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Assessing Goodness-of-Fit of Generalized Logit Models Based on Case-Control Data

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  • Zhang, Biao

Abstract

We consider testing the validity of the generalized logit model with I+1 categories based on case-control data. After reparametrization, the assumed logit model is equivalent to an (I+1)-sample semiparametric model in which the IÂ log ratios of two unspecified density functions are linear in data. By identifying this (I+1)-sample semiparametric model, which is of intrinsic interest in general (I+1)-sample problems, with a biased sampling model, we propose a weighted Kolmogorov-Smirnov-type statistic to test the validity of the generalized logit model. We establish some asymptotic results associated with the proposed test statistic. We also propose a bootstrap procedure along with some results on simulation and on analysis of three real data sets.

Suggested Citation

  • Zhang, Biao, 2002. "Assessing Goodness-of-Fit of Generalized Logit Models Based on Case-Control Data," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 17-38, July.
    • Handle: RePEc:eee:jmvana:v:82:y:2002:i:1:p:17-38
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    Cited by:

    1. Zhang, Archer Gong & Chen, Jiahua, 2022. "Density ratio model with data-adaptive basis function," Journal of Multivariate Analysis, Elsevier, vol. 191(C).
    2. Wang, Chunlin & Marriott, Paul & Li, Pengfei, 2017. "Testing homogeneity for multiple nonnegative distributions with excess zero observations," Computational Statistics & Data Analysis, Elsevier, vol. 114(C), pages 146-157.
    3. Ori Davidov & Konstantinos Fokianos & George Iliopoulos, 2010. "Order-Restricted Semiparametric Inference for the Power Bias Model," Biometrics, The International Biometric Society, vol. 66(2), pages 549-557, June.
    4. Yufan Wang & Xingzhong Xu, 2023. "Homogeneity Test for Multiple Semicontinuous Data with the Density Ratio Model," Mathematics, MDPI, vol. 11(17), pages 1-28, September.
    5. OrI Davidov & Konstantinos Fokianos & George Iliopoulos, 2014. "Semiparametric Inference for the Two-way Layout Under Order Restrictions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(3), pages 622-638, September.
    6. Yufan Wang & Xingzhong Xu, 2023. "A Posterior p -Value for Homogeneity Testing of the Three-Sample Problem," Mathematics, MDPI, vol. 11(18), pages 1-25, September.

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