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Structural Equation Modeling. Model Specification. Model Specification Procedures Path Diagrams Illustration Identification Strategies and Related Issues Disconfirmability/Equivalent Models/Strategies Conclusion. Model Specification. Involve one or more models General model
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Structural Equation Modeling Model Specification • Model Specification Procedures • Path Diagrams • Illustration • Identification • Strategies and Related Issues Disconfirmability/Equivalent Models/Strategies • Conclusion
Model Specification • Involve one or more models • General model • factor analysis(心理計量學) • path analysis(經濟計量學) • simultaneous equation models
Model Specification Procedures • Include two varianles • measured variables(MVs) measures/indicators • latent variables(LVs) intelligence/depression/attitude • Exist two types of relationships • directional • nondirectional
Model Specification Procedures • Stress causes Depression directional • Hypothesized correlational associations between variables nondirectional 兩變項之間的預測關係—直接 估計變項之間的效果—間接
Model Specification Procedures • Define three classes of Parameters • variances of exogenous variables • covariances among exogenous variables • weights representing directional linear influences among variables
Path Diagrams • Use squares or rectangles to represent MVs • Use circles or ellipsess to represent LVs • Use single-headed arrows to represent Directional effects between variables • Use double-headed arrows to represent Nondirectional relationships • Use double-headed arrows to represent from a variable to itself
Path Diagrams • Exception :specify the variance of an endogenous LVs as being fixed at 1.0 • Use mathematical smbols,usually Greek letters to denote Parameters
Identification( 模型辨識) • 參數的類型 • 迴歸分析中,各預測變項對於效標變 • 項預測力的Beta係數即是迴歸分析的 • 參數 • 變異數分析中,主要效果與交互效果 • 是估計參數 • 因素分析中,因素負荷量是估計參數 • 在結構方程模式可能包括上述各種參 • 數的估計
SEM參數的設定原則 • 所有的外衍變項的變異數都是模型的參數。 • 所有的外衍變項之間的共變數都是模型的參數(除了基於理論假設被設定為0或特定數值者)。 • 所有與潛在變項有關的因素負荷量都是模型的參 數(除了基於理論假設被設定為0或特定數值者)。 • 所有觀察變項之間或潛在變項之間的迴歸係數都 是模型的參數(除了基於理論假設被設定為0或特 定數值者)。 • 與內衍變項有關的量數(例如內衍變項的變異數, 或是內衍變項之間的共變數,或是內衍與外衍變 項之間的共變數),都不是模型的參數。 • 對於每一個潛在變項,必須給定一個適當的潛在 量尺。
六種原則所決定的參數,都必須利用SEM來進 行估計,因此都是自由參數,除非某些參數被 設定特殊的限制條件。 • SEM模型當中的參數,有時因為某些理由被設 定為常數(通常是1.00)而不被估計者,稱為 固定參數。 • 限定參數的使用,多半與多樣本間的比較有關, 例如某一個參數在甲樣本與乙樣本間被設定為 等同(equivalent),此時SEM對於這兩個參 數僅進行一次的估計,是為限定參數。
Identification( 模型辨識) 利用資料測量數與參數估計數的比較來判斷模型的辨識性,提出了一個衡量辨識性的必要但非充分的辨識條件計算法則t法則(t-Rule)。 測量資料數(the numbers of data points; DP) DP=p(p+1)/2 當t<DP,稱為過度辨識(over-identified),好比我們有過多的方程式,但是只需要求取少數幾個因子解; 當t=DP,稱為恰好辨識(just-identified),好比我們用兩個方程式來求二元因子的解; 當t>DP,稱為辨識不足(under-identified),如同我們用太少的方程式求取過多的因子解,在SEM分析中,辨識不足的情況將導致無法進行任何參數估計。
Strategies and Related Issues in Model Specification • Disconfirmality 針對單一的先驗假設模型,評估其適切性(Fitness) Df equals the number of MV variance/covariances minus the effective number of parameters
Strategies and Related Issues in Model Specification • Equivalent Models Models are equivalent when they cannot be distinguished in terms of overall fit. As an example, look at these three models for the relations between two common factors or latent constructs: These three models imply, alternatively, that B is dependent on A, that A is dependent on B, or that A and B covary due to reasons other than a dependence relationship. While the substantive implications of the three models are very different, the fit of the three to any data set will be identical. Thus, in terms of fit, SEM cannot resolve the issue of which model should be preferred.
Strategies and Related Issues in Model Specification • Strategies • Model confirmation • 作為驗證(confirmatory)的基礎 • 針對單一的先驗假設模型,評估其適切性 • Model generation • 先設定一個起始模型,在與實際觀察資料進行比較之後,進行必要的修正,反覆進行估計的程序以得到最佳契合的模型 • Model competation • 利用不同模型的比較以決定何者最能反應真實資料