## Testing Structural Equation ModelsWhat 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. |

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### Contents

Introduction | 1 |

Multifaceted Conceptions of Fit in Structural | 10 |

Monte Carlo Evaluations of Goodness of Fit Indices | 40 |

Some Specification Tests for | 66 |

Bootstrapping GoodnessofFtt Measures | 111 |

Alternative Ways of Assessing Model | 136 |

### Common terms and phrases

alternative applied approximation assessment assumptions asymptotic Bentler Bollen Bonett Browne categorical chi-square test coefficients components computed considered correctly specified correlation covariance structure analysis covariance structure models Cudeck degrees of freedom DELTA2 discrepancy function discussed ECVI eigenvalues empirical evaluate example expected value factor analysis fit function fit index fit indices fit measures fixed parameters free parameters goodness-of-fit heteroscedasticity Joreskog kurtosis latent variables least squares likelihood ratio linear LISREL LM statistic maximum likelihood estimation misspecification model fit modified bootstrap multivariate noncentrality parameter nonnormal null hypothesis null model observed variables obtained overall parameter estimates polychoric positive definite probit problem procedure Psychological Psychometrika regression rejected RESET test residuals restrictions robust sample covariance matrix sample size sample sizes Saris Satorra saturated model Sorbom specification tests specified model standard errors Steiger structural equation models substantive Table Tanaka test statistic tetrachoric tion variance vector zero