How can I obtain the cross loadings with lavaan?

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Abc Abc

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Jun 22, 2019, 12:52:46 PM6/22/19
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Dear lavaan team,

In my understanding, cross loadings can only be obtained from Structural Equation modeling (i.e. not from CFA). Am I correct? (I read another answer mentioning that CFA can generate cross loading after certain proceures, but I do not really understand the idea. https://groups.google.com/forum/#!searchin/lavaan/cross$20loading|sort:date/lavaan/X_yaIobn7Xo/s1FTUEfhBwAJ)

How should I obtain the cross loadings with lavaan?

Code for reference:
model1 <- 'O  =~ o1 + o2 + o3 + o4 + o5
T  =~  t1 + t2 + t3 + t4
G =~ g1 + g2 + g3
P =~ p1 + p2 + p3
P ~ OC + TC + TGC'

fit1 <- sem(model1, data=data)

Thank you in advance for your help.

car...@web.de

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Jun 22, 2019, 1:31:40 PM6/22/19
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If you do not specify cross loadings, you will not get cross loadings. This has nothing to do with CFA or SEM. You could pull information from the modification indiced or specify an E/CFA.
Am 22.06.19, 18:52, Abc Abc <tuo...@gmail.com> schrieb:
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Abc Abc

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Jun 22, 2019, 1:55:12 PM6/22/19
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How can I specify cross loading? Can you give me an example with the code I provided?


On Saturday, June 22, 2019 at 7:31:40 PM UTC+2, car...@web.de wrote:
If you do not specify cross loadings, you will not get cross loadings. This has nothing to do with CFA or SEM. You could pull information from the modification indiced or specify an E/CFA.
Am 22.06.19, 18:52, Abc Abc <tuo...@gmail.com> schrieb:
Dear lavaan team,

In my understanding, cross loadings can only be obtained from Structural Equation modeling (i.e. not from CFA). Am I correct? (I read another answer mentioning that CFA can generate cross loading after certain proceures, but I do not really understand the idea. https://groups.google.com/forum/#!searchin/lavaan/cross$20loading|sort:date/lavaan/X_yaIobn7Xo/s1FTUEfhBwAJ)

How should I obtain the cross loadings with lavaan?

Code for reference:
model1 <- 'O  =~ o1 + o2 + o3 + o4 + o5
T  =~  t1 + t2 + t3 + t4
G =~ g1 + g2 + g3
P =~ p1 + p2 + p3
P ~ OC + TC + TGC'

fit1 <- sem(model1, data=data)

Thank you in advance for your help.

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car...@web.de

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Jun 22, 2019, 2:14:16 PM6/22/19
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[...]
T =~ t1 + t2 + t3 + t4 + g2

G =~ g1 + g2 + g3
[...]

Now g2 is related to more than one factor. If you want something in EFA style, fit an E/CFA.
Am 22.06.19, 19:55, Abc Abc <tuo...@gmail.com> schrieb:
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Abc Abc

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Jun 22, 2019, 2:50:47 PM6/22/19
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Thank you.

How can I obtain cross loading after this? With inspect()? If yes, which matrix should I look at?

car...@web.de

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Jun 22, 2019, 3:24:56 PM6/22/19
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Am 22.06.19, 20:50, Abc Abc <tuo...@gmail.com> schrieb:
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Edward Rigdon

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Jun 22, 2019, 3:31:41 PM6/22/19
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     If you are a PLS path modeling user, then "cross-loadings" are correlations between the component observed variables of one composite and a different composite. They, of course, are not "loadings" because PLS path modeling is a method of composites, not a method of common factors.
     The closest analogy in CFA / factor-based SEM are "structure coefficients," which are the correlations between observed variables and common factors. You can find these by multiplying the loading matrix times the factor correlation matrix. They don't provide any new information in factor-based methods, since they are precisely the product of those two parameter matrices. In particular, they don't have diagnostic value, because, again, they contain no new information.

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Abc Abc

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Jun 22, 2019, 3:34:53 PM6/22/19
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Just to make sure: it is the same as factor loading, except the model specification part?

car...@web.de

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Jun 22, 2019, 3:49:43 PM6/22/19
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Ed, thanks for clarification. Independently of this, the term "cross loading" can also be found in the CB SEM vocabulary. You can find it for example on slides provided by Yves: https://users.ugent.be/~yrosseel/lavaan/zurich2017/INTRO/lavaan_intro_zurich2017.pdf

Now if ABC ABC wants to check whether an indicator loads on multiple factors, then I can't see a mistake in my answers. Is there any?
Am 22.06.19, 21:31, Edward Rigdon <edward...@gmail.com> schrieb:
     If you are a PLS path modeling user, then "cross-loadings" are correlations between the component observed variables of one composite and a different composite. They, of course, are not "loadings" because PLS path modeling is a method of composites, not a method of common factors.
     The closest analogy in CFA / factor-based SEM are "structure coefficients," which are the correlations between observed variables and common factors. You can find these by multiplying the loading matrix times the factor correlation matrix. They don't provide any new information in factor-based methods, since they are precisely the product of those two parameter matrices. In particular, they don't have diagnostic value, because, again, they contain no new information.

On Sat, Jun 22, 2019 at 1:55 PM Abc Abc <tuo...@gmail.com> wrote:
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Edward Rigdon

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Jun 28, 2019, 11:30:39 AM6/28/19
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Yes, you can even mention the same observed variable twice in the same line of syntax with different modifiers, as in
f =~ a*x1 + start(2)*x1
which labeles teh loading of x1 "a" and gives it a starting value of 2

Statistical identification becomes more complex with indicators loading on multiple factors.  This is different from composite-based methods like PLS path modeling. So you have to be on the lookout for evidence of identification problems. There are better methods for assessing statistical identification beforehand, but they have not caught on with this literature.

On Fri, Jun 28, 2019 at 10:20 AM Abc Abc <tuo...@gmail.com> wrote:
Are you sure that e.g. g2 can be written twice in the groups of definition?


On Saturday, June 22, 2019 at 8:14:16 PM UTC+2, car...@web.de wrote:

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