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Structural equation models are often used to test a theory about relationships between theoretical constructs. We give a short and non-technical account of the main issues involved in the translation of a theory to a structural equation model and the fitting and testing of this model by empirical data. For a fuller account of these issues, see Bollen (1989a), Jöreskog (1993) and other chapters in Bollen & Long (1993), and Jöreskog & Aish (1994). In particular, we discuss issues of model evaluation and assessment of fit that we have only touched upon in the examples of the previous chapters of the SIMPLIS User's Guide.

Finally, a brief guide to the interpretation of some of these measures is given.

Fitting and Testing

• From theory to statistical model
• Nature of Inference
• Fitting and Testing a Covariance Structure
• Selection of One of Several a priori Specified Models
• Model Assessment and Modification
• Illustration

Fit measures

• Chi-square
• Goodness-of-Fit Indices
• Fit Measures Based on Population Error of Aprroximation
• Information Measures of Fit
• Other Fit Indices

Detailed Assessment of Fit

If, on the basis of overall measures of fit or other considerations, it is concluded that the model does not fit sufficiently well, one can examine the fit more closely to determine possible sources of the lack of fit. For this purpose, fitted and standardized residuals and modification indices are useful.

• Fitted and Standardized Residuals
• Modification Index

Interpretation of fit measures

• Overview