A Hierarchical Item Response Theory Model and Its Applications in Large-scale Assessment This paper is to explore the model building, estimates of parameters, equation methods and applications in large-scale assessment based on a hierarchical item response theory (HIRT). A hierarchical structure of ability organization, the general ability on the top and multiple more specialized (domain) abilities at the lower levels, has been well adopted in large-scale assessment settings. Under this framework, if the correlations between the general ability and domain abilities are ignored, the ability estimates will be unreliable. Some studies have been conducted using simultaneous estimation of HIRT regarding the general and domain abilities to increase precision of estimates. However, these studies have some limitations: (i) focusing on between-item multidimensional model, (ii) using only single higher-order ability, (iii) normal distribution assumptions in abilities, (iv) time-consuming process of parameters estimates. Moreover, the practical applications of the HIRT model have not yet been explored, such as equation, and plausible values methodology in large-scale assessment. This study will apply MH-within-Gibbs sampling and kernel smoothing to improve the problems in estimation of parameters, and to explore within-item multidimensional model. Using Taiwan assessment of student achievement (TASA ) as a empirical example to provide insight into the equation methods and plausible values methodology based on HIRT and to establish a large-scale standardized assessment analysis procedure.
