Dear Manikandan,

here are some papers that should help you finding an answer to your question:

Hu, L. T., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural equation modeling: a multidisciplinary journal, 6(1), 1-55.

http://www.tandfonline.com/doi/abs/10.1080/10705519909540118#.VOHQKi7J6xw

Marsh, H. W., Hau, K. T., & Wen, Z. (2004). In search of golden rules: Comment on hypothesis-testing approaches to setting cutoff values for fit indexes and dangers in overgeneralizing Hu and Bentler's (1999) findings. Structural equation modeling, 11(3), 320-341.

http://www.tandfonline.com/doi/abs/10.1207/s15328007sem1103_2#.VOHQLC7J6xw

Zhonglin, W., Kit-Tai, H., & Marsh, H. W. (2004). Structural equation model testing: Cutoff criteria for goodness of fit indices and chi-square test. Acta Psychologica Sinica, 36(2), 186-194.

http://en.cnki.com.cn/Article_en/CJFDTOTAL-XLXB200402009.htm

Dear Manikandan,

here are some papers that should help you finding an answer to your question:

Hu, L. T., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural equation modeling: a multidisciplinary journal, 6(1), 1-55.

http://www.tandfonline.com/doi/abs/10.1080/10705519909540118#.VOHQKi7J6xw

Marsh, H. W., Hau, K. T., & Wen, Z. (2004). In search of golden rules: Comment on hypothesis-testing approaches to setting cutoff values for fit indexes and dangers in overgeneralizing Hu and Bentler's (1999) findings. Structural equation modeling, 11(3), 320-341.

http://www.tandfonline.com/doi/abs/10.1207/s15328007sem1103_2#.VOHQLC7J6xw

Zhonglin, W., Kit-Tai, H., & Marsh, H. W. (2004). Structural equation model testing: Cutoff criteria for goodness of fit indices and chi-square test. Acta Psychologica Sinica, 36(2), 186-194.

http://en.cnki.com.cn/Article_en/CJFDTOTAL-XLXB200402009.htm

Dear Manikandan,

Besides the well informed references provided above, in principle the most important fit index is the chi-square statistic. If you have a not-statistically significant chi-square then your model fits the data. That's all you need.

Best

Areti

Timo prposed good literature, and I would like to add one more paper:

Hu, L. and Bentler, P.M. (1998), “Fit Indices in Covariance Structure Modeling: Sensitivity to Underparameterized Model Misspecification”, Psychological Methods, Vol. 3, No. 4, pp. 424-453.

Hi,

I would like to agree with Areti. Stick to the chi-square test. A significant value does not have to mean that the model indeed has severe problems (may be violations of assumptions or irrelevant problems) but should be inspected. You do not keep sitting on the couch when the alarm bell rings (although it may be a false alarm).

Simulations investigating the fit indices have the problems that they observe the behavior of the index in a specific context where a sample model deviates *to some set degree from the population model*. Hence, you don't know the behavior in other contexts. 

Please read the following isse in Personality and Individual Differences (2007), 42(5) about model evaluation.

Best,

Holger

watch sample size and model complexity.

more complex models are likely to demonstrate mis)fit.

so what is complex?

brad

In SEM there is no one single statistic that can tell you whether your model is good or not. That's why there are so many, and why most programs give you a lot of them. According to Byrne (2010) you should make a global assessment of several statistics (CFI, GFI, PGFI, RMSEA, etc.) and based on this accept that your model fits the data adequately or not. 

There is a good discussion about this in the above mentioned book: Barbara Byrne (2010), Structural Equations Modelling with AMOS. Also you might try Kline (2011) Principles and Practice of Structural Equations Modeling. 

Also I would suggest to pay attention to what type of statistics other researchers in your field used. It would be convenient for you to use the same ones.

Good luck with your paper.

Hi,

Kindly see this video: https://www.youtube.com/playlist?list=PL3mwk0Db0keIn0sroMlmuIX6XQ806mlQa

Go through these:

http://www.ejbrm.com/issue/download.html?idArticle=183

http://www.jstor.org/discover/10.2307/3150979?sid=21105901044193&uid=3738952&uid=70&uid=2129&uid=2&uid=4

https://faculty-gsb.stanford.edu/larcker/PDF/6%20Unobservable%20Variables.pdf

https://stat.utexas.edu/images/SSC/Site/AMOS_Tutorial.pdf

It's also often a good idea to compare the fit of your model to other plausible alternative models. If you have nested models, you can evaluate whether the model fit is significantly different using the chi-square difference test:

Comparison Chi-square = [(Larger model chi-Square) - (Smaller model chi-square)]

Comparison DF = [(Larger model DF) - (Smaller model DF)]

If the comparison chi-square value is significant at the comparison DF, then the models differ significantly in terms of fit (at least as evaluated by the chi-square). If the comparison chi-square is not significant at its DF, then the models do not differ significantly in fit, and the more parsimonious one should be preferred.

Of course, this naturally renders your analyses somewhat more exploratory. But it can also be helpful in confirmatory analysis, in order to increase your confidence in your target model.

I would like to add to Timothy's proposal that

a) in order to compare two nested model, the baseline model has to have a clean fit:

Yuan, K.-H., & Bentler, P. M. (2004). On chi-square difference and z tests in mean and covariance structure analysis when the base model is misspecified. Educational and Psychological Measurement, 64(5), 737–757.

b) in case of two compared model that BOTH do not fit, it can not be concluded that the model with "better" fit (in terms of fit indices) is better in terms of causal specification. 

Best,

Holger