Residual analysis of linear mixed models using a simulation approach

Computational Statistics and Data Analysis

Volumn 56, Issue 6, 2012, Pages 1405-1416

  Schützenmeister, André ^a   Piepho, Hans Peter ^a  

^a UNIVERSITY OF HOHENHEIM   (Germany)

Author keywords

Conditional residual; Diagnostic plot; Empirical size; Simultaneous tolerance band; Simultaneous tolerance interval; Studentized residual

Indexed keywords

CONDITIONAL RESIDUAL; DIAGNOSTIC PLOT; EMPIRICAL SIZE; SIMULTANEOUS TOLERANCE BAND; STUDENTIZED RESIDUALS; TOLERANCE INTERVAL;

STATISTICS;

COMPUTER SIMULATION;

EID: 84857652265     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2011.11.006     Document Type: Article

References (38)

1. A.C. Atkinson Two graphical displays for outlying and influential observations in regression Biometrika 68 1981 13 20
2. A.C. Atkinson Plots, Transformations and Regression 1985 Oxford University Press Oxford
3. R. Christensen, L.M. Pearson, and W. Johnson Case-deletion diagnostics for mixed models Technometrics 34 1992 38 45
4. W.G. Cochran, and D.R. Cox Experimental Designs second ed. 1957 Wiley New York
5. R.D. Cook, and S. Weisberg Residuals and Influence in Regression 1982 Chapman and Hall London
6. D.R. Cox, and D.V. Hinkley Theoretical Statistics 1974 Chapman and Hall London
7. T. Deutler Grubbs-type estimators for reproducibility variances in an interlaboratory test study Journal of Quality Technology 23 1991 324 333
8. J.-M. Dufour, A. Farhat, L. Gardiol, and L. Khalaf Simulation-based finite sample normality tests in linear regression Econometrics Journal 1 1998 154 173
9. B. Efron, and R.J. Tibshirani An Introduction to the Bootstrap 1993 Chapman and Hall New York
10. F.N. Gumedze, S.J. Welham, B.J. Gogel, and R. Thompson A variance shift model for detection of outliers in the linear mixed model Computational Statistics and Data Analysis 54 2010 2128 2144
11. J. Haslett, and D. Dillane Application of delete=replace to deletion diagnostics for variance component estimation in the linear mixed model Journal of the Royal Statistical Society, Series B 66 2004 131 143
12. C.R. Henderson Estimation of genetic parameters Abstract Ann.Math.Sci. 21 1950 309 310
13. X. Huang Detecting random-effects model misspecification via coarsened data Computational Statistics and Data Aanalysis 55 2011 703 714
14. Hilden-Minton, J.A.; 1995. Multilevel diagnostics for mixed and hierarchical linear models. PhD Thesis. University of California, Los Angeles.
15. A.N. Kackar, and D.A. Harville Unbiasedness of two-stage estimation and precision procedures for mixed linear models J. Amer. Statist. Assoc. 10 1984 1249 1261
16. N.M. Laird, and J.H. Ware Random effects models for longitudinal data Biometrics 38 1982 963 974
17. N. Lange, and L. Ryan Assessing normality in random effects models Ann. Statist. 17 1989 624 642
18. N.T. Longford Simulation-based diagnostics in random-coefficient models Journal of the Royal Statistical Society, Series A 164 2001 259 273
19. T.H.E. Meuwissen, B.J. Hayes, and M.E. Goddard Prediction of total genetic value using genome-wide dense marker maps Genetics 157 2001 1819 1829
20. J.S. Nobre, and J.M. Singer Residual analysis for linear mixed models Biometrical Journal 49 2007 863 875
21. H.P. Piepho Weighted estimates of interlaboratory consensus values Computational Statistics and Data Analysis 22 1996 471 479
22. H.P. Piepho Ridge regression and extensions for genome-wide selection in maize Crop Science 49 2009 1165 1176
23. J.C. Pinheiro, and D.M. Bates Mixed-Effects Models in S and S-PLUS 2000 Springer New York
24. R Development Core Team 2011. R: a language and environment for statistical computing, R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, URL
25. G.K. Robinson That BLUP is a good thing: The estimation of random effects Statistical Science 6 1991 15 51
26. D.M. Rocke Robust statistical analysis of interlaboratory studies Biometrika 70 1983 421 431
27. L. Rmisch-Margl, G. Spielbauer, A. Schützenmeister, W. Schwab, H.P. Piepho, U. Genschel, and A. Gierl Heterotic patterns of sugar and amino acid components in developing maize kernels Theoretical and Applied Genetics 120 2010 369 381
28. A. Schützenmeister, U. Jensen, and H.P. Piepho Checking the assumptions of normality and homoscedasticity in the general linear model using diagnostic plots Communications in StatisticsSimulation and Computation 41 2012 141 154
29. S.R. Searle, G. Casella, and C.E. McCulloch Variance Components 1992 John Wiley & Sons New York
30. G.A.F. Seber Linear Regression Analysis 1977 John Wiley & Sons New York
31. L. Shi, and M. Huang Stepwise local influence analysis Computational Statistics and Data Analysis 55 2011 973 982
32. L. Shi, and H. Chen Deletion, replacement and mean-shift for diagnostics in linear mixed models Computational Statistics and Data Analysis 56 2012 202 208
33. J.M. Singer, and D.F. Andrade Regression models for the analysis of pretest/posttest data Biometrics 53 1997 729 735
34. J.M. Singer, J.S. Nobre, and H.C. Sef Regression models for pretest/posttest data in blocks Statistical Modelling 4 2004 324 338
35. R. Thompson A note on restricted maximum likelihood estimation with an alternative outlier model Journal of the Royal Statistical Society, Series B 47 1985 53 55
36. F.A. van Eeuwijk Linear and bilinear models for the analysis of multi-environment trials: I. An inventory of models Euphytica 84 1995 1 7
37. G. Verbeke, and E. Lesaffre A linear mixed-effects model with heterogeneity in the random-effects population J. Amer. Statist. Assoc. 91 1996 217 221
38. G. Verbeke, and G. Molenberghs Linear Mixed Models for Longitudinal Data 2000 Springer Berlin