Abstract
This article considers the analysis of experiments with missing data from various experimental designs frequently used in agricultural research (randomized complete blocks, split plots, strip plots). We investigate the small sample properties of REML-based Wald-type F tests using linear mixed models. Several methods for approximating the denominator degrees of freedom are employed, all of which are available with the MIXED procedure of the SAS System (8.02). The simulation results show that the Kenward-Roger method provides the best control of the Type I error rate and is not inferior to other methods in terms of power.
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References
Ahrens, H. (1967), Die Varianzanalyse, Berlin: Akademie-Verlag.
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 Computing and Simulation, 54, 363–378.
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.
Guiard, V., Spilke, J., and Dänicke, S. (2003), “Evaluation and Interpretation of the Results for Three Cross-Over Designs,” Archives of Animal Nutrition, 57, 177–195.
Hartley, H. O., and Rao, C. R. (1967), “Maximum Likelihood Estimation for the Mixed Analysis of Variance Model,” Biometrika, 54, 93–108.
Henderson, C. R. (1963), “Selection Index and Expected Genetic Advance,” Statistical Genetics and Plant Breeding, NAS-NRC Publ. No. 982, 141–163.
— (1984), Application of Linear Models in Animal Breeding, Guelph: University of Guelph.
— (1990), “Statistical Method in Animal Improvement: Historical Overview,” in Advances in Statistical Methods for Genetic Improvement of Livestock, New York: Springer.
Kackar, A. N., and Harville, D. A. (1981), “Unbiasedness of Two-Stage Estimation and Precision Procedures for Mixed Linear Models,” Communications in Statistics A, 10, 1249–1261.
— (1984), “Approximation for Standard Errors of Estimators of Fixed and Random Effects in Mixed Linear Models,” Journal of the American Statistical Association, 79, 853–861.
Kenward, M. G., and Roger, J. H. (1997), “Small Sample Inference for Fixed Effects from Restricted Maximum Likelihood,” Biometrics, 53, 983–997.
Keselman, H. J., Kowalchuk, R. K., Algina, J., and Wolfinger, R. D. (1999), “The Analysis of Repeated Measurements: A Comparison of Mixed-Model Satterthwaite F tests and a Nonpooled Adjusted Degrees of Freedom Multivariate Test,” Communications in Statistics A, 28, 2967–2999.
Khuri, A. I., Mathew, T., and Sinha, B. K. (1998), Statistical Tests for Mixed Linear Models, New York: Wiley.
Lamotte, L. R. (1973), “Quadratic Estimation of Variance Components,” Biometrics, 29, 311–330.
Patterson, H. D., and Thompson, R. (1971), “Recovery of Inter-Block Information When Block Sizes are Unequal,” Biometrika, 58, 545–554.
Piepho, H. P. (1997), “Analysis of a Randomized Complete Block Design with Unequal Subclass Numbers,” Agronomy Journal, 89, 718–723.
Rao, C. R. (1971), “Minimum Variance Quadratic Unbiased Estimation of Variance Components,” Journal of Multivariate Analysis, 1, 445–456.
Remmenga, M. D., and Johnson, D. E. (1995), “A Comparison of Inference Procedures in Unbalanced Split-Plot Designs,” Journal of Statistical Computation and Simulation, 51, 353–367.
SAS Institute Inc. (1999), SAS OnlineDoc®, Version 8, Cary, NC: SAS Institute Inc.
Satterthwaite, F. E. (1941), “Synthesis of Variance,” Psychometrika, 6, 309–316.
Schaalje, G. B., McBride, J. B., and Fellingham, G. W. (2002), “Adequacy of Approximation to Distributions of Test Statistics in Complex Mixed Linear Models,” Journal of Agricultural, Biological, and Environmental Statistics, 7, 512–524.
Searle, S. R. (1971), “Topics in Variance Component Estimation,” Biometrics, 27, 1–76.
— (1987), Linear Models for Unbalanced Data, New York: Wiley.
Searle, S. R., Casella, G., and McCulloch, C. E. (1992), Variance Components, New York: Wiley.
Spilke, J., and Tuchscherer, A. (2001), “Simulationsuntersuchungen zum Einfluss verschiedener Strategien der Varianzkomponentenschätzung und Hypothesenprüfung auf die statistischen Risiken in gemischten line aren Modellen mit ungleicher Klassenbesetzung,” Zeitschrift für Agrarinformatik, 4, 66–75.
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Spilke, J., Piepho, HP. & Hu, X. A simulation study on tests of hypotheses and confidence intervals for fixed effects in mixed models for blocked experiments with missing data. JABES 10, 374–389 (2005). https://doi.org/10.1198/108571105X58199
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DOI: https://doi.org/10.1198/108571105X58199