Survival Analysis of Time-to-First birth after marriage in Nigeria using three parameter inverse gaussian distribution

Abstract

Overpopulation is a huge problem for the people of sub-Sahara African countries, including Nigeria. In order to tackle this problem, demographers have in the last five decades made immense efforts towards understanding the causes and mechanisms of fertility, and to explain the variations inherent in it. Several theoretical approaches that have been proposed mainly focus on cumulative or completed fertility as the main dependent variable. Moreover, it is equally important to examine variations in fertility in such entities such as timing and spacing of births. Data on birth interval offers rich and more detailed information for the analysis of reproductive behavior than does the data on number of births. And more importantly, timing of first birth after marriage which also corresponds to first-birth-interval (FBI) is strongly correlated to the number of children a woman would have by the end of her reproductive life. In this research, FBI is modeled stochastically as a survival response variable. Suitability of a class of some standard parametric models is investigated and the study comes up with a novel three-parameter inverse Gaussian model through the exponentiation of probability distribution approach. Estimations of parameters are obtained by maximizing the log-likelihood functions of the data in R software programming. Different approaches employed to discriminate between the distribution and the existing ones considered, suggests that the new model, Lehmann type II inverse Gaussian, provides a better fit for the FBI and other lifetime data. Akaike Information Criterion (AIC) which is a resemblance of coefficient of determination in linear regression, also shows a significant reduction in value as covariates are introduced into it in comparison with regressions from other distributions. This research finds that age of women at marriage, education attainment and region where women reside are significant prognostic factors that influence the chance of first birth after marriage. The thesis concludes by calling on agencies and organizations working on population control, especially in Nigeria, to initiate programs that will encourage girl-child education to higher level.