<p>Longitudinal twin data provide important information for exploring sources of variation in human traits. In statistical models for twin data, unobserved genetic and environmental factors influencing the trait are represented by latent variables. In this way, trait variation can be decomposed into genetic and environmental components. With repeated measurements on twins, latent variables can be used to describe individual trajectories, and the genetic and environmental variance components are assessed as functions of age. This thesis contributes to statistical methodology for analysing longitudinal twin data by (i) exploring the use of random change point models for modelling variance as a function of age, (ii) assessing how nonresponse in twin studies may affect estimates of genetic and environmental influences, and (iii) providing a method for hypothesis testing of genetic and environmental variance components. The random change point model, in contrast to linear and quadratic random effects models, is shown to be very flexible in capturing variability as a function of age. Approximate maximum likelihood inference through first-order linearization of the random change point model is contrasted with Bayesian inference based on Markov chain Monte Carlo simulation. In a set of simulations based on a twin model for informative nonresponse, it is demonstrated how the effect of nonresponse on estimates of genetic and environmental variance components depends on the underlying nonresponse mechanism. This thesis also reveals that the standard procedure for testing variance components is inadequate, since the null hypothesis places the variance components on the boundary of the parameter space. The asymptotic distribution of the likelihood ratio statistic for testing variance components in classical twin models is derived, resulting in a mixture of chi-square distributions. Statistical methodology is illustrated with applications to empirical data on cognitive function from a longitudinal twin study of aging. </p>

Longitudinal twin data provide important information for exploring sources of variation in human traits. In statistical models for twin data, unobserved genetic and environmental factors influencing the trait are represented by latent variables. In this way, trait variation can be decomposed into genetic and environmental components. With repeated measurements on twins, latent variables can be used to describe individual trajectories, and the genetic and environmental variance components are assessed as functions of age. This thesis contributes to statistical methodology for analysing longitudinal twin data by (i) exploring the use of random change point models for modelling variance as a function of age, (ii) assessing how nonresponse in twin studies may affect estimates of genetic and environmental influences, and (iii) providing a method for hypothesis testing of genetic and environmental variance components. The random change point model, in contrast to linear and quadratic random effects models, is shown to be very flexible in capturing variability as a function of age. Approximate maximum likelihood inference through first-order linearization of the random change point model is contrasted with Bayesian inference based on Markov chain Monte Carlo simulation. In a set of simulations based on a twin model for informative nonresponse, it is demonstrated how the effect of nonresponse on estimates of genetic and environmental variance components depends on the underlying nonresponse mechanism. This thesis also reveals that the standard procedure for testing variance components is inadequate, since the null hypothesis places the variance components on the boundary of the parameter space. The asymptotic distribution of the likelihood ratio statistic for testing variance components in classical twin models is derived, resulting in a mixture of chi-square distributions. Statistical methodology is illustrated with applications to empirical data on cognitive function from a longitudinal twin study of aging.