Though the value you mentioned seems unusual, the fit of the model doesn't depend on only one index (i.e, CMIN/df); rather you have to integrate other indices in interpreting your analysis (e.g., CFI, GFI, NFI, RMSEA, SRMR etc.). These fit indices are again subject to sample size, complexity of the model (e.g., number of parameters ) etc. 

Hi Godfrey

I second Khan's answer. There is a catalogue of fit indices to look for and report on.  Needless to say, as a researcher we need to be objective and avoid cherry-picking style of reporting the indices. We 'owe' our duty of care to others whom may rely on our results to base their decisions and practical exercises. 

Ideally, report on what is considered acceptable and justify any deviation from the norms.

Here's a good reading on fit indices for co-variance based SEM. The one that AMOS is based on.

http://davidakenny.net/cm/fit.htm

Good luck.

saiyidi

http://davidakenny.net/cm/fit.htm

There are three categories of fitness such as parsiminius fit,incremental fit and absolute fit. You have to select at least one fit index to represent for each categories.

1. Incremental fit: IFI,CFI,TLI,NFI,RFI,NNFI

2. Absolute fit: RMSEA, AGFI,GFI

3. Parsiminius fit: cmin/df

since your problem is caused from the chisquare, it might happen because the correlation between latent construct is too high or there's a lot of items have been removed from your model.

Best regards

The latest is that the ratio should less than 3.0. To me the ratio Chisq/Df  less than 1.0 is quite strange. However, you need to consider another indexes namely RMSEA and GFI. If RMSEA is much less than 0.08 and GFI is higher than 0.95 then what you obtained is correct.

CMIN is one of the fit indices used for model fit in SEM. value less than 1 is not a concern as Chi-Square value depends on sample size. Check for other indices like GFI, AGFI, CFI, TLI, PNFI, PGFI, and most important RMSEA with PClose. 

See attached file.

I am using secondary data so my sample size is quite large (10000). I am getting CMIN/Df= 596.45. I am quite surprised to see such a result. can some one suggets. RMSEA is lower to.08 and NFI is >0.95

HE TRABAJADO ANALIZANDO LA BARETÍA DE ÍNDICEA DE AJUSTE CONSIDERANDO CIMN/DF >3

CON LOS DEMÁS ÍNDICES >0,9

The Chi Square is one of the non parametric measures. The value is no longer valid if sample size exceed 200. In your case, I guess the sample size you use is large. Thus, for large sample size the Chisq/n will be very small. So, look for other indices as well.

FOR SAMPLE SIZE:

Rules of Thumb: Ratio of Sample Size to the Number of Free Parameters Tanaka (1987): 20 to 1, and Bentler & Chou (1987): 5 to 1, 200 is seen as a goal for SEM research

Chi square affected by the size of the correlations in the model: the larger the correlations, the poorer the fit. so, you can take alternative measures fit like CFI, TLI, RMSEA , SRMR: https://www.tandfonline.com/doi/abs/10.1080/10705519909540118?journalCode=hsem20

Jos M. C. Schijns what is the source of this table, please? thank you

Dear Dr. Jos M. C. Schijns,

Could you please provide us the reference of the table you attached earlier?

Thank you.

Sarah

Dear Sarah ,

I hope these articles may help you and find the cut point of the model fit.

1. Barbara M. Byrne (2001): Structural Equation Modeling With

AMOS, EQS, and LISREL: Comparative Approaches to Testing for the Factorial Validity of a Measuring Instrument, International Journal of Testing, 1:1, 55-86

To link to this article: http://dx.doi.org/10.1207/S15327574IJT0101_4

2.

Hooper, D., Coughlan, J., & Mullen, M. R. (2008). Structural Equation Modelling : Guidelines for Determining Model Fit. Electronic Journal of Business Research Methods Volume, 6(1), 53–60. Retrieved from www.ejbrm.com

Dear Girum Tareke Zewude,

Thank you very much for providing me the references. It will help me to make my study smooth.

Sarah

The source for the table I refferred to is: http://statwiki.kolobkreations.com/index.php?title=Confirmatory_Factor_Analysis Katarzyna Hamer Hamer Farah Hasan Sarah

Dear, Jos M. C. Schijns and Farah Hasan Sarah

The source of the table that I used for my current research is :

1. Li‐tze Hu & Peter M. Bentler (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, DOI: 10.1080/10705519909540118

To link to this article: https://doi.org/10.1080/10705519909540118

Thank you very much Dr. Jos M. C. Schijns and Mr. Girum Tareke Zewude for providing me the references you used. Now I can also get the help from these materials accordingly.

Thank you once again Mr. Girum Tareke Zewude for helping me in details.

Fit idices are most often contradictory. Some are good enough to show model fit. Some are low. So decide on a collective assessment.

Thank you all for your educative answers

quoting some references. See they help

▪"...Wheaton et al. (1977) suggest that the researcher also compute a relative chi-square (📷) .... They suggest a ratio of approximately five or less 'as beginning to be reasonable.' In our experience, however, 📷 to degrees of freedom ratios in the range of 2 to 1 or 3 to 1 are indicative of an acceptable fit between the hypothetical model and the sample data." (Carmines and McIver, 1981, page 80)

▪"... different researchers have recommended using ratios as low as 2 or as high as 5 to indicate a reasonable fit." (Marsh & Hocevar, 1985).

▪"... it seems clear that a 📷 ratio > 2.00 represents an inadequate fit." (Byrne, 1989, p. 55).

Dear Godfrey Tumwesigye, Normed Chi-Square /CMIN/df = .981 may be less than 1. But it is diffciult and impossible in the large sample data. This x2/df will be 5 for acceptable or less 3 is associated with better-fitting models, except in circumstances with larger samples (greater than 750) (Zewude & Hercz, 2022). Check this publication The Teacher Well-Being Scale (TWBS): Construct validity, model comparisons and measurement invariance in an Ethiopian setting |Article The Teacher Well-Being Scale (TWBS): Construct validity, mod...

The value is to confirm with existing body of knowledge with set of data being analysed.

hence it is not advisable to be very identical to theoretical model..

pls refer the literature

Hooper, D., Coughlan, J., & Mullen, M. R. (2008). Structural equation modelling: Guidelines for determining model fit. Electronic journal of business research methods, 6(1), pp53-60.

um valor abaixo de 1,00, considero ajuste forçado...