IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v54y2010i12p3371-3378.html
   My bibliography  Save this article

Robustness of design for the testing of lack of fit and for estimation in binary response models

Author

Listed:
  • Wiens, Douglas P.

Abstract

Experimentation in scientific or medical studies is often carried out in order to model the 'success' probability of a binary random variable. Experimental designs for the testing of lack of fit and for estimation, for data with binary responses depending upon covariates which can be controlled by the experimenter, are constructed. It is supposed that the preferred model is one in which the probability of the occurrence of the target outcome depends on the covariates through a link function (logistic, probit, etc.) evaluated at a regression response -- a function of the covariates and of parameters to be estimated from the data, once gathered. The fit of this model is to be tested within a broad class of alternatives over which the regression response varies. To this end, the problem is phrased as one of discriminating between the preferred model and the class of alternatives. This, in turn, is a hypothesis testing problem, for which the asymptotic power of the test statistic is directly related to the Kullback-Leibler divergence between the models, averaged over the design. 'Maximin' designs, which maximize (through the design) the minimum (among the class of alternative models) value of this power together with a measure of the efficiency of the parameter estimates are also constructed. Several examples are presented in detail; two of these relate to a medical study of fluoxetine versus a placebo in depression patients. The method of design construction is computationally intensive, and involves a steepest descent minimization routine coupled with simulated annealing.

Suggested Citation

  • Wiens, Douglas P., 2010. "Robustness of design for the testing of lack of fit and for estimation in binary response models," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3371-3378, December.
  • Handle: RePEc:eee:csdana:v:54:y:2010:i:12:p:3371-3378
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(09)00083-8
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    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. Biedermann, Stefanie & Dette, Holger, 2001. "Optimal designs for testing the functional form of a regression via nonparametric estimation techniques," Statistics & Probability Letters, Elsevier, vol. 52(2), pages 215-224, April.
    2. Bischoff, Wolfgang & Miller, Frank, 2006. "Lack-of-fit-efficiently optimal designs to estimate the highest coefficient of a polynomial with large degree," Statistics & Probability Letters, Elsevier, vol. 76(15), pages 1701-1704, September.
    3. Wiens, Douglas P., 1991. "Designs for approximately linear regression: two optimality properties of uniform designs," Statistics & Probability Letters, Elsevier, vol. 12(3), pages 217-221, September.
    4. Adewale, Adeniyi J. & Wiens, Douglas P., 2006. "New criteria for robust integer-valued designs in linear models," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 723-736, November.
    5. Tekle, Fetene B. & Tan, Frans E.S. & Berger, Martijn P.F., 2008. "Maximin D-optimal designs for binary longitudinal responses," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5253-5262, August.
    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. Dette, Holger & Melas, Viatcheslav B. & Shpilev, Petr, 2017. "T-optimal discriminating designs for Fourier regression models," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 196-206.

    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. Mandal, Nripes Kumar & Pal, Manisha, 2013. "Maximin designs for the detection of synergistic effects," Statistics & Probability Letters, Elsevier, vol. 83(7), pages 1632-1637.
    2. Linglong Kong & Douglas P. Wiens, 2015. "Model-Robust Designs for Quantile Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 233-245, March.
    3. Renata Eirini Tsirpitzi & Frank Miller & Carl-Fredrik Burman, 2023. "Robust optimal designs using a model misspecification term," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(7), pages 781-804, October.
    4. Bischoff, Wolfgang & Miller, Frank, 2006. "Lack-of-fit-efficiently optimal designs to estimate the highest coefficient of a polynomial with large degree," Statistics & Probability Letters, Elsevier, vol. 76(15), pages 1701-1704, September.
    5. Dette, Holger & Wiens, Douglas P., 2007. "Robust designs for 3D shape analysis with spherical harmonic descriptors," Technical Reports 2007,12, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    6. Douglas P. Wiens, 2009. "Robust discrimination designs," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(4), pages 805-829, September.
    7. Fetene B. Tekle & Dereje W. Gudicha & Jeroen K. Vermunt, 2016. "Power analysis for the bootstrap likelihood ratio test for the number of classes in latent class models," 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. 10(2), pages 209-224, June.
    8. Ueckert, Sebastian & Mentré, France, 2017. "A new method for evaluation of the Fisher information matrix for discrete mixed effect models using Monte Carlo sampling and adaptive Gaussian quadrature," Computational Statistics & Data Analysis, Elsevier, vol. 111(C), pages 203-219.
    9. Sheng Wu & Weng Kee Wong & Catherine M. Crespi, 2017. "Maximin optimal designs for cluster randomized trials," Biometrics, The International Biometric Society, vol. 73(3), pages 916-926, September.
    10. Hengzhen Huang & Hong†Bin Fang & Ming T. Tan, 2018. "Experimental design for multi†drug combination studies using signaling networks," Biometrics, The International Biometric Society, vol. 74(2), pages 538-547, June.
    11. Huang, Hengzhen & Chen, Xueping, 2021. "Compromise design for combination experiment of two drugs," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    12. Karvanen, Juha, 2009. "Approximate cost-efficient sequential designs for binary response models with application to switching measurements," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1167-1176, February.
    13. Hong-Yan Jiang & Rong-Xian Yue, 2019. "Pseudo-Bayesian D-optimal designs for longitudinal Poisson mixed models with correlated errors," Computational Statistics, Springer, vol. 34(1), pages 71-87, March.
    14. Jóźwiak, Katarzyna & Moerbeek, Mirjam, 2012. "Cost-effective designs for trials with discrete-time survival endpoints," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 2086-2096.
    15. Xiao-Dong Zhou & Yun-Juan Wang & Rong-Xian Yue, 2021. "Optimal designs for discrete-time survival models with random effects," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(2), pages 300-332, April.
    16. Candel, Math J.J.M. & Van Breukelen, Gerard J.P., 2010. "D-optimality of unequal versus equal cluster sizes for mixed effects linear regression analysis of randomized trials with clusters in one treatment arm," Computational Statistics & Data Analysis, Elsevier, vol. 54(8), pages 1906-1920, August.
    17. H. Abebe & F. Tan & G. Breukelen & M. Berger, 2014. "Robustness of Bayesian D-optimal design for the logistic mixed model against misspecification of autocorrelation," Computational Statistics, Springer, vol. 29(6), pages 1667-1690, December.
    18. Adewale, Adeniyi J. & Xu, Xiaojian, 2010. "Robust designs for generalized linear models with possible overdispersion and misspecified link functions," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 875-890, April.
    19. Xiaojian Xu & Xiaoli Shang, 2017. "D-optimal designs for full and reduced Fourier regression models," Statistical Papers, Springer, vol. 58(3), pages 811-829, September.
    20. Biedermann, Stefanie & Dette, Holger, 2000. "Optimal designs for testing the functional form of a regression via nonparametric estimation techniques," Technical Reports 2000,41, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.

    More about this item

    Statistics

    Access and download statistics

    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:eee:csdana:v:54:y:2010:i:12:p:3371-3378. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.