Biometrics, 53, 983–997.

  • Kenward, M. G. and Roger, J. H. (2009), “An Improved Approximation to the Precision of Fixed Effects from Restricted Maximum Likelihood,” Computational Statistics and Data Analysis, 53, 2583–2595.

  • Koch, G. G., Carr, G. J., Amara, I. A., Stokes, M. E., and Uryniak, T. J. (1990), Statistical Methodology in the Pharmaceutical Sciences, chapter Categorical Data Analysis, New York: Marcel Dekker.

  • Kramer, C. Y. (1956), “Extension of Multiple Range Tests to Group Means with Unequal Numbers of Replications,” Biometrics, 12, 307–310.

  • Lange, K. (1999), Numerical Analysis for Statisticians, New York: Springer-Verlag.

  • Liang, K.-Y. and Zeger, S. L. (1986), “Longitudinal Data Analysis Using Generalized Linear Models,” Biometrika, 73, 13–22.

  • Lin, X. and Breslow, N. E. (1996), “Bias Correction in Generalized Linear Mixed Models with Multiple Components of Dispersion,” Journal of the American Statistical Association, 91, 1007–1016.

  • 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.

  • Long, J. S. and Ervin, L. H. (2000), “Using Heteroscedasticity Consistent Standard Errors in the Linear Regression Model,” The American Statistician, 54, 217–224.

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

  • MacKinnon, J. G. and White, H. (1985), “Some Heteroskedasticity-Consistent Covariance Matrix Estimators with Improved Finite Sample Properties,” Journal of Econometrics, 29, 305–325.

  • Mancl, L. A. and DeRouen, T. A. (2001), “A Covariance Estimator for GEE with Improved Small-Sample Properties,” Biometrics, 57, 126–134.

  • Matérn, B. (1986), Spatial Variation, Second Edition, New York: Springer-Verlag.

  • McCullagh, P. (1980), “Regression Models for Ordinal Data,” Journal of the Royal Statistical Society, Series B, 42, 109–142.

  • McCullagh, P. and Nelder, J. A. (1989), Generalized Linear Models, Second Edition, London: Chapman & Hall.

  • McLean, R. A. and Sanders, W. L. (1988), “Approximating Degrees of Freedom for Standard Errors in Mixed Linear Models,” Proceedings of the Statistical Computing Section.

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

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

  • Moré, J. J. (1978), “The Levenberg-Marquardt Algorithm: Implementation and Theory,” in G. A. Watson, ed., Lecture Notes in Mathematics, volume 30, 105–116, Berlin: Springer-Verlag.

  • Moré, J. J. and Sorensen, D. C. (1983), “Computing a Trust-Region Step,” SIAM Journal on Scientific and Statistical Computing, 4, 553–572.

  • Morel, J. G. (1989), “Logistic Regression under Complex Survey Designs,” Survey Methodology, 15, 203–223.

  • Morel, J. G., Bokossa, M. C., and Neerchal, N. K. (2003), “Small Sample Correction for the Variance of GEE Estimators,” Biometrical Journal, 4, 395–409.

  • Moriguchi, S., ed. (1976), Statistical Method for Quality Control, (in Japanese), Tokyo: Japan Standards Association.

  • Mosteller, F. and Tukey, J. W. (1977), Data Analysis and Regression, Reading, MA: Addison-Wesley.

  • Murray, D. M., Varnell, S. P., and Blitstein, J. L. (2004), “Design and Analysis of Group-Randomized Trials: A Review of Recent Methodological Developments,” American Journal of Public Health, 94, 423–432.

  • National Institute of Standards and Technology (1998), “Statistical Reference Data Sets,” http://www.itl.nist.gov/div898/strd/general/dataarchive.html, last accessed June 6, 2011.

  • Nelder, J. A. and Wedderburn, R. W. M. (1972), “Generalized Linear Models,” Journal of the Royal Statistical Society, Series A, 135, 370–384.

  • Nelson, P. R. (1982), “Exact Critical Points for the Analysis of Means,” Communications in Statistics, Part A: Theory and Methods, 699–709.

  • Nelson, P. R. (1991), “Numerical Evaluation of Multivariate Normal Integrals with Correlations $\rho _{lj} = -\alpha _ l\alpha _ j$,” Frontiers of Statistical Scientific Theory and Industrial Applications, 97–114.

  • Nelson, P. R. (1993), “Additional Uses for the Analysis of Means and Extended Tables of Critical Values,” Technometrics, 35, 61–71.

  • 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.

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

  • Pawitan, Y. (2001), In All Likelihood: Statistical Modelling and Inference Using Likelihood, Oxford: Clarendon Press.

  • Pinheiro, J. C. and Bates, D. M. (1995), “Approximations to the Log-Likelihood Function in the Nonlinear Mixed-Effects Model,” Journal of Computational and Graphical Statistics, 4, 12–35.

  • Pinheiro, J. C. and Chao, E. C. (2006), “Efficient Laplacian and Adaptive Gaussian Quadrature Algorithms for Multilevel Generalized Linear Mixed Models,” Journal of Computational and Graphical Statistics, 15, 58–81.

  • Polak, E. (1971), Computational Methods in Optimization, New York: Academic Press.

  • 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.

  • Powell, M. J. D. (1977), “Restart Procedures for the Conjugate Gradient Method,” Mathematical Programming, 12, 241–254.

  • Prasad, N. G. N. and Rao, J. N. K. (1990), “The Estimation of Mean Squared Error of Small-Area Estimators,” Journal of the American Statistical Association, 85, 163–171.

  • Pringle, R. M. and Rayner, A. A. (1971), Generalized Inverse Matrices with Applications to Statistics, New York: Hafner Publishing.

  • Raudenbush, S. M., Yang, M.-L., and Yosef, M. (2000), “Maximum Likelihood for Generalized Linear Models with Nested Random Effects via Higher-Order, Multivariate Laplace Approximation,” Journal of Computational and Graphical Statistics, 9, 141–157.

  • Royen, T. (1989), “Generalized Maximum Range Tests for Pairwise Comparisons of Several Populations,” Biometrical Journal, 31, 905–929.

  • Ruppert, D., Wand, M. P., and Carroll, R. J. (2003), Semiparametric Regression, Cambridge: Cambridge University Press.

  • Saxton, A., ed. (2004), Genetic Analysis of Complex Traits Using SAS, Cary, NC: SAS Institute Inc.

  • Schabenberger, O. and Gregoire, T. G. (1996), “Population-Averaged and Subject-Specific Approaches for Clustered Categorical Data,” Journal of Statistical Computation and Simulation, 54, 231–253.

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

  • Schabenberger, O. and Pierce, F. J. (2002), Contemporary Statistical Models for the Plant and Soil Sciences, Boca Raton, FL: CRC Press.

  • Schall, R. (1991), “Estimation in Generalized Linear Models with Random Effects,” Biometrika, 78, 719–727.

  • Schluchter, M. D. and Elashoff, J. D. (1990), “Small-Sample Adjustments to Tests with Unbalanced Repeated Measures Assuming Several Covariance Structures,” Journal of Statistical Computation and Simulation, 37, 69–87.

  • 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.

  • Self, S. G. and Liang, K.-Y. (1987), “Asymptotic Properties of Maximum Likelihood Estimators and Likelihood Ratio Tests under Nonstandard Conditions,” Journal of the American Statistical Association, 82, 605–610.

  • Shaffer, J. P. (1986), “Modified Sequentially Rejective Multiple Test Procedures,” Journal of the American Statistical Association, 81, 826–831.

  • Shapiro, A. (1988), “Towards a Unified Theory of Inequality Constrained Testing in Multivariate Analysis,” International Statistical Review, 56, 49–62.

  • Shun, Z. (1997), “Another Look at the Salamander Mating Data: A Modified Laplace Approximation Approach,” Journal of the American Statistical Association, 92, 341–349.

  • Shun, Z. and McCullagh, P. (1995), “Laplace Approximation of High Dimensional Integrals,” Journal of the Royal Statistical Society, Series B, 57, 749–760.

  • Silvapulle, M. J. and Sen, P. K. (2004), Constrained Statistical Inference: Order, Inequality, and Shape Constraints, New York: John Wiley & Sons.

  • Silvapulle, M. J. and Silvapulle, P. (1995), “A Score Test against One-Sided Alternatives,” Journal of the American Statistical Association, 429, 342–349.

  • Stenstrom, F. H. (1940), The Growth of Snapdragons, Stocks, Cinerarias and Carnations on Six Iowa Soils, Master’s thesis, Iowa State College.

  • Stram, D. O. and Lee, J. W. (1994), “Variance Components Testing in the Longitudinal Mixed Effects Model,” Biometrics, 50, 1171–1177.

  • Stram, D. O. and Lee, J. W. (1995), “Correction to 'Variance Components Testing in the Longitudinal Mixed Effects Model',” Biometrics, 51, 1196.

  • Tamhane, A. C. (1979), “A Comparison of Procedures for Multiple Comparisons of Means with Unequal Variances,” Journal of the American Statistical Association, 74, 471–480.

  • Thall, P. F. and Vail, S. C. (1990), “Some Covariance Models for Longitudinal Count Data with Overdispersion,” Biometrics, 46, 657–671.

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

  • Verbeke, G. and Molenberghs, G. (2003), “The Use of Score Tests for Inference on Variance Components,” Biometrics, 59, 254–262.

  • Vonesh, E. F. (1996), “A Note on Laplace’s Approximation for Nonlinear Mixed-Effects Models,” Biometrika, 83, 447–452.

  • Vonesh, E. F. and Chinchilli, V. M. (1997), Linear and Nonlinear Models for the Analysis of Repeated Measurements, New York: Marcel Dekker.

  • Vonesh, E. F., Chinchilli, V. M., and Pu, K. (1996), “Goodness-of-Fit in Generalized Nonlinear Mixed-Effects Models,” Biometrics, 52, 572–587.

  • Wedderburn, R. W. M. (1974), “Quasilikelihood Functions, Generalized Linear Models, and the Gauss-Newton Method,” Biometrika, 61, 439–447.

  • Westfall, P. H. (1997), “Multiple Testing of General Contrasts Using Logical Constraints and Correlations,” Journal of the American Statistical Association, 92, 299–306.

  • Westfall, P. H. and Tobias, R. D. (2007), “Multiple Testing of General Contrasts: Truncated Closure and the Extended Shaffer-Royen Method,” Journal of the American Statistical Association, 478, 487–494.

  • Westfall, P. H., Tobias, R. D., Rom, D., Wolfinger, R. D., and Hochberg, Y. (1999), Multiple Comparisons and Multiple Tests Using the SAS System, Cary, NC: SAS Institute Inc.

  • Westfall, P. J. and Young, S. S. (1993), Resampling-Based Multiple Testing, New York: John Wiley & Sons.

  • White, H. (1980), “A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity,” Econometrica, 48, 817–838.

  • White, H. (1982), “Maximum Likelihood Estimation of Misspecified Models,” Econometrica, 50, 1–25.

  • Whittle, P. (1954), “On Stationary Processes in the Plane,” Biometrika, 41, 434–449.

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

  • Wolfinger, R. D. (1993), “Laplace’s Approximation for Nonlinear Mixed Models,” Biometrika, 80, 791–795.

  • Wolfinger, R. D. and O’Connell, M. (1993), “Generalized Linear Mixed Models: A Pseudo-likelihood Approach,” Journal of Statistical Computation and Simulation, 48, 233–243.

  • 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.

  • Zeger, S. L. and Liang, K.-Y. (1986), “Longitudinal Data Analysis for Discrete and Continuous Outcomes,” Biometrics, 42, 121–130.