Table 11.
Goodness of fit statistical terms
| Goodness of fit statistics | Terms 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) |
| P | The probability is ideally non-significant; however, significant models can still yield valuable theoretical construct information |
| Number of free parameters | Multiple times 5–10 to estimate required sample size for the study |
| χ2/df | Use 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 |
| RMR | Root 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 |
| TLI | The 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 |
| RMSEA | Should 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.