Checking for lack of fit in linear models with parametric variance functions

Technometrics

Volumn 42, Issue 3, 2000, Pages 226-236

  Bedrick, Edward J ^a  

^a UNIVERSITY OF NEW MEXICO   (United States)

Author keywords

Near replicates; Omnibus test; Regression diagnostics

Indexed keywords

COMPUTATIONAL COMPLEXITY; COMPUTER SIMULATION; GRAPHIC METHODS; MATHEMATICAL MODELS; STATISTICAL TESTS;

LACK-OF-FIT TESTS; LOG-LINEAR MODELS; NEAR REPLICATES; OMNIBUS TESTS; PARAMETRIC VARIANCE FUNCTIONS;

REGRESSION ANALYSIS;

EID: 0034246860     PISSN: 00401706     EISSN: 15372723     Source Type: Journal    
DOI: 10.1080/00401706.2000.10486044     Document Type: Article

References (24)

1. Aitkin, M, (1987), “Modelling Variance Heterogeneity Using GLIM,” Applied Statistics, 36, 332-339.
2. Atwood, C. L., and Ryan, T. A., Jr. (1977), “A Class of Tests for Lack of Fit to a Regression Model,” unpublished manuscript.
3. Breusch, T., and Pagan, A. R. (1980), “The Lagrange Multiplier Test and its Applications to Model Misspecification in Econometrics,” Review of Economic Studies, 47, 239-253.
4. Brown, M. B., and Forsythe, A. B. (1974), “Robust Tests for the Equality of Variances,” Journal of the American Statistical Association, 69, 364-367.
5. Carroll, R. J., and Ruppert, D. (1988), Transformation and Weighting in Regression, New York: Chapman and Hall.
6. Christensen, R. (1989), “Lack of Fit Tests Based on Near or Exact Replicates,” The Annals of Statistics, 17, 673-683.
7. Christensen, R. (1991), “Small-Sample Characterizations of Near Replicate Lack- of-Fit Tests,” Journal of the American Statistical Association, 86, 752-756.
8. Cohen, M., Dalai, S. R. and Tukey, J. W. (1993), “Robust, Smoothly Heterogeneous Variance Regression,” Applied Statistics, 42, 339-353.
9. Cook, R. D., and Weisberg, S. (1983), “Diagnostics for Heteroscedasticity in Regression,” Biometrika, 70, 1-10.
10. Daniel, C., and Wood, F. S. (1971), Fitting Equations to Data, New York: Wiley Interscience.
11. Farnum, N. R. (1994), Statistical Quality Control and Improvement, Belmont, CA: Duxbury.
12. Fienberg, S. E., and Gong, G. D. (1984), Comment on “Graphical Methods for Assessing Logistic Regression Models,” by J. M. Landwehr, D. Pregibon, and A. C. Shoemaker, Journal of the American Statistical Association, 79, 72-77.
13. Fisher, R. A. (1950), Statistical Methods for Research Workers (11th ed.), London: Oliver and Boyd.
14. Grego, J. M. (1993), “Generalized Linear Models and Process Variation,” Journal of Quality Technology, 25, 288-295.
15. Jobson, J. D., and Fuller, W. A. (1980), “Least Squares Estimation When the Covariance Matrix and Parameter Vector Are Functionally Related,” Journal of the American Statistical Association, 75, 176-181.
16. Miller, F. R., Neill, J. W., and Sherfey, B. W. (1998), “Maximin Clusters for a Near-Replicate Regression Lack of Fit Tests,” The Annals of Statistics, 26, 1411-1433.
17. Nair, V. N., and Pregibon, D. (1988), “Analyzing Dispersion Effects From Replicated Factorial Experiments,” Technometrics, 30, 247-257 (corrigenda, vol. 31, p. 133).
18. Neill, J. W. and Johnson, D. E. (1984), “Testing for Lack of Fit in Regression-A Review,” Communications in Statistics, Part A-Theory and Methods, 13, 485-511.
19. Nelder, J. A. (1994), “An Alternative View of the Splicing Data,” Applied Statistics, 43, 469-476.
20. Rao, C. R. (1948), “Large Sample Tests of Statistical Hypotheses Concerning Several Parameters With Applications to Problems of Estimation,” Proceedings of the Cambridge Philosophical Society, 44, 50-57.
21. Silvey, S. D. (1959), “The Lagrangian Multiplier Test,” The Annals of Mathematical Statistics, 30, 389-407.
22. Tsiatis, A. A. (1980), “A Note on a Goodness-of-Fit Test for a Logistic Regression Model,” Biometrika, 67, 250-251.
23. Verbyla, A. P. (1993), “Modelling Variance Heterogeneity: Residual Maximum Likelihood and Diagnostics,” Journal of the Royal Statistical Society, Ser. B, 55, 493-508.
24. Weisberg, S. (1985), Applied Linear Regression (2nd ed.), New York: Wiley.