A novel approach for estimating fertility rates in finite populations using count regression models

Demographic health surveys (DHS) contain in-depth information about the demographic characteristics and the factors affecting them. However, fertility rates which are the important indicators of population growth have been estimated by utilizing the design-based approaches. Model-based approach, on the other hand, facilitates efficient predictive estimates for these rates by utilizing the demographic and other family planning related characters. In this article, we first attempt to observe the effect of various socio-demographic and family planing related factors on births counts by fitting different regression models to Pakistan Demographic Health Survey 2017-2018 data under classical as well as Bayesian frameworks. The births occurred during the time periods of 1-year, 3-years and 5-years are taken as the responses and modeled using different non-linear models. The model-based approach is then used for estimation of the fertility measures including age-specific fertility rates, total fertility rate, general fertility rate, and gross reproduction rate for ever-married women in Pakistan. The performance of the model-based estimators is examined using a bootstrapped sampling algorithm. While the age-specific fertility rates are over-estimated for some age groups and under-estimated for others. The model-based fertility estimates are recommended for estimating the demographic indicators at national and sub-national levels when survey data contains incomplete or missing responses.