Basic concepts of structural equation modeling

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1 Basic concepts of structural equation modeling
結構方程模式 Structural Equation Modeling Basic concepts of structural equation modeling

2 十問結構方程模式（SEM） SEM為何？ SEM的重要性為何？ SEM的發生起源為何？ SEM的作用為何？ SEM的特性為何？

3 What is SEM? SEM是Structural Equation Modeling的縮寫
SEM又稱為causal modeling, causal analysis, simultaneous equation modeling, analysis of covariance structures, path analysis, confirmatory factor analysis SEM是一種統計方法學(statistical methodology) (Byrne, 1994) SEM是統計技術 SEM是方法學 SEM一次量化技術的大整合，也是量化方法的典範大革命

4 Specialty of SEM Latent variables Measurement error Theory testing
Multivariate statistical analysis Controlling for the errors due to statistical decision-making

5 Historical roots of SEM
心理計量根源 Galton（relationship in quantitative study ） Spearman: 因素分析（factor analysis） Thurston:最簡化結構（simple structure） Jöreskog與Lawley:最大概率模式（maximum likelihood） 生物與經濟計量根源 Wright: path analysis Haavelmo:聯立方程式分析（simultaneous equation）

6 Applications of SEM Confirmatory factor analysis (M1)
Path analysis (M2) Structural regression analysis (M3) Time-dependent/longitudinal data (M4) Recursive and non-recursive models for cross-sectional data Covariance structure models Multi-sample analysis Multi-level analysis

7 Four Basic Model of SEM I CFA model

8 Four Basic Model of SEM II Path Analysis model

9 Four Basic Model of SEM III Structural Regression model

10 Four Basic Model of SEM IV Latent Change model

11 Features of SEM SEM具有理論先驗性 SEM同時兼具觀察變項與潛在變項 SEM以共變數的運用為核心，亦可處理平均數估計與比較

12 Methodological Concepts of SEM
一、假設考驗 (hypothesis-testing) 研究者為了驗證自己所提出理論模式的適切性，提出理論性的建構，而以假設考驗的方式來檢驗之。 二、結構化驗證 (structural confirmatory) 一組變項之間潛在的因果性（causality）或階層性（hierarchy）結構關係的探討 三、模型比較分析（modeling analysis & comparison） 將一系列的研究假設同時結構成一個有意義的假設模型，然後經由統計的程序對於此一模型進行檢證。

13 Modeling of SEM Effects Basic elements: Direct effect Indirect effect
觀察變項(observed variable) or 測量變項(measured variable) 潛在變項(latent variable) Model specification 測量模式(measurement model) 指實際觀察值與其背後的潛在特質的相互關係 結構模式(structural model) 顯示潛在變項之間的關係 Effects Direct effect Indirect effect Total effect

14 Procedures of SEM

15 技術原理：參數估計  Matrix

16 Parameters in SEM Fixed parameters Constrained parameters
assigned specific values (usually 0 or 1) Constrained parameters unknown but equal to a function of one or more other unknown parameters Free parameters unknown and not constrained to be equal to other parameters

17 技術原理：Model Equations

18 Modeling strategies of SEM
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

19 SEM/LISREL syntax

20 SEM/EQS syntax /TITLE V11 = + *F2 + E11;
WPI 26 ITEM 4 FACTOR MODEL Taiwan FA based /SPECIFICATIONS DATA='EQS26.dat'; VARIABLES= 26; CASES= 414; METHODS=ML; MATRIX=RAW; /LABELS V1=V1; V2=V2; V3=V3; V4=V4; V5=V5; V6=V6; V7=V7; V8=V8; V9=V9; V10=V10; V11=V11; V12=V12; V13=V13; V14=V14; V15=V15; V16=V16; V17=V17; V18=V18; V19=V19; V20=V20; V21=V21; V22=V22; V23=V23; V24=V24; V25=V25; V26=V26; /EQUATIONS V1 = + 1F4 + E1; V2 = + 1F3 + E2; V3 = + 1F2 + E3; V4 = + 1F1 + E4; V5 = + *F3 + E5; V6 = + *F2 + E6; V7 = + *F1 + E7; V8 = + *F2 + E8; V9 = + *F2 + E9 ; V10 = + *F4 + E10; V11 = + *F2 + E11; V12 = + *F3 + E12; V13 = + *F4 + E13; V14 = + *F1 + E14; V15 = + *F3 + E15; V16 = + *F3 + E16; V17 = + *F1 + E17; V18 = + *F3 + E18; V19 = + *F4 + E19; V20 = + *F1 + E20; V21 = + *F3 + E21; V22 = + *F3 + E22; V23 = + *F2 + E23; V24 = + *F1 + E24; V25 = + *F3 + E25; V26 = + *F1 + E26; /VARIANCES F1 to F4= *; E1 to E26= *; /cov f1 to f4=*; /wtest /lmtest /END

21 Path diagram of LISREL analysis

22 LISREL的矩陣概念

23 LISREL的原始設定與替代設定代碼對照表

24 完整LISREL模型的參數圖示