Abstract
In this paper, a unified diagnostic method for linear models with random effects based upon the joint likelihood given by Robinson (in 1991) is presented. The case deletion model is equivalent to mean shift outlier model, as well as case weights model. From this point of view, several new diagnostic measures, such as Cook distance, WK diagnostics are derived. Some previous results are improved. Numerical examples illustrate the method is available.
Similar content being viewed by others
References
Robinson, G.K., That BLUP is a good thing: the estimation of random effects, Statistical Science, 1991 (1):15–51.
Shi, L. et al., Influence analysis on linear mixed model (in Chinese), Acta Mathematica Scientia, 1996, 16(3):316–323.
William, H. F., Robust estimation of variance components, Technometrics, 1986, 28:51–60.
Beckman, R. J., Nachtsheim, C. J., Diagnostics for mixed-model analysis of variance, Technometrics, 1987, 29:413–426.
Chistensen, R., Pearson, L. M., Case-deletion diagnostics for mixed models, Technometrics, 1992, 34: 38–45.
Zhuan, D. C., Mao S. S., Estimates of linear mixed models. (in Chinese), Chinese Journal of Applied Probability and Statistics, 1995(1):81–85.
Cook, R. D., Weisberg, S., Residual and Influence in Regression, Chapman and Hall, New York, 1982.
Wei, B. C., et al., Introduction to statistical diagnostics (in Chinese), Southeast University Press, Nanjing, 1991.
Cook, R. D., Assessment of local influence (with discussion), J. Roy. Statist. Soc. B, 1986, 48:133–169.
Beckman, R. J., Cook, R. D., OUTLIER…S., Technometrics, 1983, 25:119–149.
Author information
Authors and Affiliations
Additional information
The research supported by NSFC (19631040) and NSFJ.
Rights and permissions
About this article
Cite this article
Xuping, Z., Bocheng, W. Influence analysis on linear models with random effects. Appl. Math. Chin. Univ. 14, 169–176 (1999). https://doi.org/10.1007/s11766-999-0023-0
Received:
Issue Date:
DOI: https://doi.org/10.1007/s11766-999-0023-0