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Regression analysis under non‐standard situations: a pairwise pseudolikelihood approach

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  • Kung‐Yee Liang
  • Jing Qin

Abstract

Regression analysis is one of the most used statistical methods for data analysis. There are, however, many situations in which one cannot base inference solely on f(y∣x; β), the conditional probability (density) function for the response variable Y, given x, the covariates. Examples include missing data where the missingness is non‐ignorable, sampling surveys in which subjects are selected on the basis of the Y‐values and meta‐analysis where published studies are subject to ‘selection bias’. The conventional approaches require the correct specification of the missingness mechanism, sampling probability and probability for being published respectively. In this paper, we propose an alternative estimating procedure for β based on an idea originated by Kalbfleisch. The novelty of this method is that no assumption on the missingness probability mechanisms etc. mentioned above is required to be specified. Asymptotic efficiency calculations and simulation studies were conducted to compare the method proposed with the two existing methods: the conditional likelihood and the weighted estimating function approaches.

Suggested Citation

  • Kung‐Yee Liang & Jing Qin, 2000. "Regression analysis under non‐standard situations: a pairwise pseudolikelihood approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 773-786.
    • Handle: RePEc:bla:jorssb:v:62:y:2000:i:4:p:773-786
    DOI: 10.1111/1467-9868.00263
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    Cited by:

    1. Tianyi Lu & Shuwei Li & Liuquan Sun, 2023. "Combined estimating equation approaches for the additive hazards model with left-truncated and interval-censored data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(3), pages 672-697, July.
    2. Xuerong Chen & Guoqing Diao & Jing Qin, 2020. "Pseudo likelihood‐based estimation and testing of missingness mechanism function in nonignorable missing data problems," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(4), pages 1377-1400, December.
    3. Hua Yun Chen, 2007. "A Semiparametric Odds Ratio Model for Measuring Association," Biometrics, The International Biometric Society, vol. 63(2), pages 413-421, June.
    4. Chuan Hong & Yang Ning & Peng Wei & Ying Cao & Yong Chen, 2017. "A semiparametric model for vQTL mapping," Biometrics, The International Biometric Society, vol. 73(2), pages 571-581, June.
    5. Yang Ning & Yong Chen, 2015. "A Class of Pseudolikelihood Ratio Tests for Homogeneity in Exponential Tilt Mixture Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(2), pages 504-517, June.
    6. Breunig, Christoph, 2017. "Testing Missing At Random Using Instrumental Variables," Rationality and Competition Discussion Paper Series 59, CRC TRR 190 Rationality and Competition.
    7. Li Liu & Liming Xiang, 2014. "Semiparametric estimation in generalized linear mixed models with auxiliary covariates: A pairwise likelihood approach," Biometrics, The International Biometric Society, vol. 70(4), pages 910-919, December.
    8. Fan Wu & Sehee Kim & Jing Qin & Rajiv Saran & Yi Li, 2018. "A pairwise likelihood augmented Cox estimator for left†truncated data," Biometrics, The International Biometric Society, vol. 74(1), pages 100-108, March.
    9. Marchese, Scott & Diao, Guoqing, 2017. "Density ratio model for multivariate outcomes," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 249-261.
    10. Liu, Tianqing & Yuan, Xiaohui & Sun, Jianguo, 2021. "Weighted rank estimation for nonparametric transformation models with nonignorable missing data," Computational Statistics & Data Analysis, Elsevier, vol. 153(C).
    11. Ning, Jing & Pak, Daewoo & Zhu, Hong & Qin, Jing, 2022. "Conditional independence test of failure and truncation times: Essential tool for method selection," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    12. Yu-Jen Cheng & Mei-Cheng Wang, 2012. "Estimating Propensity Scores and Causal Survival Functions Using Prevalent Survival Data," Biometrics, The International Biometric Society, vol. 68(3), pages 707-716, September.
    13. Hua Yun Chen & Daniel E. Rader & Mingyao Li, 2015. "Likelihood Inferences on Semiparametric Odds Ratio Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1125-1135, September.
    14. Fang Fang & Jiwei Zhao & S. Ejaz Ahmed & Annie Qu, 2021. "A weak‐signal‐assisted procedure for variable selection and statistical inference with an informative subsample," Biometrics, The International Biometric Society, vol. 77(3), pages 996-1010, September.
    15. Maomao Ding & Ruosha Li & Jin Qin & Jing Ning, 2023. "A double‐robust test for high‐dimensional gene coexpression networks conditioning on clinical information," Biometrics, The International Biometric Society, vol. 79(4), pages 3227-3238, December.
    16. Zhong Guan & Jing Qin, 2017. "Empirical likelihood method for non-ignorable missing data problems," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(1), pages 113-135, January.
    17. Christoph Breunig, 2015. "Testing Missing at Random using Instrumental Variables," SFB 649 Discussion Papers SFB649DP2015-016, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    18. C.-Y. Huang & J. Qin & M.-C. Wang, 2010. "Semiparametric Analysis for Recurrent Event Data with Time-Dependent Covariates and Informative Censoring," Biometrics, The International Biometric Society, vol. 66(1), pages 39-49, March.
    19. Rui Duan & Yang Ning & Shuang Wang & Bruce G. Lindsay & Raymond J. Carroll & Yong Chen, 2020. "A fast score test for generalized mixture models," Biometrics, The International Biometric Society, vol. 76(3), pages 811-820, September.
    20. Kano, Yutaka & Takai, Keiji, 2011. "Analysis of NMAR missing data without specifying missing-data mechanisms in a linear latent variate model," Journal of Multivariate Analysis, Elsevier, vol. 102(9), pages 1241-1255, October.
    21. Cristiano Varin, 2008. "On composite marginal likelihoods," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 92(1), pages 1-28, February.
    22. Christoph Breunig, 2017. "Testing Missing at Random using Instrumental Variables," SFB 649 Discussion Papers SFB649DP2017-007, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    23. Diao Guoqing & Ning Jing & qin jing, 2012. "Maximum Likelihood Estimation for Semiparametric Density Ratio Model," The International Journal of Biostatistics, De Gruyter, vol. 8(1), pages 1-29, June.
    24. Chuan Hong & Yang Ning & Shuang Wang & Hao Wu & Raymond J. Carroll & Yong Chen, 2017. "PLEMT: A Novel Pseudolikelihood-Based EM Test for Homogeneity in Generalized Exponential Tilt Mixture Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1393-1404, October.
    25. Jiwei Zhao, 2017. "Reducing bias for maximum approximate conditional likelihood estimator with general missing data mechanism," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(3), pages 577-593, July.

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