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 and only through , and each depends monotonically on . Thus each measure gives the same rank-ordering of models. For this reason, the specification search procedure reports only RMSEA.
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The following fit measures depend on and only through , and they depend monotonically on . The specification search procedure reports only CFI as representative of them all.
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The following fit measures depend monotonically on , and not at all on . The specification search procedure reports only as representative of them all.
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Each of the following fit measures is a weighted sum of and , and can produce a distinct rank order of models. The specification search procedure reports each of them except for CAIC.
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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.
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The following fit measures are the only ones reported by Amos that are not functions of and in the case of maximum likelihood estimation. The specification search procedure does not report these measures.
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