Checking normality and homoscedasticity in the general linear model using diagnostic plots

Communications in Statistics: Simulation and Computation

Volumn 41, Issue 2, 2012, Pages 141-154

  Schutzenmeister A ^a   Jensen, U ^a   Piepho, H P ^a  

^a UNIVERSITY OF HOHENHEIM   (Germany)

Author keywords

Constant residual variance; Model checking; Monte Carlo; Multiplicity; Residual plot; Simulation; Simultaneous tolerance band; Tolerance interval; Tolerance region

Indexed keywords

MONTE CARLO; MULTIPLICITY; RESIDUAL PLOT; RESIDUAL VARIANCE; SIMULATION; SIMULTANEOUS TOLERANCE BAND; TOLERANCE INTERVAL; TOLERANCE REGIONS;

MODEL CHECKING; STATISTICS;

MONTE CARLO METHODS;

EID: 84857646870     PISSN: 03610918     EISSN: 15324141     Source Type: Journal    
DOI: 10.1080/03610918.2011.582560     Document Type: Article

References (28)

1. Atkinson, A. C. (1981). Two graphical displays for outlying and influential observations in regression. Biometrika 68:13-20.
2. Atkinson, A. C. (1985). Plots, Transformations and Regression. Oxford: Oxford University Press.
3. Atkinson, A. C., Riani, M. (2000). Robust Diagnostic Regression Analysis. New York: Springer.
4. Beckman, R. J., Trussell, H. J. (1974). The distribution of an arbitrary studentized residual and the effects of updating in multiple regression. Journal of the American Statistical Association 69:199-201.
5. Bradley, J. V. (1980). Nonrobustness in Zt, and F tests at large sample sizes. Bulletin of the Psychonomic Society 16:333-336.
6. Bradley, J. V. (1984). The complexity of nonrobustness effects. Bulletin of the Psychonomic Society 22:250-253.
7. Bürkert, A., Bationo, A., Piepho, H.-P. (2001). Efficient phosphorus application strategies for increased crop production in sub-Saharan West Africa. Field Crops Research 72:1-15.
8. Cook, R. D., Weisberg, S. (1982). Residuals and Influence in Regression. London: Chapman and Hall.
9. Cook, R. D., Weisberg, S. (1994). An Introduction to Regression Graphics. New York: Wiley.
10. Cox, D. R., Hinkley, D. V. (1974). Theoretical Statistics. London: Chapman and Hall.
11. Csorgo, M., Seshadri, V., Yalovsky, M. (1973). Some exact tests for normality in the presence of unknown parameters. Journal of the Royal Statistical Society B 35:507-522.
12. Denis, J.-B., Piepho, H.-P., van Eeuwijk, F. A. (1997). Modelling expectation and variance for genotype by environment data. Heredity 79:162-171.
13. Draper, N. R., Smith, H. (1998). Applied Regression Analysis. New York: Wiley.
14. Dufour, J.-M., Farhat, A., Gardiol, L., Khalaf, L. (1998). Simulation-based finite sample normality tests in linear regression. Econometrics Journal 1:154-173.
15. Eskridge, K. M. (1990). Selection of stable cultivars using a safety first rule. Crop Science 30:369-374.
16. Levene, H. (1960). Robust tests for equality of variances. In: Olkin, I., Ghurye, S. G., Hoeffding, W. G., Mann, H. B., eds. Contributions to Probability and Statistics. Essays in honor of Harold Hotelling. Stanford, CA: Stanford University Press, pp. 278-292.
17. Nelson, W. (1982). Applied Life Data Analysis. New York: Wiley.
18. Meeker, W. O., Escobar, L. A. (1998). Statistical Methods for Reliability Data. New York: Wiley.
19. Piepho, H.-P. (1995a). A robust test for homoscedasticity in a two-way layout. Biometrical Journal 37:151-160.
20. Piepho, H.-P. (1995b). Detecting, interpreting and handling heteroscedasticity in yield trial data. Communications in Statistics B-Simulation and Computation 24:243-274.
21. Piepho, H.-P. (1996a). A Monte Carlo test for variance homogeneity in linear models. Biometrical Journal 38:461-473.
22. Piepho, H.-P. (1996b). Weighted estimates of interlaboratory consensus values. Computational Statistics & Data Analysis 22:471-479.
23. Piepho, H.-P. (1998). Methods for comparing the yield stability of cropping systems. Journal of Agronomy & Crop Science 180:193-213.
24. Press, W. H., Flannery, B. P., Teukolsky, S. A., Vetterling, W. T. (1989). Numerical Recipes in PASCAL. Cambridge: Cambridge University Press.
25. Römisch-Margl, L., Spielbauer, G., Schützenmeister A., Schwab, W., Piepho, H.-P., Genschel, U., Gierl, A. (2010). Heterotic patterns of sugar and amino acid components in developing maize kernels. Theoretical and Applied Genetics 120:369-381.
26. Seber, G. A. F. (1977). Linear Regression Analysis. New York: Wiley.
27. Seber, G. A. F., Lee, A. J. (2003). Linear Regression Analysis. 2nd ed. New Jersey: Wiley.
28. Thode, H. C. (2002). Testing for Normality. New York: Marcel Dekker.