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Estimating the propagation rate of a viral infection of potato plants via mixtures of regressions. (English) Zbl 0971.62076
Summary: 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 [ibid., Ser. B 44, 226-233 (1982; Zbl 0488.62018)] 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.

MSC:
62P10 Applications of statistics to biology and medical sciences; meta analysis
62J20 Diagnostics, and linear inference and regression
62F40 Bootstrap, jackknife and other resampling methods
62J05 Linear regression; mixed models
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