取樣權重值於應用 SEM 模式分析之參數估算正確性研究

Abstract

在調查研究中，因不同組群的個數在母群體所占的比例不相等，以致於抽樣機率不相等，必須加上取樣權重（sampling weights），才可能正確地推估母群體的樣貌（Martin & Kelly， 1996）。目前取樣權重的實質應用僅局限於基礎統計方法，較高階的統計分析方法，例如：結構方程模式（Structural Equation Modeling， SEM）、因素分析（Factor Analysis， FA）便很少應用取樣權重的概念。Asparouhov（2005）對此一問題進行初步研究，他進行了含取樣權重的潛藏變數估算模擬研究，其研究結果顯現出需考慮取樣權重，才能得到正確的參數估算值。本研究延伸Asparouhov的實驗，設計了五個觀察變項及一個因子（factor）模式，利用電腦模擬以探討取樣權重對因素分析參數估算結果的影響性。研究結果發現，使用取樣權重能有較高的參數估算正確性。

The goal of the investigation is to evaluate the use of sampling weights in the structural equation modeling context through a simulation study. The statistical inference in this study is carried out by using a basic factor analysis model with one latent variable and five continue observe variables. In this study， three independent variables were manipulated by various proportions of samples versus population， sampling stratum sizes， and differences in factor loading between strata. Estimations are conducted by using the altered maximum likelihood estimation (MLE) algorithm. Our simulation results demonstrate that adapted processes of sampling weight are crucial and incorporating weights into the parameter estimation procedures of SEM is a non-ignorable top-priority.