I conducted a ML estimation in LISREL with Sattora-Bentler adjustment. Now I have multiple chi-square values (C1, C2_NT, C2_NNT, C3, C4). As much as I understand, the C3 is the mean-adjusted S-B chi-square and C4 is the mean- and variance-adjusted S-B chi-square. Now I am not sure based on which chi-sqaure were the other fit indices (CFI, RMSEA etc.) calculated and which ones I should report?
Here is the output:
Degrees of Freedom for (C1)-(C3),C(5) 4
Maximum Likelihood Ratio Chi-Square (C1) 15.006 (P = 0.0047)
Browne's (1984) ADF Chi-Square (C2_NT) 14.798 (P = 0.0051)
Browne's (1984) ADF Chi-Square (C2_NNT) 13.532 (P = 0.0089)
Satorra-Bentler (1988) Scaled Chi-Square (C3) 13.590 (P = 0.0087)
Satorra-Bentler (1988) Adjusted Chi-Square (C4) 13.366 (P = 0.0091)
Degrees of Freedom for C4 3.934
Chi-Square Scaled and Shifted (C5) 13.511 (P = 0.0090)
P-Value of C1 under Non-Normality = 0.0093
Estimated Non-centrality Parameter (NCP) 11.006
90 Percent Confidence Interval for NCP (2.699 ; 26.853)
Minimum Fit Function Value 0.0280
Population Discrepancy Function Value (F0) 0.0206
90 Percent Confidence Interval for F0 (0.00504 ; 0.0502)
Root Mean Square Error of Approximation (RMSEA) 0.0717
90 Percent Confidence Interval for RMSEA (0.0355 ; 0.112)
P-Value for Test of Close Fit (RMSEA < 0.05) 0.145
Expected Cross-Validation Index (ECVI) 0.148
90 Percent Confidence Interval for ECVI (0.132 ; 0.177)
ECVI for Saturated Model 0.135
ECVI for Independence Model 2.019
Chi-Square for Independence Model (28 df) 1064.176
Normed Fit Index (NFI) 0.987
Non-Normed Fit Index (NNFI) 0.935
Parsimony Normed Fit Index (PNFI) 0.141
Comparative Fit Index (CFI) 0.991
Incremental Fit Index (IFI) 0.991
Relative Fit Index (RFI) 0.911
Critical N (CN) 522.675
Root Mean Square Residual (RMR) 0.0191
Standardized RMR 0.0235
Goodness of Fit Index (GFI) 0.993
Adjusted Goodness of Fit Index (AGFI) 0.938
Parsimony Goodness of Fit Index (PGFI) 0.110
What you report depends on the research questions and not on the output per se.
What I meant was answer your research questions because that is the most important thing.
Hello Jošt Bartol ,
I'd report both C3 and C4, and note that they were virtually identical, such that the variance adjustment didn't impact the results to any degree. As is obvious, it wouldn't really matter which of the chi-square tests you'd choose to report, as all are "significant" at typical alpha levels, and almost always, people choose to rely on other model-data fit indices anyhow. That is largely because the chi-square was intended as a measure of departure from _exact_ model-data fit, and the larger the sample size, the more sensitive the statistic (no matter which form) is to even negligible departures from exact fit.
David Kenny's overview of fit indices may be helpful:http://davidakenny.net/cm/fit.htm
Of course, as Dr. Booth correctly indicates, choice of fit index/indices should be driven by your specific research aims.
Good luck with your work.
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