多層次嵌套資料加權估計策略之比較研究:以TALIS資料庫為例

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2021

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調查研究需仰賴嚴謹的抽樣設計使樣本反應母體的狀況,若研究者使用分層抽樣使得資料帶有嵌套特性,採用多層次模型(multi-level modeling, MLM)能夠就個體與總體不同層次的數據進行整合分析。當多層次模型考慮到加權議題時,樣本除了其個體層加權,會因其歸屬的組別(顯性或隱性分層變數)而再次調整權重,進一步地影響估計結果。為探討加權在階層模型係數估計議題,本研究使用經濟合作暨發展組織(OECD)主導的教學與學習國際調查(Teaching and Learning International Survey, TALIS)探討估計法、加權以及樣本規模對係數估計之影響。TALIS資料庫的抽樣設計為二階段抽樣法,台灣於2018年所參與的調查工作共抽取553所學校(含高中、國中及國小,總體層次),共10,129名教師(個體層)。本研究採用國小部分資料(200所學校與3,494名教師)進行多層次分析。為了瞭解樣本規模的影響,本研究依據TALIS分層抽樣的顯性分層(公私立別、城鄉別),設計五種樣本規模(200、150、100、50與20)。基於工作壓力模式,在個體層次至入教職定向、壓力指數兩變數;總體層次至入學校公私立別、城鄉別(都市、市鎮與鄉村),解釋國小教師產生教職退縮(後悔從事教職)的多層次模型。另外,由於依變數為Likert五點量表,估計法以適合數值為量尺型態的MLR與WLSMV,並設置使用加權估計與不使用加權估計兩種設定。在五種樣本規模下,透過MLR與WLSMV反覆10次估計個體層與總體層係數,藉由反覆估計平均數與變異數,對照使用加權與未使用加權的係數估計結果。 研究結果顯示在樣本量充足的情況下(150所學校與100所),MLR與WLSMV兩種估計法在加權與未加權情況下的參數估計表現皆穩定,但WLSMV的參數估計數值普遍大於MLR估計數值約1.5至2倍,以及WLSMV估計法的標準誤明顯比MLR小,所以有著較好的檢定力,因此WLSMV會比MLR更適合被使用在依變數為分類變數的研究。不過當樣本不足時,兩種估計法在總體層次係數估計皆出現過度校正的情況,但在使用加權估計的情況下,過度校正的次數較少發生。在比較加權估計與未加權估計方面,本研究結果發現加權會降低估計的穩定度,但同時也會減少總體層級變數的估計偏誤度,因此在小樣本下層級係數雖有負數的估計結果,但仍能透過加權減少估計法過度修正的情況。綜合本研究分析結果,認為加權估計雖會降低總體係數估計精準度,但會提升係數估計的標準誤,使得估計較不穩定。因此建議研究者建立加權估計對照組以及使用不同估計法多方比較加權對係數估計之影響。
Survey research relies on rigorous sampling design to make the sample reflecting the status of the population. If the researcher implements stratified sampling, and use multi-level modeling (MLM), which could help researcher to estimate parameters from the individual level(level-1) and macro level(level-2), simultaneously. When the MLM integrated weighting issues, the sample shouldn’t only adjust by its own weights on level-1, but also have to be adjusted again by the level-2 weights (explicit stratification or implicit stratification) because of the group which the sample belongs to. In order to examine the weighting issue on coefficient estimation at MLM, this study uses the Teaching and Learning International Survey (TALIS) led by the Organization for Economic Cooperation and Development (OECD).The sampling design of the TALIS database is two-stage sampling method. The TALIS Taiwan survey select the number of 553 schools (including elementary schools, junior high schools, high schools, level-2), and the number of 10,129 teachers (individual level-1) in 2018. Using the elementary schools data (200 schools and 3,494 teachers) to conduct multi-level analysis. In order to figure out the impact of sample size, there design five sample sizes which is based on the explicit stratification ofTALIS stratified sampling (public and private& urban, town and rural). Since the dependent variable is the Likert five-point scale, using the appropriate estimation method MLR and WLSMV. Results indicate that, MLR and WLSMV are suitable for estimation under the sufficient sample size ( both of the change rate of repeating sampling variation and the change rate of coefficient on 150 schools and 100 schools are stable). Moreover, WLSMV produce samller standard error than MLR. For the case of the dependent variable of research taking categorical dependent variable, WLMSV is better choice than MLR. In terms of comparing weighted and unweighted results, although the weighting could reduce the bias of level-2 variables, it also increasing the instability (standard error) at level-1 and level-2 variables. It is recommended that the control group of weighting treatment should be used with different estimatiors to examine the results of weighted coefficient estimates.

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加權, 多層次模型, 樣本規模, 強韌最大概似估計法, 斜對角線加權最小平方法, weighting, multi-level modeling, sample size, robust maximum likelihood estimator, diagonally weighted least squares

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