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Scale-constrained approaches for maximum likelihood estimation and model selection of clusterwise linear regression models

Author

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  • Roberto Mari

    (University of Catania)

  • Roberto Rocci

    (University of Rome Tor Vergata)

  • Stefano Antonio Gattone

    (University G. d’Annunzio)

Abstract

We consider an equivariant approach imposing data-driven bounds for the variances to avoid singular and spurious solutions in maximum likelihood estimation of clusterwise linear regression models. We investigate its use in the choice of the number of components and we propose a computational shortcut, which significantly reduces the computational time needed to tune the bounds on the data. In the simulation study and the two real-data applications, we show that the proposed methods guarantee a reliable assessment of the number of components compared to standard unconstrained methods, together with accurate model parameters estimation and cluster recovery.

Suggested Citation

  • Roberto Mari & Roberto Rocci & Stefano Antonio Gattone, 2020. "Scale-constrained approaches for maximum likelihood estimation and model selection of clusterwise linear regression models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(1), pages 49-78, March.
    • Handle: RePEc:spr:stmapp:v:29:y:2020:i:1:d:10.1007_s10260-019-00480-y
    DOI: 10.1007/s10260-019-00480-y
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    References listed on IDEAS

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