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Valentine Ignatov
Valentine Ignatov

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The modification indices might suggest improving the fit by freeing the fixed measurement error variance on y5 (putatively the best available indicator), but this should not be done without a thorough reconsideration of the features discussed above. The corresponding "expected parameter change" statistic might suggest increasing or decreasing y5's fixed measurement error variance, where increases or decreases should be thought of as moving up or down among latents like η3A, η3B, and η3C. But remember that latents like η3A might never be modelable if both y5 and y6 are used as multiple indicators in the model. Instead of freeing y5's measurement error variance at the behest of the modification index, the researcher might decide to drop y6 and thereby permit changing the fixed error variance on y5 to locate η3A. Or the researcher might decide to make y5 an indicator of η3C and y6 an indicator of η3B so that both y5 and y6 receive fixed measurement error variances, and the model contains two similar yet distinct η3 latents (η3B and η3C). With y5 and y6 as single indicators of separate latents, the complex but theory-beneficial reconsiderations would focus on how theory could incorporate two slightly different versions of what previously had been incorrectly thought of as a single latent η3.




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