What is the role of fit measures when respecifying a model? Should the means of the sampling distributions of a fit index be unrelated to the size of the sample? Is it better to estimate the statistical power of the chi-square test than to turn to fit indices? Exploring these and related questions, well-known scholars examine the methods of testing structural equation models (SEMS) with and without measurement error, as estimated by such programs as EQS, LISREL and CALIS.What is the role of fit measures when respecifying a model? Should the means of the sampling distributions of a fit index be unrelated to the size of the sample? Is it better to estimate the statistical power of the chi-square test than to turn to fit indices? Exploring these and related questions, well-known scholars examine the methods of testing structural equation models (SEMS) with and without measurement error, as estimated by such programs as EQS, LISREL and CALIS.Introduction - Kenneth A Bollen and J Scott Long Multifaceted Conceptions of Fit in Structural Equation Models - J S Tanaka Monte Carlo Evaluations of Goodness-of-Fit Indices for Structural Equation Models - David W Gerbing and James C Anderson Some Specification Tests for the Linear Regression Model - J Scott Long and Pravin K Trivedi Bootstrapping Goodness-of-Fit Measures in Structural Equation Models - Kenneth A Bollen and Robert A Stine Alternative Ways of Assessing Model Fit - Michael W Browne and Robert Cudeck Bayesian Model Selection in Structural Equation Models - Adrian E Raftery Power Evaluations in Structural Equation Models - Willem E Saris and Albert Satorra Goodness-of-Fit with Categorical and Other Nonnormal Variables - Bengt O Muth&eacute;n Some New Covariance Structure Model Improvement Statistics - P M Bentler and Chih-Ping Chou Nonpositive Definite Matrices in Structural Modeling - Werner Wothke<lC<