CFA with only formative indicators... PreviousNext
Mplus Discussion > Confirmatory Factor Analysis >
 Jordan posted on Monday, February 08, 2016 - 10:12 am

I am conducting a CFA involving 7 dimensions of a "second-order"/multi-dimensional construct. To be clear, the dimensions are latent and reflective, each with four indicators; however, the second-order latent factor is theorized to be aggregate (the latent dimensions serving as formative indicators).

Is it possible to conduct a CFA of such a model? This is the input I have used when attempting to do so:

dim1 by [indicators];
dim2 by [indicators];

secondorder by; !defining the formative factor
secondorder on dim1@1 dim2 dim3 etc. ; !defining the formative relationships between the latent dimensions and the second order factor.

Any guidance?
 Linda K. Muthen posted on Monday, February 08, 2016 - 11:08 am
See the Topic 1 course handout on the website where there are examples of formative indicators using Mplus.
 Jordan posted on Monday, February 08, 2016 - 12:11 pm
The examples given on the course handout all include an outcome variable/construct. But I am only doing interested in the measurement model that relates indicators to dimensions and those dimensions to a second-order factor (vs. relating the second order factor to some outcome).

When I try to follow the handout without an outcome variable (e.g. "friends", as in the handout), I get an error with respect to model identification. I'm unsure as to whether this means I cannot do what I aim to do, or whether I'm not constraining the model in some necessary way which I may be ignorant of (or both!).

I suppose the main difference is that I'm dealing with a multi-dimensional construct only vs. a unidimensional construct.
 Bengt O. Muthen posted on Monday, February 08, 2016 - 1:32 pm
I don't think the formative model is identified without the formative factors predicting something.
 Nguyen Pham posted on Tuesday, February 21, 2017 - 5:30 pm

I conducted CFA with Mplus and the model fit is not good (RMSEA is about 0.1 or higher). The modification indices offered suggested remedies by covarying error terms with other error terms that are not part of the same factor. Can I modify the model by covarying error terms with other error terms that are not part of the same factor?

Thank you.
 Linda K. Muthen posted on Wednesday, February 22, 2017 - 10:07 am
Parameters should be added based on modification indices only if they make theoretical sense. You may want to consider changing your CFA model. Try an EFA to see if your CFA model is supported by the results.
 Michael Covell posted on Tuesday, July 16, 2019 - 7:08 pm
I used the syntax for a formative indicator model presented in Topic 1 to run a multilvel CFA with two latent variables, one with reflective indicators and one with formative indicators. I got this error for each formative indicator...

"Unrestricted x-variables for analysis with TYPE=TWOLEVEL and ALGORITHM=INTEGRATION
must be specified as either a WITHIN or BETWEEN variable. The following variable
cannot exist on both levels"
 Bengt O. Muthen posted on Wednesday, July 17, 2019 - 5:28 pm
We need to see your full output - send to Support along with your license number.
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