With the Advent of Software like Lisrel and Amos, Research Community Treats Sem as a Black Box

UNRAVELING STRUCTURAL EQUATION MODELING

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DEPARTMENT OF MANAGEMENT STUDIES

NATIONAL INSTITUTE OF TECHNOLOGY

(DEEMED UNIVERSITY)

Tiruchirappalli-620015

MAY 2011

CONTENTS

Contents

1. OBJECTIVE        4

Inspiration        4

Objective        4

2. INTRODUCTION        4

Variables        4

Factor Analysis        5

Exploratory factor analysis        5

Confirmatory factor analysis        7

SEM        9

Path Diagram        11

Estimation of model parameters        12

Model identification        12

Identification of Structural equation model        15

Optimization Algorithms        19

3. PROBLEM        21

4. UNRESTRICTED ESTIMATION        28

Initial solution        28

Flecther and powell optimization        29

Rotating Factors        34

5. RESTRICTED ESTIMATION        35

Flecther and powell optimization        36

Path diagram        41

6. INTERPRETING THE INDICES        41

Degrees Of Freedom        41

Chi Square        42

Non Centrality Parameter        45

Population Discrepancy Function        46

Root Mean Square Error Of Approximation        46

Goodness Of Fit Index        47

Adjusted Goodness Of Fit Index        49

Parsimony Goodness Of Fit Index        49

Akaike Information Criterion        50

Consistent Version Of AIC        51

Expected Cross Validation Index        52

Normed Fit Index        53

Non - Normed Fit Index        54

Parsimony Normed Fit Index        54

Comparative Fit Index        55

Incremental Fit Index        56

Relative Fit Index        57

Critical N        57

Root Mean Square Residual        58

Standardized Root Mean Square Residuals        59

7. CONCLUSION        59