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From:
Published online 2012 July 2. doi: 10.2147/CIA.S29656

Table 11

Goodness of fit statistical terms

Goodness of fit statisticsTerms and understanding statistical output
χ2 (chi-square)Best for models with sample sizes between 75–100; for n > 100 chi-square is almost always significant since the magnitude is affected by the sample size; also affected by the size of correlations in the model, the larger the correlations the poorer the fit
Degrees of freedom (df)The number of degrees of freedom and equals p-q (the # of sample moments subtract the # of parameters estimated)
PThe probability is ideally non-significant; however, significant models can still yield valuable theoretical construct information
Number of free parametersMultiple times 5–10 to estimate required sample size for the study
χ2/dfUse to compare models; this number should decrease from model to model; <5 is good, but must have P > 0.05; close to 1.0 means it is a correct model
RMRRoot mean square residual is the square root of the average amount that the sample variances and covariances differ from their estimates, smaller values are better
GFI (also GOF)Slightly less than or equal (0–1) to 1 indicates a perfect fit; acceptable values are above 0.90; affected by sample size and can be large for poorly specified models
TLIThe Tucker-Lewis coefficient should be between 0–1, values close to 1 indicate a very good fit
AGFI (also AGOF)Adjusted goodness of fit index, takes into account the df available for testing the model; AGFI is bound by 1, which indicates a perfect fit; however is not bound by 0
RMSEAShould be less than 0.05; score of less than 0.05 indicates a close fit of the model in relation to the df. Not definitive but the rule of thumb is an RMSEA of 0.01 is an exact fit, a score of 0.08 or less indicates a reasonable error of approximation. A model with an RMSEA of greater than 0.1 should not be used – indicates a poor fit
Hoelter (0.05)The largest sample size for which one would accept the hypothesis that the model is correct; the index should only be calculated if the chi-square is statistically significant. How small one’s sample size would have to be for chi-square to no longer be significant. Hoelter recommends values of at least 200, values ≤75 indicate a poor fit

Abbreviations: AGFI, adjusted goodness of fit index; AGOF, adjusted goodness of fit; GFI, goodness of fit index; GOF, goodness of fit; RMR, root mean square residual; RMSEA, root mean square error of approximation; TLI, tucker-lewis index.

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