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Semiparametric inference in generalized mixed effects models

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  • María José Lombardía
  • Stefan Sperlich

Abstract

Summary. The paper presents a study of the generalized partially linear model including random effects in its linear part. We propose an estimator that combines likelihood approaches for mixed effects models, with kernel methods. Following the methodology of Härdle and co‐workers, we introduce a test for the hypothesis of a parametric mixed effects model against the alternative of a semiparametric mixed effects model. The critical values are estimated by using a bootstrap procedure. The asymptotic theory for the methods is provided, as are the results of a simulation study. These verify the feasibility and the excellent behaviour of the methods for samples of even moderate size. The usefulness of the methodology is illustrated with an application in which the objective is to estimate forest coverage in Galicia, Spain.

Suggested Citation

  • María José Lombardía & Stefan Sperlich, 2008. "Semiparametric inference in generalized mixed effects models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 913-930, November.
    • Handle: RePEc:bla:jorssb:v:70:y:2008:i:5:p:913-930
    DOI: 10.1111/j.1467-9868.2008.00655.x
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    Cited by:

    1. Chen, Ziqi & Shi, Ning-Zhong & Gao, Wei & Tang, Man-Lai, 2011. "Efficient semiparametric estimation via Cholesky decomposition for longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3344-3354, December.
    2. Patrick Munyangabo & Anthony Waititu & Anthony Kibira Wanjoya, 2019. "Estimation of Nested Error Non-parametric Unit Level Model," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 8(1), pages 1-3.
    3. Jing Dai & Stefan Sperlich & Walter Zucchini, 2016. "A Simple Method for Predicting Distributions by Means of Covariates with Examples from Poverty and Health Economics," Swiss Journal of Economics and Statistics (SJES), Swiss Society of Economics and Statistics (SSES), vol. 152(I), pages 49-80, March.
    4. Gerda Claeskens & Jeffrey Hart, 2009. "Goodness-of-fit tests in mixed models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(2), pages 213-239, August.
    5. Jianhong Wu & Lixing Zhu, 2012. "Estimation of and testing for random effects in dynamic panel data models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 477-497, September.
    6. Tang, Min & Slud, Eric V. & Pfeiffer, Ruth M., 2014. "Goodness of fit tests for linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 176-193.
    7. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 361-411, September.
    8. Gonzales Manteiga, Wenceslao & Maria Dolores, Martinez Miranda & Van Keilegom, Ingrid, 2012. "Goodness-of-fit Test in Parametric Mixed-Effects Models based on the Estimation of the Error Distribution," LIDAM Discussion Papers ISBA 2012022, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    9. Isabel Proença & Stefan Sperlich & Duygu Savaşcı, 2015. "Semi-mixed effects gravity models for bilateral trade," Empirical Economics, Springer, vol. 48(1), pages 361-387, February.
    10. Stefan Sperlich, 2013. "Comments on: Model-free model-fitting and predictive distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 227-233, June.
    11. Lei Liu & Zhihua Sun, 2017. "Kernel-based global MLE of partial linear random effects models for longitudinal data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(3), pages 615-635, July.
    12. González Manteiga, Wenceslao & Lombardía, María José & Martínez Miranda, María Dolores & Sperlich, Stefan, 2013. "Kernel smoothers and bootstrapping for semiparametric mixed effects models," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 288-302.
    13. Salvati, Nicola & Chandra, Hukum & Giovanna Ranalli, M. & Chambers, Ray, 2010. "Small area estimation using a nonparametric model-based direct estimator," Computational Statistics & Data Analysis, Elsevier, vol. 54(9), pages 2159-2171, September.
    14. Stefan Sperlich & María José Lombardía, 2010. "Local polynomial inference for small area statistics: estimation, validation and prediction," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(5), pages 633-648.
    15. Ziqi Chen & Man†Lai Tang & Wei Gao, 2018. "A profile likelihood approach for longitudinal data analysis," Biometrics, The International Biometric Society, vol. 74(1), pages 220-228, March.
    16. Ziqi Chen & Man-Lai Tang & Wei Gao & Ning-Zhong Shi, 2014. "New Robust Variable Selection Methods for Linear Regression Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(3), pages 725-741, September.
    17. Xuemei Hu & Weiming Yang, 2019. "Semi-parametric small area inference in generalized semi-varying coefficient mixed effects models," Statistical Papers, Springer, vol. 60(4), pages 1039-1058, August.
    18. José Lombardía, María & Sperlich, Stefan, 2012. "A new class of semi-mixed effects models and its application in small area estimation," Computational Statistics & Data Analysis, Elsevier, vol. 56(10), pages 2903-2917.

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