Abstract: the data of Taiwanese 8th grader in the 4th cycle of
Trends in International Mathematics and Science Study (TIMSS) are
analyzed to examine the influence of the science teachers- preference
in experimental teaching on the relationships between the affective
variables ( the perceived usefulness of science, ease of using science
and science learning interest) and the academic achievement in science.
After dealing with the missing data, 3711 students and 145 science
teacher-s data were analyzed through a Hierarchical Linear Modeling
technique. The major objective of this study was to determine the role
of the experimental teaching moderates the relationship between
perceived usefulness and achievement.
Abstract: Among various HLM techniques, the Multivariate Hierarchical Linear Model (MHLM) is desirable to use, particularly when multivariate criterion variables are collected and the covariance structure has information valuable for data analysis. In order to reflect prior information or to obtain stable results when the sample size and the number of groups are not sufficiently large, the Bayes method has often been employed in hierarchical data analysis. In these cases, although the Markov Chain Monte Carlo (MCMC) method is a rather powerful tool for parameter estimation, Procedures regarding MCMC have not been formulated for MHLM. For this reason, this research presents concrete procedures for parameter estimation through the use of the Gibbs samplers. Lastly, several future topics for the use of MCMC approach for HLM is discussed.