title: Two-stage hierarchical modeling for analysis of subpopulations in conditional distributions.
abstract: In this work, we develop modeling and estimation approach for the analysis of cross-sectional clustered data with multimodal conditional distributions where the main interest is in analysis of subpopulations. It is proposed to model such data in a hierarchical model with conditional distributions viewed as finite mixtures of normal components. With a large number of observations in the lowest level clusters, a two-stage estimation approach is used. In the first stage, the normal mixture parameters in each lowest level cluster are estimated using robust methods. Robust alternatives to the maximum likelihood estimation are used to provide stable results even for data with conditional distributions such that their components may not quite meet normality assumptions. Then the lowest level cluster-specific means and standard deviations are modeled in a mixed effects model in the second stage. A small simulation study was conducted to compare performance of finite normal mixture population parameter estimates based on robust and maximum likelihood estimation in stage 1. The proposed modeling approach is illustrated through the analysis of mice tendon fibril diameters data. Analyses results address genotype differences between corresponding components in the mixtures and demonstrate advantages of robust estimation in stage 1.
authors.affiliation: Division of Biostatistics, Department of Pharmacology and Experimental Therapeutics, Thomas Jefferson University, Philadelphia, Pennsylvania 19107, U.S.A.
authors.forename: Inna
authors.initials: I
authors.lastname: Chervoneva
authors.forename: Tingting
authors.initials: T
authors.lastname: Zhan
authors.forename: Boris
authors.initials: B
authors.lastname: Iglewicz
authors.forename: Walter W
authors.initials: WW
authors.lastname: Hauck
authors.forename: David E
authors.initials: DE
authors.lastname: Birk