Identifiability of bivariate mixtures: An application to infant mortality models

摘要

The problem of identifiability is basic to statistical methods and data analysis. One specific issue is the identifiability of mixtures that use the density of a phenotypic trait to help control heterogeneity in infant mortality. The determination of a unique characterization of the parameters in any mixture model is a necessary condition for consistent parameter estimates. Indeed, such models are often modified by restrictions that achieves uniqueness and these restrictions are often chosen because of their interpretative power.;Identifiability of the parameters for a Mixture of Bivariate Densities (MBD) in the form f(x, y; beta,theta,pi) = pi f (y|x; beta 1) f (x; theta1) + (1 -- pi) f (y| x; beta2) f (x; theta 2) is considered with particular attention in this thesis given to case where theta1 ≠ theta2 (i.e. marginal of x is a nondegenerate mixture). Characterizations of identifiability that includes clusterwise regression models (Hennig 2000), symmetric distribution models (Hunter 2007) and Gage (2004).;The study developed broad conditions for identifiability of bivariate mixture models. Additionally, sufficient conditions are given to determine when an identifiable MBD is still identifiable for parameters associated with exogenous variables introduced as covariates for the MBD parameters. These identified models are applied to characterize latent subpopulations related to infant mortality and survival.;To investigate the proposed identified models in depth, they are applied to weight specific infant survival data. The dataset used for illustrations and analyses of the proposed models in this study are obtained from the NCHS National Linked Birth/Infant Death files for the birth cohort born in 2001.;The proposed model gives a resolution of the phenomenon that at t = 365, lower birth weight specific infant mortalities among African Americans are smaller compared to European Americans despite their larger infant mortality. This results actually holds for all values of t . Hazard/mortality in the Secondary subpopulation at each birth weight is lower compared to the Primary subpopulation. The model fits the data adequately well.