Skip to main content
SpringerLink
Log in

Testing Homogeneity in Weibull Error in Variables Models

  • Published:
Annals of the Institute of Statistical Mathematics Aims and scope Submit manuscript

An Erratum to this article was published on 15 November 2006

Abstract

We discuss properties of the score statistics for testing the null hypothesis of homogeneity in a Weibull mixing model in which the group effect is modelled as a random variable and some of the covariates are measured with error. The statistics proposed are based on the corrected score approach and they require estimation only under the conventional Weibull model with measurement errors and does not require that the distribution of the random effect be specified. The results in this paper extend results in Gimenez, Bolfarine, and Colosimo (Annals of the Institute of Statistical Mathematics, 52, 698–711, 2000) for the case of independent Weibull models. A simulation study is provided.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Bolfarine H., Arellano-Valle R.B. (1998). Weak nondifferential measurement error models. Statistics and Probability Letters 40:279–287

    Article  MATH  MathSciNet  Google Scholar 

  • Bolfarine H., Valença D.M. (2005). Score tests for Weibull-regression models with random effect. Biometrical Journal 47:707–720

    Article  Google Scholar 

  • Breslow N.E., Clayton D.G. (1993). Approximate inference in generalized linear mixed models. Journal of the American Statistical Association 88:9–25

    Article  MATH  Google Scholar 

  • Carroll R.J., Ruppert D., Stefanski L.A. (1995). Measurement error in nonlinear models. Chapman and Hall, New York

    MATH  Google Scholar 

  • Chant D. (1974). On asymptotic tests of composite hypotheses in nonstandard conditions. Biometrika 61:291–298

    Article  MATH  MathSciNet  Google Scholar 

  • Commenges D., Andersen P.K. (1995). Score test of homogeneity for survival data. Lifetime Data Analysis 1:145–156

    Article  PubMed  MathSciNet  MATH  Google Scholar 

  • Commenges D., Jaqmin-Gadda H. (1997). Generalized score test of homogeneity based on correlated random effects models. Journal of the Royal Statistical Society B 59:157–171

    Article  MATH  Google Scholar 

  • Commenges D., Letenneur L., Jacqmin H., Moreau T., Dartigues J. (1994). Test of homogeneity of binary data with explanatory variables. Biometrics 50: 613–620

    Article  PubMed  MathSciNet  MATH  Google Scholar 

  • Cook J., Stefanski L.A. (1994). A simulation extrapolation method for parametric measurement error models. Journal of the American Statistical Association 89:1314–1328

    Article  MATH  Google Scholar 

  • Cox D.R. (1983). Some remarks on overdispersion. Biometrika 70:269–274

    Article  MATH  MathSciNet  Google Scholar 

  • Dean C. (1992). Testing for overdispersion in Poisson and binomial regression models. Journal of the American Statistical Association 87:451–457

    Article  MathSciNet  Google Scholar 

  • Doornik, J.A. (2001). Object-oriented matrix programming using ox, 4th edn. London: Timberlake.

  • Gimenez P., Bolfarine H. (1997). Corrected score functions in classical error-in-variables and incidental parameter models. Australian Journal of Statistics 39:325–344

    MATH  MathSciNet  Google Scholar 

  • Gimenez P., Bolfarine H., Colosimo E. (2000). Hypotheses testing in measurement error models. Annals of the Institute of Statistical Mathematics 52:698–711

    Article  MathSciNet  MATH  Google Scholar 

  • Gray R.J. (1995). Test for variation over groups in survival data. Journal of the American Statistical Association 90:198–203

    Article  MATH  MathSciNet  Google Scholar 

  • Hamerle A. (1990). On a simple teste for neglected heterogeneity in panel studies. Biometrics 46:193–199

    Article  MATH  Google Scholar 

  • Hougaard P., Myglegaard P., Borch-Johnsen K. (1994). Heterogeneity models of disease susceptibility, with application to diabetic nephropathy. Biometrika 50:1178–1188

    Google Scholar 

  • Jacqmin-Gadda H., Commenges D. (1995). Tests of homogeneity for generalized linear models. Journal of the American Statistical Association 90:1237–1246

    Article  MATH  MathSciNet  Google Scholar 

  • Keiding N., Andersen P.K., Klein J.P. (1997). The role of frailty models and accelerated failure time models in describing heterogeneity due to omitted covariates. Statistics in Medicine 16:215–224

    Article  PubMed  Google Scholar 

  • Kimber A.C. (1996). A Weibull-based score test for homogeneity. Lifetime Data Analysis 2:63–71

    Article  PubMed  MATH  Google Scholar 

  • Lagakos S.W. (1988). Effects of mismodelling and mismeasuring explanatory variables on tests of their association with a response variable. Statistics in Medicine 7:257–274

    Article  PubMed  Google Scholar 

  • Li Y., Lin X. (2003). Functional inference in frailty measurement error models for clustered survival data using the SIMEX approach. Journal of the American Statistical Association 98:191–203

    Article  MATH  MathSciNet  Google Scholar 

  • Liang K.Y. (1987). A locally most powerful test for homogeneity with many strata. Biometrika 74:259–264

    Article  MathSciNet  MATH  Google Scholar 

  • Lin X. (1997). Variance components testing in generalized linear models with random erros. Biometrika 84:309–326

    Article  MATH  MathSciNet  Google Scholar 

  • Lin X., Carroll R.J. (1999). Simex variance component tests in generalized linear mixed measurement error models. Biometrics 55:613–619

    Article  PubMed  MATH  Google Scholar 

  • Moran P.A.P. (1971). Maximum-likelihood estimation in non-standard conditions. Proceedings of the Cambridge Philosophical Society 70: 441–450

    Article  MATH  Google Scholar 

  • Nakamura T. (1990). Corrected score functions for errors-in-variables models: Methodology and application to generalized linear models. Biometrika 77:127–137

    Article  MATH  MathSciNet  Google Scholar 

  • Paula G.A., Artes R. (2000). One-sided test to assess correlation in linear logistic models using estimating equations. Biometrical Journal 42:701–714

    Article  MATH  MathSciNet  Google Scholar 

  • Self G., Liang K.Y. (1987). Asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions. Journal of the American Statistical Association 82:605–610

    Article  MATH  MathSciNet  Google Scholar 

  • Silvapulle M.J., Silvapulle P. (1995). A score test against one-sided alternatives. Journal of the American Statistical Association 90:342–349

    Article  MATH  MathSciNet  Google Scholar 

  • Tosteson T., Tsiatis A. (1988). The asymptotic relative efficiency of score tests in a generalized linear model with surrogate covariates. Biometrika 75:507–514

    Article  MATH  MathSciNet  Google Scholar 

  • Tsiatis A.A., DeGruttola V., Wulfsohn M.S. (1995). Modeling the relationship of survival to longitudinal data measured with error. Applications to survival and CD4 counts in patients with AIDS. Journal of the American Statistical Association 90:27–37

    Google Scholar 

  • Valença, D.M. (2003). Testes de homogeneidade e estimação para dados de sobrevivência agrupados e com erros de medida. Doctoral Thesis, Department of Statistics, University of São Paulo

  • Vu H.T.V., Zhou S. (1997). Generalization of likelihood ratio tests under nonstandard conditions. The Annals of Statistics 25:897–916

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Estatística, Universidade Federal do Rio Grande do Norte, CCET, CEP 59072-970, Natal, R.N., Brazil

    Dione M. Valença & Heleno Bolfarine

Authors
  1. Dione M. Valença
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Heleno Bolfarine
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dione M. Valença.

Additional information

An erratum to this article can be found at http://dx.doi.org/10.1007/s10463-006-0091-3

About this article

Cite this article

Valença, D.M., Bolfarine, H. Testing Homogeneity in Weibull Error in Variables Models. Ann Inst Stat Math 58, 115–129 (2006). https://doi.org/10.1007/s10463-005-0006-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10463-005-0006-8

Keywords

Search

Navigation