### Abstract

The root mean square error of approximation (RMSEA) and the comparative fit index (CFI) are two widely applied indices to assess fit of structural equation models. Because these two indices are viewed positively by researchers, one might presume that their values would yield comparable qualitative assessments of model fit for any data set. When RMSEA and CFI offer different evaluations of model fit, we argue that researchers are likely to be confused and potentially make incorrect research conclusions. We derive the necessary as well as the sufficient conditions for inconsistent interpretations of these indices. We also study inconsistency in results for RMSEA and CFI at the sample level. Rather than indicating that the model is misspecified in a particular manner or that there are any flaws in the data, the two indices can disagree because (a) they evaluate, by design, the magnitude of the model's fit function value from different perspectives; (b) the cutoff values for these indices are arbitrary; and (c) the meaning of “good” fit and its relationship with fit indices are not well understood. In the context of inconsistent judgments of fit using RMSEA and CFI, we discuss the implications of using cutoff values to evaluate model fit in practice and to design SEM studies.

Original language | English (US) |
---|---|

Pages (from-to) | 1-20 |

Number of pages | 20 |

Journal | Multivariate Behavioral Research |

DOIs | |

State | Accepted/In press - Feb 1 2016 |

### Fingerprint

### Keywords

- comparative fit index
- fit indices
- root mean square error of approximation
- Structural equation modeling

### ASJC Scopus subject areas

- Experimental and Cognitive Psychology
- Statistics and Probability
- Arts and Humanities (miscellaneous)

### Cite this

*Multivariate Behavioral Research*, 1-20. https://doi.org/10.1080/00273171.2015.1134306

**The Problem with Having Two Watches : Assessment of Fit When RMSEA and CFI Disagree.** / Lai, Keke; Green, Samuel B.

Research output: Contribution to journal › Article

*Multivariate Behavioral Research*, pp. 1-20. https://doi.org/10.1080/00273171.2015.1134306

}

TY - JOUR

T1 - The Problem with Having Two Watches

T2 - Assessment of Fit When RMSEA and CFI Disagree

AU - Lai, Keke

AU - Green, Samuel B.

PY - 2016/2/1

Y1 - 2016/2/1

N2 - The root mean square error of approximation (RMSEA) and the comparative fit index (CFI) are two widely applied indices to assess fit of structural equation models. Because these two indices are viewed positively by researchers, one might presume that their values would yield comparable qualitative assessments of model fit for any data set. When RMSEA and CFI offer different evaluations of model fit, we argue that researchers are likely to be confused and potentially make incorrect research conclusions. We derive the necessary as well as the sufficient conditions for inconsistent interpretations of these indices. We also study inconsistency in results for RMSEA and CFI at the sample level. Rather than indicating that the model is misspecified in a particular manner or that there are any flaws in the data, the two indices can disagree because (a) they evaluate, by design, the magnitude of the model's fit function value from different perspectives; (b) the cutoff values for these indices are arbitrary; and (c) the meaning of “good” fit and its relationship with fit indices are not well understood. In the context of inconsistent judgments of fit using RMSEA and CFI, we discuss the implications of using cutoff values to evaluate model fit in practice and to design SEM studies.

AB - The root mean square error of approximation (RMSEA) and the comparative fit index (CFI) are two widely applied indices to assess fit of structural equation models. Because these two indices are viewed positively by researchers, one might presume that their values would yield comparable qualitative assessments of model fit for any data set. When RMSEA and CFI offer different evaluations of model fit, we argue that researchers are likely to be confused and potentially make incorrect research conclusions. We derive the necessary as well as the sufficient conditions for inconsistent interpretations of these indices. We also study inconsistency in results for RMSEA and CFI at the sample level. Rather than indicating that the model is misspecified in a particular manner or that there are any flaws in the data, the two indices can disagree because (a) they evaluate, by design, the magnitude of the model's fit function value from different perspectives; (b) the cutoff values for these indices are arbitrary; and (c) the meaning of “good” fit and its relationship with fit indices are not well understood. In the context of inconsistent judgments of fit using RMSEA and CFI, we discuss the implications of using cutoff values to evaluate model fit in practice and to design SEM studies.

KW - comparative fit index

KW - fit indices

KW - root mean square error of approximation

KW - Structural equation modeling

UR - http://www.scopus.com/inward/record.url?scp=84961637017&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84961637017&partnerID=8YFLogxK

U2 - 10.1080/00273171.2015.1134306

DO - 10.1080/00273171.2015.1134306

M3 - Article

SP - 1

EP - 20

JO - Multivariate Behavioral Research

JF - Multivariate Behavioral Research

SN - 0027-3171

ER -