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Suppose I have a scale with four items meant to measure, say, happiness. I ran a confirmatory factor analysis and the model fits well with two factors and let's say that the two factors are 1) positive affect and 2) energy.

Putting all four items into a standard reliability analysis produces a Cronbach's alpha that is more than acceptable at 0.80.

If I wanted to use happiness as a predictor or outcome variable in a linear regression, is it adequate to still just average the four items into one composite score despite it consisting of two factors in the CFA?

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Yes. Your composite is a proxy for "happiness." You don't have much evidence that it is a good proxy, but as long as you recognize its tentative nature, then your inference won't go far wrong. As is too common in behavioral research, you have (mentioned) no concrete standard against which to judge your proxy. If you had a criterion that was known to correlate strongly with happiness, then you might assess whether one composite or some sub-composite matches up better with the criterion, thus establishing "criterion validity." But your set of items need not be unidimensional to be a good proxy for happiness. Clinical screening tools are very often or even typically multidimensional. On the other hand, you might create sub-composites and stay on the lookout for evidence that one of them performs better.

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