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Parametric Frailty Analysis in Presence of Collinearity: An Application to Assessment of Infant Mortality

Author

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  • Olayan Albalawi

    (Department of Statistics, Faculty of Science, University of Tabuk, Tabuk 47512, Saudi Arabia)

  • Anu Sirohi

    (Department of Mathematics, Sharda University, Greater Noida 201310, India)

  • Piyush Kant Rai

    (Department of Statistics, Institute of Science, Banaras Hindu University, Varanasi 221005, India)

  • Ayed R. A. Alanzi

    (Department of Mathematics, College of Science and Arts in Gurayat, Jouf University, Gurayat 77454, Saudi Arabia)

Abstract

This paper analyzes the time to event data in the presence of collinearity. To address collinearity, the ridge regression estimator was applied in multiple and logistic regression as an alternative to the maximum likelihood estimator (MLE), among others. It has a smaller mean square error (MSE) and is therefore more precise. This paper generalizes the approach to address collinearity in the frailty model, which is a random effect model for the time variable. A simulation study is conducted to evaluate its performance. Furthermore, the proposed method is applied on real life data taken from the largest sample survey of India, i.e., national family health survey (2005–2006 ) data to evaluate the association of different determinants on infant mortality in India.

Suggested Citation

  • Olayan Albalawi & Anu Sirohi & Piyush Kant Rai & Ayed R. A. Alanzi, 2022. "Parametric Frailty Analysis in Presence of Collinearity: An Application to Assessment of Infant Mortality," Mathematics, MDPI, vol. 10(13), pages 1-10, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2255-:d:849214
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    References listed on IDEAS

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    1. D. Omariba & Roderic Beaujot & Fernando Rajulton, 2007. "Determinants of infant and child mortality in Kenya: an analysis controlling for frailty effects," Population Research and Policy Review, Springer;Southern Demographic Association (SDA), vol. 26(3), pages 299-321, June.
    2. Heckman, James J & Hotz, V Joseph & Walker, James R, 1985. "New Evidence on the Timing and Spacing of Births," American Economic Review, American Economic Association, vol. 75(2), pages 179-184, May.
    3. Narayan Sastry, 1996. "Community characteristics, individual and household attributes, and child survival in brazil," Demography, Springer;Population Association of America (PAA), vol. 33(2), pages 211-229, May.
    4. Hans-Peter Blossfeld & Alfred Hamerle, 1992. "Unobserved heterogeneity in event history models," Quality & Quantity: International Journal of Methodology, Springer, vol. 26(2), pages 157-168, May.
    5. Anne Pebley & Noreen Goldman & Germán Rodríguez, 1996. "Prenatal and delivery care and childhood immunization in guatemala: Do family and community matter?," Demography, Springer;Population Association of America (PAA), vol. 33(2), pages 231-247, May.
    6. James Vaupel & Kenneth Manton & Eric Stallard, 1979. "The impact of heterogeneity in individual frailty on the dynamics of mortality," Demography, Springer;Population Association of America (PAA), vol. 16(3), pages 439-454, August.
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