### Abstract

Previous research indicates that relative fit indices in structural equation modeling may vary across estimation methods. Sugawara and MacCallum (1993) explained that the discrepancy arises from difference in the function values for the null model with no further derivation given. In this study, we derive explicit solutions for parameters of the null model. The null model specifies the variances of the observed variables as model parameters and fixes all the covariances to be zero. Three methods of estimation are considered: the maximum likelihood (ML) method, the ordinary least squares (OLS) method, and the generalized least squares (GLS) method. Results indicate that ML and LS yield an identical estimator, which is different from GLS. Function values and associated chi-square statistics of the null model vary across estimation methods. Consequently, relative fit indices using the null model as the reference point in computation may yield different results depending on the estimation method chosen. An illustration example is given and implications of this study are discussed.

Original language | English |
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Pages (from-to) | 121-128 |

Number of pages | 8 |

Journal | Structural Equation Modeling |

Volume | 4 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1997 Dec 1 |

### All Science Journal Classification (ASJC) codes

- Decision Sciences(all)
- Modelling and Simulation
- Sociology and Political Science
- Economics, Econometrics and Finance(all)

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## Cite this

*Structural Equation Modeling*,

*4*(2), 121-128. https://doi.org/10.1080/10705519709540065