### Abstract

This study examines the unscaled and scaled root mean square error of approximation (RMSEA), comparative fit index (CFI), and Tucker–Lewis index (TLI) of diagonally weighted least squares (DWLS) and unweighted least squares (ULS) estimators in structural equation modeling with ordered categorical data. We show that the number of categories and threshold values for categorization can unappealingly impact the DWLS unscaled and scaled fit indices, as well as the ULS scaled fit indices in the population, given that analysis models are misspecified and that the threshold structure is saturated. Consequently, a severely misspecified model may be considered acceptable, depending on how the underlying continuous variables are categorized. The corresponding CFI and TLI are less dependent on the categorization than RMSEA but are less sensitive to model misspecification in general. In contrast, the number of categories and threshold values do not impact the ULS unscaled fit indices in the population.

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

Pages (from-to) | 731-755 |

Number of pages | 25 |

Journal | Multivariate Behavioral Research |

Volume | 53 |

Issue number | 5 |

DOIs | |

State | Published - Sep 3 2018 |

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### Keywords

- Structural equation modeling
- diagonally weighted least squares
- fit index
- ordered categorical data
- unweighted least squares

### ASJC Scopus subject areas

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

### Cite this

**The Influence of Number of Categories and Threshold Values on Fit Indices in Structural Equation Modeling with Ordered Categorical Data.** / Xia, Yan; Yang, Yanyun.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - The Influence of Number of Categories and Threshold Values on Fit Indices in Structural Equation Modeling with Ordered Categorical Data

AU - Xia, Yan

AU - Yang, Yanyun

PY - 2018/9/3

Y1 - 2018/9/3

N2 - This study examines the unscaled and scaled root mean square error of approximation (RMSEA), comparative fit index (CFI), and Tucker–Lewis index (TLI) of diagonally weighted least squares (DWLS) and unweighted least squares (ULS) estimators in structural equation modeling with ordered categorical data. We show that the number of categories and threshold values for categorization can unappealingly impact the DWLS unscaled and scaled fit indices, as well as the ULS scaled fit indices in the population, given that analysis models are misspecified and that the threshold structure is saturated. Consequently, a severely misspecified model may be considered acceptable, depending on how the underlying continuous variables are categorized. The corresponding CFI and TLI are less dependent on the categorization than RMSEA but are less sensitive to model misspecification in general. In contrast, the number of categories and threshold values do not impact the ULS unscaled fit indices in the population.

AB - This study examines the unscaled and scaled root mean square error of approximation (RMSEA), comparative fit index (CFI), and Tucker–Lewis index (TLI) of diagonally weighted least squares (DWLS) and unweighted least squares (ULS) estimators in structural equation modeling with ordered categorical data. We show that the number of categories and threshold values for categorization can unappealingly impact the DWLS unscaled and scaled fit indices, as well as the ULS scaled fit indices in the population, given that analysis models are misspecified and that the threshold structure is saturated. Consequently, a severely misspecified model may be considered acceptable, depending on how the underlying continuous variables are categorized. The corresponding CFI and TLI are less dependent on the categorization than RMSEA but are less sensitive to model misspecification in general. In contrast, the number of categories and threshold values do not impact the ULS unscaled fit indices in the population.

KW - Structural equation modeling

KW - diagonally weighted least squares

KW - fit index

KW - ordered categorical data

KW - unweighted least squares

UR - http://www.scopus.com/inward/record.url?scp=85057612732&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85057612732&partnerID=8YFLogxK

U2 - 10.1080/00273171.2018.1480346

DO - 10.1080/00273171.2018.1480346

M3 - Article

C2 - 30477318

AN - SCOPUS:85057612732

VL - 53

SP - 731

EP - 755

JO - Multivariate Behavioral Research

JF - Multivariate Behavioral Research

SN - 0027-3171

IS - 5

ER -