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I want to test the hypothesis that observed variables can be explained by one latent variable (factor), does a confirmatory factor analysis allow me to test such a hypothesis?

Example:

  • Data: 200 responses on 23 questions (measured on a 5-point Likert scale)
  • Method: confirmatory factor analysis with one factor loading on all the questions
  • Hypothesis: One factor is sufficient to explain the variation in the observed variables

Can I say it tests my hypothesis that a one factor is sufficient to explain the observed data? What is the null hypothesis in confirmatory factor analysis?

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  • $\begingroup$ It seems you are mixing up exploratry and confirmatory analysis. Kaiser may (perhaps) help to suggest the number of factors in exploratoty analysis. Confirmatory analysis is not the alternative to the exploratory, they have different destinations. $\endgroup$ – ttnphns Mar 19 '15 at 15:45
  • $\begingroup$ @ttnphns I understand, but since at my department not many people use CFA (they usually use EFA because it is provided with SPSS) I have to explain why it is inappropriate to give the number of factors based on the Kiser criterion as a test of the number of factors hypothesis, and if CFA is appropriate instead. $\endgroup$ – Chris Novak Mar 19 '15 at 15:53
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    $\begingroup$ I don't see why people are suggesting to close as "unclear". This is a reasonable, although a novice's, question on CFA. $\endgroup$ – StasK Mar 20 '15 at 14:21
  • $\begingroup$ @StasK: I did not vote here, but it seems to have been less clear before the edit. Now it's good, +1 both to the Q and to your A. $\endgroup$ – amoeba Mar 20 '15 at 14:25
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Testing the model structure is exactly what confirmatory factor analysis does. The null hypothesis is "The hypothesized structure fits the data well" vs. a non-committal alternative "The hypothesized structure does not fit the data well enough", which includes alternatives like "more factors are needed" or "some unique errors for items are correlated", but you need to construct these specific alternatives to look into these specific tests.

Personally, I think EFA is only applicable when you know NOTHING about your object of the study. If you constructed your instrument with an idea in mind of measuring some psychological construct, you implicitly have that single factor model built into it. If you know that you have several subscales, then you should fit a CFA that has that many factors, or may be a hierarchical CFA with one higher level factor. But running an EFA to say "Gee, turns out we have three factors in this scale... or wait, let me try a different rotation" -- that does not seem very scientific to me.

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  • $\begingroup$ So I understand that the Chi-squared test does not test the hypothesis that the hypothesised structure fits the data well, but rather, if it fits the data poorly? $\endgroup$ – Chris Novak Mar 21 '15 at 14:23

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