IDEAS home Printed from https://ideas.repec.org/a/spr/advdac/v13y2019i1d10.1007_s11634-018-0337-y.html
   My bibliography  Save this article

Finite mixture of regression models for censored data based on scale mixtures of normal distributions

Author

Listed:
  • Camila Borelli Zeller

    (Universidade Federal de Juiz de Fora)

  • Celso Rômulo Barbosa Cabral

    (Universidade Federal do Amazonas)

  • Víctor Hugo Lachos

    (University of Connecticut)

  • Luis Benites

    (Pontificia Universidad Católica del Perú)

Abstract

In statistical analysis, particularly in econometrics, the finite mixture of regression models based on the normality assumption is routinely used to analyze censored data. In this work, an extension of this model is proposed by considering scale mixtures of normal distributions (SMN). This approach allows us to model data with great flexibility, accommodating multimodality and heavy tails at the same time. The main virtue of considering the finite mixture of regression models for censored data under the SMN class is that this class of models has a nice hierarchical representation which allows easy implementation of inferences. We develop a simple EM-type algorithm to perform maximum likelihood inference of the parameters in the proposed model. To examine the performance of the proposed method, we present some simulation studies and analyze a real dataset. The proposed algorithm and methods are implemented in the new R package CensMixReg.

Suggested Citation

  • Camila Borelli Zeller & Celso Rômulo Barbosa Cabral & Víctor Hugo Lachos & Luis Benites, 2019. "Finite mixture of regression models for censored data based on 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. 13(1), pages 89-116, March.
    • Handle: RePEc:spr:advdac:v:13:y:2019:i:1:d:10.1007_s11634-018-0337-y
    DOI: 10.1007/s11634-018-0337-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11634-018-0337-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11634-018-0337-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Powell, James L, 1986. "Symmetrically Trimmed Least Squares Estimation for Tobit Models," Econometrica, Econometric Society, vol. 54(6), pages 1435-1460, November.
    2. Melenberg, Bertrand & van Soest, Arthur, 1996. "Parametric and Semi-parametric Modelling of Vacation Expenditures," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(1), pages 59-76, Jan.-Feb..
    3. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    4. Ann Dryden Witte, 1980. "Estimating the Economic Model of Crime With Individual Data," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 94(1), pages 57-84.
    5. Powell, James L., 1984. "Least absolute deviations estimation for the censored regression model," Journal of Econometrics, Elsevier, vol. 25(3), pages 303-325, July.
    6. Basso, Rodrigo M. & Lachos, Víctor H. & Cabral, Celso Rômulo Barbosa & Ghosh, Pulak, 2010. "Robust mixture modeling based on scale mixtures of skew-normal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 2926-2941, December.
    7. Aldo M. Garay & Heleno Bolfarine & Victor H. Lachos & Celso R.B. Cabral, 2015. "Bayesian analysis of censored linear regression models with scale mixtures of normal distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(12), pages 2694-2714, December.
    8. Reinaldo Arellano-Valle & Luis Castro & Graciela González-Farías & Karla Muñoz-Gajardo, 2012. "Student-t censored regression model: properties and inference," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 21(4), pages 453-473, November.
    9. Galimberti, Giuliano & Soffritti, Gabriele, 2014. "A multivariate linear regression analysis using finite mixtures of t distributions," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 138-150.
    10. Cabral, Celso Rômulo Barbosa & Lachos, Víctor Hugo & Prates, Marcos O., 2012. "Multivariate mixture modeling using skew-normal independent distributions," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 126-142, January.
    11. Mroz, Thomas A, 1987. "The Sensitivity of an Empirical Model of Married Women's Hours of Work to Economic and Statistical Assumptions," Econometrica, Econometric Society, vol. 55(4), pages 765-799, July.
    12. Lachos, Víctor H. & Moreno, Edgar J. López & Chen, Kun & Cabral, Celso Rômulo Barbosa, 2017. "Finite mixture modeling of censored data using the multivariate Student-t distribution," Journal of Multivariate Analysis, Elsevier, vol. 159(C), pages 151-167.
    13. Steven Caudill, 2012. "A partially adaptive estimator for the censored regression model based on a mixture of normal distributions," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 21(2), pages 121-137, June.
    14. Maria Karlsson & Thomas Laitila, 2014. "Finite mixture modeling of censored regression models," Statistical Papers, Springer, vol. 55(3), pages 627-642, August.
    15. Nicolas Depraetere & Martina Vandebroek, 2014. "Order selection in finite mixtures of linear regressions," Statistical Papers, Springer, vol. 55(3), pages 871-911, August.
    16. Saieed Ateya, 2014. "Maximum likelihood estimation under a finite mixture of generalized exponential distributions based on censored data," Statistical Papers, Springer, vol. 55(2), pages 311-325, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Andrey Gorshenin & Victor Kuzmin, 2022. "Statistical Feature Construction for Forecasting Accuracy Increase and Its Applications in Neural Network Based Analysis," Mathematics, MDPI, vol. 10(4), pages 1-21, February.
    2. Wan-Lun Wang & Yu-Chen Yang & Tsung-I Lin, 2024. "Extending finite mixtures of nonlinear mixed-effects models with covariate-dependent mixing weights," 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. 18(2), pages 271-307, June.
    3. Wan-Lun Wang & Tsung-I Lin, 2022. "Robust clustering of multiply censored data via mixtures of t factor analyzers," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 22-53, March.
    4. Mirfarah, Elham & Naderi, Mehrdad & Chen, Ding-Geng, 2021. "Mixture of linear experts model for censored data: A novel approach with scale-mixture of normal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 158(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Víctor H. Lachos & Celso R. B. Cabral & Marcos O. Prates & Dipak K. Dey, 2019. "Flexible regression modeling for censored data based on mixtures of student-t distributions," Computational Statistics, Springer, vol. 34(1), pages 123-152, March.
    2. Lachos, Víctor H. & Moreno, Edgar J. López & Chen, Kun & Cabral, Celso Rômulo Barbosa, 2017. "Finite mixture modeling of censored data using the multivariate Student-t distribution," Journal of Multivariate Analysis, Elsevier, vol. 159(C), pages 151-167.
    3. Mirfarah, Elham & Naderi, Mehrdad & Chen, Ding-Geng, 2021. "Mixture of linear experts model for censored data: A novel approach with scale-mixture of normal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 158(C).
    4. Francisco H. C. Alencar & Christian E. Galarza & Larissa A. Matos & Victor H. Lachos, 2022. "Finite mixture modeling of censored and missing data using the multivariate skew-normal distribution," 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. 16(3), pages 521-557, September.
    5. Maria Karlsson & Thomas Laitila, 2014. "Finite mixture modeling of censored regression models," Statistical Papers, Springer, vol. 55(3), pages 627-642, August.
    6. Anil Kumar, 2012. "Nonparametric estimation of the impact of taxes on female labor supply," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(3), pages 415-439, April.
    7. P. Čížek & S. Sadikoglu, 2018. "Bias-corrected quantile regression estimation of censored regression models," Statistical Papers, Springer, vol. 59(1), pages 215-247, March.
    8. Kenneth Y. Chay & James L. Powell, 2001. "Semiparametric Censored Regression Models," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 29-42, Fall.
    9. Michelli Barros & Manuel Galea & Víctor Leiva & Manoel Santos-Neto, 2018. "Generalized Tobit models: diagnostics and application in econometrics," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(1), pages 145-167, January.
    10. Steven Caudill, 2012. "A partially adaptive estimator for the censored regression model based on a mixture of normal distributions," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 21(2), pages 121-137, June.
    11. Randall A. Lewis & James B. McDonald, 2014. "Partially Adaptive Estimation of the Censored Regression Model," Econometric Reviews, Taylor & Francis Journals, vol. 33(7), pages 732-750, October.
    12. Yoo, Seung-Hoon & Kim, Tai-Yoo & Lee, Jai-Ki, 2001. "Modeling zero response data from willingness to pay surveys: A semi-parametric estimation," Economics Letters, Elsevier, vol. 71(2), pages 191-196, May.
    13. James B. McDonald & Hieu Nguyen, 2012. "Heteroskedasticity and Distributional Assumptions in the Censored Regression Model," BYU Macroeconomics and Computational Laboratory Working Paper Series 2012-09, Brigham Young University, Department of Economics, BYU Macroeconomics and Computational Laboratory.
    14. Azzalini, Adelchi, 2022. "An overview on the progeny of the skew-normal family— A personal perspective," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    15. Falk, Martin, 2001. "Diffusion of information technology, internet use and the demand of heterogeneous labor," ZEW Discussion Papers 01-48, ZEW - Leibniz Centre for European Economic Research.
    16. Angelo Mazza & Antonio Punzo, 2020. "Mixtures of multivariate contaminated normal regression models," Statistical Papers, Springer, vol. 61(2), pages 787-822, April.
    17. Chen, Songnian & Khan, Shakeeb, 2000. "Estimating censored regression models in the presence of nonparametric multiplicative heteroskedasticity," Journal of Econometrics, Elsevier, vol. 98(2), pages 283-316, October.
    18. Jason Cook & James McDonald, 2013. "Partially Adaptive Estimation of Interval Censored Regression Models," Computational Economics, Springer;Society for Computational Economics, vol. 42(1), pages 119-131, June.
    19. Myoung-jae Lee, 2017. "Extensive and intensive margin effects in sample selection models: racial effects on wages," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(3), pages 817-839, June.
    20. Wan-Lun Wang & Tsung-I Lin, 2022. "Robust clustering of multiply censored data via mixtures of t factor analyzers," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 22-53, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:advdac:v:13:y:2019:i:1:d:10.1007_s11634-018-0337-y. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.