| The overarching aims of this research were to find a way to evaluate assumptions about patterns of missing data and minimize adverse effects on statistical inferences and conclusions if data are missing not at random. The Bayesian approach, implemented through the MCMC algorithms, provided possible bridges to these aims and received multi-phase investigations under a longitudinal twin design in this research. In simulation study I and II, the performances of the Bayesian approach were compared to the direct Maximum likelihood (ML) estimation when data were missing completely at random (MCAR) or not at random (MNAR), respectively. Robustness of different approaches to varying fractions of missing information was also examined. The Bayesian approach, despite being less robust than ML in estimating unique environmental components and residual error, was effectively capable of capturing true models from MNAR when an appropriate logistic regression was formulated about the missingness pattern. In simulation study III, the sensitivity of the Bayesian approach itself to misspecifications of the missingness pattern received further investigation. The results suggested that, as long as the logistic regression equation in the Bayesian model was a saturated one taking into account as many predictors as possible, the Bayesian approach could correctly detect misspecifications with an acceptable type-I error. Finally, the Bayesian model was applied to an empirical study of psychopathic traits to demonstrate the influence of MNAR data and what different conclusions from regular ML estimation it could achieve. The implications of these different conclusions regarding the theory of psychopathy itself were also discussed. |
