Estimation of marriage incidence rates by combining two cross-sectional retrospective designs: Event history analysis of two dependent processes

TL;DR

This paper develops a likelihood-based method to estimate marriage incidence rates by combining data from two different retrospective cross-sectional study designs, accounting for endogenous covariates like education and their correlation with marriage processes.

Contribution

It introduces a joint modeling approach for two types of retrospective data to accurately estimate marriage incidence rates, addressing endogenous covariates and data combination challenges.

Findings

Combining data improves estimation efficiency.

Method performs well in simulations under correct assumptions.

Application to Indian surveys demonstrates practical utility.

Abstract

The aim of this work is to develop methods for studying the determinants of marriage incidence using marriage histories collected under two different types of retrospective cross-sectional study designs. These designs are: sampling of ever married women before the cross-section, a prevalent cohort, and sampling of women irrespective of marital status, a general cross-sectional cohort. While retrospective histories from a prevalent cohort do not identify incidence rates without parametric modelling assumptions, the rates can be identified when combined with data from a general cohort. Moreover, education, a strong endogenous covariate, and marriage processes are correlated. Hence, they need to be modelled jointly in order to estimate the marriage incidence. For this purpose, we specify a multi-state model and propose a likelihood-based estimation method. We outline the assumptions under which a likelihood expression involving only marriage incidence parameters can be derived. This is of particular interest when either retrospective education histories are not available or related parameters are not of interest. Our simulation results confirm the gain in efficiency by combining data from the two designs, while demonstrating how the parameter estimates are affected by violations of the assumptions used in deriving the simplified likelihood expressions. Two Indian National Family Health Surveys are used as motivation for the methodological development and to demonstrate the application of the methods.