Confirmatory Factor Analysis is basically for normal data. In Amos, there are a lot of of goodness of fit such as GFI, AGFI, IFI, CFI, and others. Thus, there are three types categories namely incremental fit (CFI, IFI, AGFI) absolute fit (RMSEA, GFI) and parsiminous fit (Chisq/df). We have to ensure all of these fitness achieve the requirement level.                                                                       

Sharma, S., Mukherjee, S., Kumar, A., and Dillon, W.R. (2005), "A simulation study to investigate the use of cutoff values for assessing model fit in covariance structure models," Journal of Business Research, 58 (1), 935-43.

This research paper can help you in finding out which fit indices you should use. This paper also says that the use of GFI should be discouraged.

Thanks for your replies on my question. I have read the article suggested by Sumedha and I have found an interesting article (Hooper et al 2008; EJBRM) on the three categories of fit indices as suggested by Wan and Patrick. This will further help me to select the fit indices I will report.

Hi Rolinde, my colleagues and I recently published a paper using ordinal CFA with these parameters (WLS and the asymptotic covariance matrix as the weight matrix) in the International Journal of Selection and Assessment. Here is a quote from our methods section that may help you (please see the full reference below the quote):

"To assess model fit, we examined both absolute and incremental fit indices including the root mean square error of approximation (RMSEA) and its 90% confidence interval, the non-normed fit index (NNFI), the comparative fit index (CFI), and the Satorra-Bentler chi-square (Jackson, Gillaspy, & Purc-Stephenson, 2009). The selection of fit indices and their cutoff values are idiosyncratic and of much debate. Given our data, sample sizes, and estimation procedures, we set cutoff values of ≤.06 for the RMSEA, and >.95 for both the NNFI and CFI (Fan & Sivo, 2005; Hu & Bentler, 1998, 1999; Jackson et al., 2009; Marsh, Hau, & Wen, 2004; Nye & Drasgow, 2011). Additionally, due to the sensitivity of chi-square indices to sample size, a common alternative to the overall chi-square test is to divide the test statistic by its degrees of freedom and accept values less than or equal to 2.0 as indicative of good model fit (Meade, Johnson, & Braddy, 2008)." (Morse, Weinhardt, Griffeth, & DeOliveira, 2014, p. 143).

Morse, B. J., Weinhardt, J. M., Griffeth, R. W., & Ziebell, M. (2014). Cross-cultural measurement invariance of the Employment Opportunity Index (EOI) in Mexican and Brazilian professionals, International Journal of Selection and Assessment, 22(2), 139–148. doi: 10.1111/ijsa.12064

Dear Rolinde , I think it is important to make sure that when you report the findings of a study they are reported in a way that is consistent with other studies. In this case I think you should follow the conventions that are normally followed when an ordinal factor analysis is conducted using Mplus (for better or worse this is the most commonly used software for these models, and as such sets the 'standards'). It is common to see the chi-square (and df), CFI, TLI, and RMSEA. The WRMR is the 'residual' based index in Mplus, analogous to the SRMR, but this doesn't seem to work very well and is rarely reported. I tend to use the RMSEA as the primary index for deciding on how well the model fits.

You may also want to check that you are using the best method of estimation. I think in LISREL the DWLS is equivalent to WLSMV in Mplus. I seem to remember that there was a study comparing WLS and DWLS and DWLS was found to be superior.

Best wishes

Mark