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Finite mixtures of quantile and M-quantile regression models

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Abstract

In this paper we define a finite mixture of quantile and M-quantile regression models for heterogeneous and /or for dependent/clustered data. Components of the finite mixture represent clusters of individuals with homogeneous values of model parameters. For its flexibility and ease of estimation, the proposed approaches can be extended to random coefficients with a higher dimension than the simple random intercept case. Estimation of model parameters is obtained through maximum likelihood, by implementing an EM-type algorithm. The standard error estimates for model parameters are obtained using the inverse of the observed information matrix, derived through the Oakes (J R Stat Soc Ser B 61:479–482, 1999) formula in the M-quantile setting, and through nonparametric bootstrap in the quantile case. We present a large scale simulation study to analyse the practical behaviour of the proposed model and to evaluate the empirical performance of the proposed standard error estimates for model parameters. We considered a variety of empirical settings in both the random intercept and the random coefficient case. The proposed modelling approaches are also applied to two well-known datasets which give further insights on their empirical behaviour.

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Acknowledgments

The work of Salvati and Ranalli has been developed under the support of the project PRIN-SURWEY http://www.sp.unipg.it/surwey/ (Grant 2012F42NS8, Italy). Marco Alfò acknowledges the financial support from the grant RBFR12SHVV of the Italian Government (FIRB project “Mixture and latent variable models for causal inference and analysis of socio-economic data”).

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Authors and Affiliations

  1. Dipartimento di Scienze Statistiche, Sapienza Università di Roma, Rome, Italy

    Marco Alfò

  2. Dipartimento di Economia e Management, Università di Pisa, Pisa, Italy

    Nicola Salvati

  3. Dipartimento di Scienze Politiche, Università degli Studi di Perugia, Perugia, Italy

    Ranalli M. Giovanna

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  1. Marco Alfò
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  2. Nicola Salvati
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  3. Ranalli M. Giovanna
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Correspondence to Nicola Salvati.

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Alfò, M., Salvati, N. & Giovanna, R.M. Finite mixtures of quantile and M-quantile regression models. Stat Comput 27, 547–570 (2017). https://doi.org/10.1007/s11222-016-9638-1

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