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IBM® SPSS® Amos™ 28

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Appendix E: Using Fit Measures to Rank Models

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In general, it is hard to pick a fit measure because there are so many to pick from. The choice gets easier when the purpose of the fit measure is to compare models to each other, rather than to judge the merit of models by an absolute standard. For example, it turns out that it does not matter whether you use RMSEA, RFI or TLI when rank-ordering a collection of models. Each of those three measures depends on 7332 and 7333 only through 7328, and each depends monotonically on 7328. Thus each measure gives the same rank-ordering of models. For this reason, the specification search procedure reports only  RMSEA.

7329

7330

7331

The following fit measures depend on 7332 and 7333 only through 7334, and they depend monotonically on 7334. The specification search procedure reports only CFI as representative of them all.

7335

7336

7337

7338 (not reported by Amos)

The following fit measures depend monotonically on 7332, and not at all on 7333. The specification search procedure reports only 7332 as representative of them all.

7339

7340

7341

Each of the following fit measures is a weighted sum of 7332 and 7333, and can produce a distinct rank order of models. The specification search procedure reports each of them except for  CAIC.

7342

7343

7344

7345

Each of the following fit measures is capable of providing a unique rank-order of models. The rank order depends on the choice of baseline model as well. The specification search procedure does not report these measures.

7346

7347

7348

The following fit measures are the only ones reported by Amos that are not functions of 7332 and 7333 in the case of maximum likelihood estimation. The specification search procedure does not report these measures.

7349

7350

7351

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