Estimation of Nonlinear Latent Variable and Mixture Models

Abstract: In this thesis methods are developed for estimation of latent variable models. In particular nonlinear structural equation models are estimated in the presence of ordinal data and mixture models for count data. Paper I introduces an extended nonlinear structural model which allows for interactions between exogenous and endogenous latent variables in the presence of ordinal data. The adaptive Gauss-Hermite quadrature (AGHQ) and Laplace approximations are used to approximate intractable integrals.Paper II introduces a semiparametric approach for modeling a flexible nonlinear structural model in the presence of ordinal data. Intractable integrals are approximated by the AGHQ approximation.Paper III investigates and compares the error rates of three versions of the AGHQ approximation.Paper IV develops an extreme value and zero inflated regression model for modeling of count data which includes a proportion of excess zeroes and extreme values. This is a typical situation when modeling the number of fatalities in armed conflicts.