In this episode of Office Hours, Patrick provides a comprehensive review of evaluating model fit in SEMs. ...
He begins with a brief discussion of observed and model-implied values in multiple regression. He then expands this concept to the full covariance matrix in the SEM. He defines the population and model-implied covariance matrices and uses these to establish the null hypothesis in the SEM. He then describes the chi-square test of model and discusses the advantages and disadvantages of this test statistic. Next he describes relative goodness-of-fit indices (TLI, CFI, IFI) and absolute goodness-of-fit indices (RMSEA) as well as the standardized root mean residual (SRMR). He concludes with recommendations for how all of these measures of model fit can be used in practice.
Bollen, K. A., & Long, J. S. (1992). Tests for structural equation models: introduction. Sociological Methods & Research, 21, 123-131.
Browne, M. W., & Cudeck, R. (1992). Alternative ways of assessing model fit. Sociological Methods & Research, 21, 230-258.
Chen, F., Curran, P. J., Bollen, K. A., Kirby, J., & Paxton, P. (2008). An empirical evaluation of the use of fixed cutoff points in RMSEA test statistic in structural equation models. Sociological Methods & Research, 36, 462-494.
Saris, W. E., Satorra, A., & van der Veld, W. M. (2009). Testing
structural equation models or detection of misspecifications?
Structural Equation Modeling, 16, 561- 582.
West, S. G., Taylor, A. B., & Wu, W. (2012). Model fit and model selection in structural equation modeling. Handbook of structural equation modeling, 209-231.