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Estimating the propagation rate of a viral infection of potato plants via mixtures of regressions

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  • T. Rolf Turner

Abstract

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.

Suggested Citation

  • T. Rolf Turner, 2000. "Estimating the propagation rate of a viral infection of potato plants via mixtures of regressions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 49(3), pages 371-384.
  • Handle: RePEc:bla:jorssc:v:49:y:2000:i:3:p:371-384
    DOI: 10.1111/1467-9876.00198
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    Cited by:

    1. Gianfranco DI VAIO & Michele BATTISTI, 2010. "A Spatially-Filtered Mixture of Beta-Convergence Regression for EU Regions, 1980-2002," Regional and Urban Modeling 284100013, EcoMod.
    2. Ye He & Ling Zhou & Yingcun Xia & Huazhen Lin, 2023. "Center‐augmented ℓ2‐type regularization for subgroup learning," Biometrics, The International Biometric Society, vol. 79(3), pages 2157-2170, September.
    3. Di Vaio, Gianfranco & Enflo, Kerstin, 2011. "Did globalization drive convergence? Identifying cross-country growth regimes in the long run," European Economic Review, Elsevier, vol. 55(6), pages 832-844, August.
    4. Rainer Schlittgen, 2011. "A weighted least-squares approach to clusterwise regression," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 95(2), pages 205-217, June.
    5. Yuzhu Tian & Manlai Tang & Maozai Tian, 2016. "A class of finite mixture of quantile regressions with its applications," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(7), pages 1240-1252, July.
    6. Giuliano Galimberti & Lorenzo Nuzzi & Gabriele Soffritti, 2021. "Covariance matrix estimation of the maximum likelihood estimator in multivariate clusterwise linear regression," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 235-268, March.
    7. Gabriele Perrone & Gabriele Soffritti, 2023. "Seemingly unrelated clusterwise linear regression for contaminated data," Statistical Papers, Springer, vol. 64(3), pages 883-921, June.
    8. Gianfranco Di Vaio & Kerstin Enflo, 2009. "Did globalisation lead to segmentation? Identifying cross-country growth regimes in the long-run, 1870-2003," Working Papers 9013, Economic History Society.
    9. Zallé, Oumarou, 2023. "Natural resource rents and regime durability: Identifying cross-country durability regimes," Resources Policy, Elsevier, vol. 81(C).
    10. Michele Battisti & Gianfranco Vaio, 2009. "A spatially filtered mixture of β-convergence regressions for EU regions, 1980–2002," Studies in Empirical Economics, in: Giuseppe Arbia & Badi H. Baltagi (ed.), Spatial Econometrics, pages 105-121, Springer.
    11. Adrian O’Hagan & Thomas Brendan Murphy & Luca Scrucca & Isobel Claire Gormley, 2019. "Investigation of parameter uncertainty in clustering using a Gaussian mixture model via jackknife, bootstrap and weighted likelihood bootstrap," Computational Statistics, Springer, vol. 34(4), pages 1779-1813, December.
    12. Shin-Fu Tsai, 2019. "Comparing Coefficients Across Subpopulations in Gaussian Mixture Regression Models," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(4), pages 610-633, December.
    13. Gianfranco Di Vaio & Kerstin Enflo, 2009. "Did Globalization Lead to Segmentation? Identifying Cross-Country Growth Regimes in the Long-Run," Working Papers CELEG 0902, Dipartimento di Economia e Finanza, LUISS Guido Carli.
    14. Ang Shan & Fengkai Yang, 2021. "Bayesian Inference for Finite Mixture Regression Model Based on Non-Iterative Algorithm," Mathematics, MDPI, vol. 9(6), pages 1-13, March.
    15. Marco Berrettini & Giuliano Galimberti & Saverio Ranciati, 2023. "Semiparametric finite mixture of regression models with Bayesian P-splines," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(3), pages 745-775, September.
    16. Nalan Baştürk & Richard Paap & Dick van Dijk, 2012. "Structural differences in economic growth: an endogenous clustering approach," Applied Economics, Taylor & Francis Journals, vol. 44(1), pages 119-134, January.
    17. Nalan Basturk & Richard Paap & Dick van Dijk, 2008. "Structural Differences in Economic Growth," Tinbergen Institute Discussion Papers 08-085/4, Tinbergen Institute.
    18. Young, D.S. & Hunter, D.R., 2010. "Mixtures of regressions with predictor-dependent mixing proportions," Computational Statistics & Data Analysis, Elsevier, vol. 54(10), pages 2253-2266, October.
    19. Atefeh Zarei & Zahra Khodadadi & Mohsen Maleki & Karim Zare, 2023. "Robust mixture regression modeling based on two-piece scale mixtures of normal distributions," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(1), pages 181-210, March.
    20. Michele Battisti, 2013. "Reassessing Segmentation In The Labour Market: An Application For Italy 1995–2004," Bulletin of Economic Research, Wiley Blackwell, vol. 65, pages 38-55, May.
    21. Xiaoqiong Fang & Andy W. Chen & Derek S. Young, 2023. "Predictors with measurement error in mixtures of polynomial regressions," Computational Statistics, Springer, vol. 38(1), pages 373-401, March.
    22. Giuliano Galimberti & Gabriele Soffritti, 2020. "Seemingly unrelated clusterwise linear regression," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 14(2), pages 235-260, June.

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