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I am conducting a CFA on a questionnaire with 4 factors. I know that the exploratory factor analysis to obtain theses 4 factors was done using oblimin rotation. I am now wondering, if this affects the model I have to build with lavaan-package in R.

Following the tutorial on the lavaan website I built the following model:

cfa.model <- 'factor1 =~ item1 + item2 + item3 + item4 + item5 + item6
               factor2 =~ item7 + item8 + item9 + item10 + item11 + item12
               factor3 =~ item13 + item14 + item15 + item16 + item17 + item18
               factor4 =~ item19 + item20 + item21 + item22 + item23 + item24'

As the factors were calculated using oblimin type rotation I am not sure if I have to allow correlations between the factors and if so, how to include this in my model?

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It doesn't make any difference where your model comes from. Lavaan doesn't know that the model comes form an EFA, or that you used oblimin (or any other) rotation.

You should always include correlations between your factors, unless you have a very good reason to believe that they are correlated zero.

Lavaan includes factor covariances (and factor variances) by default when you use the cfa() function. You can see in the path diagram on the page that you reference that there are covariances between the factors, even though these weren't specified in the model syntax.

Additional info:

Lots of people like the defaults, but I'm easily confused when using the different functions (cfa(), sem(), lavaan()) and I forget what is included by default and what is not, so I like to specify everything.

You specify a factor variance using:

factor1 ~~ factor1

And a factor covariance using

factor1 ~~ factor2

You'll find that adding those makes no difference to the model (because cfa() puts them in by default.)

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    $\begingroup$ Thank you for the good answer @Jeremy. In case anyone wonders how to set the covariance to 0: factor1 ~~ 0 * factor2. $\endgroup$ – chonasson Jan 20 '17 at 8:59

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