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The Impact of Misspecified Random Effect Distribution in a Weibull Regression Mixed Model

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  • Freddy Hernández

    (Escuela de Estadística, Universidad Nacional de Colombia sede Medellín, Medellín 050034, Colombia)

  • Viviana Giampaoli

    (Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo 05508-090, Brazil)

Abstract

Mixed models are useful tools for analyzing clustered and longitudinal data. These models assume that random effects are normally distributed. However, this may be unrealistic or restrictive when representing information of the data. Several papers have been published to quantify the impacts of misspecification of the shape of the random effects in mixed models. Notably, these studies primarily concentrated their efforts on models with response variables that have normal, logistic and Poisson distributions, and the results were not conclusive. As such, we investigated the misspecification of the shape of the random effects in a Weibull regression mixed model with random intercepts in the two parameters of the Weibull distribution. Through an extensive simulation study considering six random effect distributions and assuming normality for the random effects in the estimation procedure, we found an impact of misspecification on the estimations of the fixed effects associated with the second parameter σ of the Weibull distribution. Additionally, the variance components of the model were also affected by the misspecification.

Suggested Citation

  • Freddy Hernández & Viviana Giampaoli, 2018. "The Impact of Misspecified Random Effect Distribution in a Weibull Regression Mixed Model," Stats, MDPI, vol. 1(1), pages 1-29, May.
    • Handle: RePEc:gam:jstats:v:1:y:2018:i:1:p:5-76:d:149901
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    References listed on IDEAS

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    1. Verbeke, Geert & Lesaffre, Emmanuel, 1997. "The effect of misspecifying the random-effects distribution in linear mixed models for longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 23(4), pages 541-556, February.
    2. Almalki, Saad J. & Nadarajah, Saralees, 2014. "Modifications of the Weibull distribution: A review," Reliability Engineering and System Safety, Elsevier, vol. 124(C), pages 32-55.
    3. Reza Drikvandi & Geert Verbeke & Geert Molenberghs, 2017. "Diagnosing misspecification of the random-effects distribution in mixed models," Biometrics, The International Biometric Society, vol. 73(1), pages 63-71, March.
    4. Silva, Giovana O. & Ortega, Edwin M.M. & Cordeiro, Gauss M., 2009. "A log-extended Weibull regression model," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4482-4489, October.
    5. Agresti, Alan & Caffo, Brian & Ohman-Strickland, Pamela, 2004. "Examples in which misspecification of a random effects distribution reduces efficiency, and possible remedies," Computational Statistics & Data Analysis, Elsevier, vol. 47(3), pages 639-653, October.
    6. Xianzheng Huang, 2009. "Diagnosis of Random-Effect Model Misspecification in Generalized Linear Mixed Models for Binary Response," Biometrics, The International Biometric Society, vol. 65(2), pages 361-368, June.
    7. Prataviera, Fábio & Ortega, Edwin M.M. & Cordeiro, Gauss M. & Pescim, Rodrigo R. & Verssani, Bruna A.W., 2018. "A new generalized odd log-logistic flexible Weibull regression model with applications in repairable systems," Reliability Engineering and System Safety, Elsevier, vol. 176(C), pages 13-26.
    8. John M. Neuhaus & Charles E. McCulloch & Ross Boylan, 2011. "A Note on Type II Error Under Random Effects Misspecification in Generalized Linear Mixed Models," Biometrics, The International Biometric Society, vol. 67(2), pages 654-656, June.
    9. Charles E. McCulloch & John M. Neuhaus, 2011. "Prediction of Random Effects in Linear and Generalized Linear Models under Model Misspecification," Biometrics, The International Biometric Society, vol. 67(1), pages 270-279, March.
    10. Filippo Domma & Francesca Condino & Božidar V. Popović, 2017. "A new generalized weighted Weibull distribution with decreasing, increasing, upside-down bathtub, N-shape and M-shape hazard rate," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(16), pages 2978-2993, December.
    11. Sohn, So Young & Chang, In Sang & Moon, Tae Hee, 2007. "Random effects Weibull regression model for occupational lifetime," European Journal of Operational Research, Elsevier, vol. 179(1), pages 124-131, May.
    12. Alonso, A. & Litière, S. & Molenberghs, G., 2008. "A family of tests to detect misspecifications in the random-effects structure of generalized linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4474-4486, May.
    13. Bagheri, S.F. & Bahrami Samani, E. & Ganjali, M., 2016. "The generalized modified Weibull power series distribution: Theory and applications," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 136-160.
    14. Sohn, So Young & Yoon, Kyung Bok & Chang, In Sang, 2006. "Random effects model for the reliability management of modules of a fighter aircraft," Reliability Engineering and System Safety, Elsevier, vol. 91(4), pages 433-437.
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