Journal
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES C-APPLIED STATISTICS
Volume 49, Issue -, Pages 371-384Publisher
BLACKWELL PUBL LTD
DOI: 10.1111/1467-9876.00198
Keywords
EM algorithm; fisher information; maximum likelihood; parametric bootstrap; prediction bands; quantile-quantile plots; regression diagnostics
Categories
Ask authors/readers for more resources
A problem arising from the study of the spread of a viral infection among potato plants by aphids appears to involve a mixture of two linear regressions on a single predictor variable. The plant scientists studying the problem were particularly interested in obtaining a 95% confidence upper bound for the infection rate. We discuss briefly the procedure for fitting mixtures of regression models by means of maximum likelihood, effected via the EM algorithm. We give general expressions for the implementation of the M-step and then address the issue of conducting statistical inference in this context. A technique due to T. A. Louis may be used to estimate the covariance matrix of the parameter estimates by calculating the observed Fisher information matrix. We develop general expressions for the entries of this information matrix. Having the complete covariance matrix permits the calculation of confidence and prediction bands for the fitted model. We also investigate the testing of hypotheses concerning the number of components in the mixture via parametric and 'semiparametric' bootstrapping. Finally, we develop a method of producing diagnostic plots of the residuals from a mixture of linear regressions.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available