# Fit indices in covariance structure modeling : Sensitivity to underparameterized model misspecification

@article{Hu1998FitII, title={Fit indices in covariance structure modeling : Sensitivity to underparameterized model misspecification}, author={Li-tze Hu and Peter M. Bentler}, journal={Psychological Methods}, year={1998}, volume={3}, pages={424-453} }

This study evaluated the sensitivity of maximum likelihood (ML)-, generalized least squares (GLS)-, and asymptotic distribution-free (ADF)-based fit indices to model misspecification, under conditions that varied sample size and distribution. The effect of violating assumptions of asymptotic robustness theory also was examined. Standardized root-mean-square residual (SRMR) was the most sensitive index to models with misspecified factor covariance(s), and Tucker-Lewis Index (1973; TLI), Bollen's…

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## References

SHOWING 1-10 OF 76 REFERENCES

### Cutoff criteria for fit indexes in covariance structure analysis : Conventional criteria versus new alternatives

- Education
- 1999

This article examines the adequacy of the “rules of thumb” conventional cutoff criteria and several new alternatives for various fit indexes used to evaluate model fit in practice. Using a 2‐index…

### A fit index for covariance structure models under arbitrary GLS estimation

- Mathematics
- 1985

A general fit index for covariance structure models is obtained for all estimators that can be considered under generalized least squares (GLS) approaches including asymptotically efficient, robust,…

### Monte Carlo Evaluations of Goodness of Fit Indices for Structural Equation Models

- Economics
- 1992

This article reviews proposed goodness-of-fit indices for structural equation models and the Monte Carlo studies that have empirically assessed their distributional properties. The cumulative…

### Effect of Estimation Method on Incremental Fit Indexes for Covariance Structure Models

- Mathematics
- 1993

In a typical study involving covariance structure modeling, fit of a model or a set of alternative models is evaluated using several indicators of fit under one estimation method, usually maximum…

### EVALUATION OF GOODNESS-OF-FIT INDICES FOR STRUCTURAL EQUATION MODELS

- Mathematics
- 1989

Discusses how current goodness-of-fit indices fail to assess parsimony and hence disconfirmability of a model and are insensitive to misspecifications of causal relations (a) among latent variables…

### Significance Tests and Goodness of Fit in the Analysis of Covariance Structures

- Mathematics
- 1980

Factor analysis, path analysis, structural equation modeling, and related multivariate statistical methods are based on maximum likelihood or generalized least squares estimation developed for…

### A New Incremental Fit Index for General Structural Equation Models

- Mathematics
- 1989

Assessing overall model fit is an important problem in general structural equation models. One of the most widely used fit measures is Bentler and Bonett's (1980) normed index. This article has three…

### Power analysis and determination of sample size for covariance structure modeling.

- Environmental Science
- 1996

A framework for hypothesis testing and power analysis in the assessment of fit of covariance structure models is presented. We emphasize the value of confidence intervals for fit indices, and we…

### Two new goodness‐of‐fit indices for covariance matrices with linear structures

- Mathematics
- 1991

Two new indices each based on two different methods of estimating the population covariance matrix Σ are derived. Certain algebraic results on these indices are also reported. A case study has been…

### A general coefficient of determination for covariance structure models under arbitrary GLS estimation

- Mathematics
- 1989

Previous results presented in Tanaka & Huba (1985) introduced a general Fit index for covariance structure models under generalized least squares (GLS) estimation which, in some cases, specialized to…