Sankhya B

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Inferences in Binary Dynamic Fixed Models in a Semi-parametric Setup

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Abstract

In a longitudinal setup, the so-called generalized estimating equations approach was a popular inference technique to obtain efficient regression estimates until it was discovered that this approach may in fact yield less efficient estimates than an independence assumption-based estimating equation approach. In this paper, we revisit this inference issue in a semi-parametric longitudinal setup for binary data and find that the semi-parametric generalized estimating equations also encounter similar efficiency drawbacks when compared with independence assumption-based approach. This makes the generalized estimating equations approach unacceptable for correlated data analysis. We analyze the repeated binary data by fitting a semi-parametric binary dynamic model. The non-parametric function and the regression parameters involved in the semi-parametric regression function are estimated by using a semi-parametric generalized quasi-likelihood and a semi-parametric quasi-likelihood approach, respectively, whereas the dynamic dependence, that is, the correlation index parameter of the model is estimated by a semi-parametric method of moments. Asymptotic and finite sample properties of the estimators are discussed. The proposed model and the estimation methodology are also illustrated by reanalyzing the well-known respiratory disease data.

Keywords and phrases

Dynamic models for repeated binary responses GEE approach in semi-parametric setup Non-parametric function in secondary covariates Parametric regression in primary covariates Semi-parametric quasi-likelihood and semi-parametric generalized quasi-likelihood estimation Time dependent covariates 

AMS (2000) subject classification

Primary 62H12 Secondary 62F10 62F12 

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Notes

Acknowledgements

This research was partially supported by a NSERC grant. The authors wish to thank two referees for their valuable comments and suggestions leading to the improvement of the paper.

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Copyright information

© Indian Statistical Institute 2018

Authors and Affiliations

  1. 1.Carleton UniversityOttawaCanada
  2. 2.Memorial UniversitySt. John’sCanada

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