| Summary: | 碩士 === 國立臺北大學 === 統計學系 === 94 === Nested data structures often exist in many empirical researches. It is traditionally handled with regression techniques to aggregate or dis-aggregate the data so that the data are treated as if they are uncorrelated. However, since the data are actually correlated within the hierarchies, as a results, inaccurate estimates and results are obtained. The recent developed Hierarchical Linear Models (HLM) handles hierarchical correlated data. Hierarchical Linear Models builds separate regression models for each hierarchy, considers variations from both within and among groups, and improves the accuracy of parameter estimates.
The objective of this research is to explore the accuracy of parameter estimate under different situations. The studied mode is “a intercept-and slopes-as-outcomes model”, and we investigate the effects of sample size, cluster size, slope random effects, intercept random effects, and correlation between slopes and intercepts. We consider binary responses. We simulated data based on the combination of the five factors above calculate bias and MSE. Finally we conducted an regression analysis to study the impact of the factors on accuracy of the parameter estimates.
The result showed variances are the most influential factors to the accuracy of parameter estimation, which are random effects of slopes and intercepts, and correlation between slopes and intercepts The bigger the variance of the intercepts and slopes or the smaller of the correlation, the less accurate of the parameter estimation. Among the variances, the random slopes effect is the most significant. However, is an exception. The accuracy does not decrease with the increase of the correlation between slopes and intercepts. Second, for the sample sizes (number of clusters and cluster size) do not have a substantial effect. In other words, the accuracy of the smaller sizes does not differ much from the accuracy of the larger sizes. The possible explanation could be due to the design of sample sizes are not too distinguishable, so the difference of accuracy of parameter estimation is not significant.
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