Analysis of test score for a twin series using Multivariate DHGLMs

Abstract

Multivariate Data Analysis refers to any statistical technique used to analyze data that arises from more than one response variable. This essentially models reality where each situation, product, or decision involves more than a single variable. Various theories regarding one response variable data have been suggested. But there is only few multivariate models because of intractable integration. Double Hierarchical Generalized Linear Models(DHGLM) proposed by Lee and Nelder is a linear model method which random effects can be specified in both the mean and the residual variances. By assuming correlationa among random effects in DHGLM for differenct responses, multivariate models are easily developed. In this thesis, we construt multivariate HGLMs for analysis of twin interaction study on the National Merit Scholarship Qualifying Test in 1962. Since we can estimate correlation between different response variables, we interpret correlation values for different response variables.