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**|**Clin Interv Aging**|**v.7; 2012**|**PMC3396050

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

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- Copyright © 2012 Burfield et al, publisher and licensee Dove Medical Press Ltd.This is an Open Access article which permits unrestricted noncommercial use, provided the original work is properly cited.

Goodness of fit statistics | Terms and understanding statistical output |
---|---|

χ^{2} (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 |

χ^{2}/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.

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