Spline functions and their application to analysis of interval data : breastfeeding durations and closed birth intervals

Hauli, Dan Emmanuel (1986) Spline functions and their application to analysis of interval data : breastfeeding durations and closed birth intervals. University of Southampton, Doctoral Thesis.

Abstract

Spline functions are amongst the most important functions for approximating smooth functions. Their theory originated in its present form with two classic papers by Schoenberg (1946a,b) and owes much of its development and most of its popularisation to the work of mathematicians in approximation theory. This thesis gives details of basic spline theory from a statistical point of view and highlights the flexibility of splines as approximating tools by demonstrating their superiority over polynomial functions. It also proposes two ways to overcome the problems of inefficient splines. There is unanimous agreement that breastfeeding is an important determinant of fertility. This thesis uses spline functions to find the unknown regimes followed by characteristics of breastfeeding, features such as weaning rates and densities of the durations of lactation. The effects of the factors of breastfeeding on these curves are assumed to be continuous and are also estimated by splines. We also propose a new spline model for analysing the two random components of the birth interval, ie the nonfecund duration and the waiting time to conception, using information from the closed birth intervals alone. These spline models are extensions of the proportional hazards of Cox (1972). The models are fitted with the WFS data from six countries and the results discussed in detail. (D73801/87)

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