| The application of item response theory models to repeated observations has demonstrated great promise in developmental research. It allows researchers to take into consideration the characteristics of both item response and measurement error in longitudinal trajectory analysis, which improves the reliability and validity of the latent growth curve (LGC) model. This thesis demonstrates the potential of Bayesian methods and proposes a comprehensive modeling framework, combining a measurement model with a structural model. That is, through the incorporation of a commonly used link function and Bayesian estimation, an item response theory model (IRT) can be naturally introduced into a latent variable model (LVM).;All proposed analyses are implemented in WinBUGS 1.4.3 (Spiegelhalter, Thomas, Best, and Lunn, 2003), which allows researchers to use Markov chain Monte Carlo (MCMC) simulation methods to fit complex statistical models and circumvent intractable analytic or numerical integrations. The utility of this IRT-LVM modeling framework was investigated with both simulated and empirical data, and promising results were obtained. As the results indicate, the IRT-LVM utilized information from individual items of the scales at each point in time, allowing the employment of item response characteristics from distinct psychometric models, permitting the separation of time-specific error and measurement error, and giving researchers a way to evaluate the factorial invariance of latent constructs across different assessment occasions. |
