Hello fellow reseachers,
currently, i'am writing my master thesis and i have a problem regarding the analysis. I want to do a Third-Order Model which looks like the one in the picture. Unfortunately, i cant find any literature on how to do this in R. My master thesis is based on another study where they did a Third-Order Model, but with SPSS AMOS. Does someone know if this is even possible in R and have any tutorials/literature about it?
Thank you very much in advance!
Can you just do this in the regressions part of the model in the sem function in lavaan? You could consider Gc and Gf to be correlated. The model does seem complex. I am always reminded by what the professor who taught me latent variables said:
"The reader already familiar with factor analysis may be surprised that our emphasis, in theory and examples, is on models with only one or two latent variables. On the other hand, we pay more attention to questions of sampling variability and goodness of fit than is usual. This shift of emphasis is deliberate because we wish to stay within the bounds of what is statistically defensible. As we proceed, it will become apparent that serious questions of identifiability, precision and interpretation arise as the complexity of the models increases. We think the advance of knowledge is best served by building on relatively secure, if modest, base rather than risking becoming lost in a morass of ambiguity and uncertainty." \citep[pp.~xi--xii]{BartholomewKnott1999}
Hi Maximilian,
the identification rules don't change whether you specify a first order factor, second-order or third-order factor: You need 3 outcomes to estimate the parameters, and 4 to test the structure. For instance, the g factor in your path diagram is neither identified (unless you impose equality constraints on either the error variances or loadings) and not testable. Hence you could use any pair of correlating factors and substitute their covariance by a "factor" although the factor is meaningless.
Please note that there is substantial danger in specifying such models (as Daniel has already pointed out), or Lee & Cadogan (2013) who stressed that you may end up with modeling pure noise. IMHO, the fascination of esp. psychology with these models is purely historically determined (e.g., the PCA / factor analysis history in IQ and personality research) that always started with many measured variables and tried to either reduce dimensionality (PCA) or find underlying factors. From a measurement perspective, I find them pretty useless. That is: If you know what g is (or have some theory), why not develop direct measures of it?
In addition, most researchers striving for such models still do not know what a second-order factor is (namely the underlying one-dimensional cause of the primary factor and not their aggregate). End of rant :)
All the best,
Holger
Lee, N., & Cadogan, J. W. (2013). Problems with formative and higher-order reflective variables. Journal of Business Research, 66(2), 242-247. doi:10.1016/j.jbusres.2012.08.004
Dear Maximilian Tüllmann
Follow these steps:
1. Install and load the package first:
2. execute install.packages("lavaan")
3. the library (lavaan)
4. The model is then defined by defining the link between items and factors:
5. Finally, fit the model and output the results:
6. Result:
Take a look to this article also: https://stats.idre.ucla.edu/r/seminars/rcfa/
Best Regards
Dr. Fatemeh Khozaei
Thank you very much for your replies!
Daniel Wright I will try to do so. It is a bit confusing for me, because in the original study they draw a Third-Order CFA-Model where every higher order is measured by at least one beneath. From my knowledge, if there is a link between to exogenes variables, then one regresses on the other, which would cause the opperate direction of the arrow within the figure.
Holger Steinmetz In the original study, there are several equality constraints between the 5 first order factors and 2 second order factors. Right now, i'am struggeling a little bit with finding a comprehensive description on how to do this in R. I got several literatur on commands in R lavaan, but none are describing them fully.
Regarding your rant, it is probably true that these complex models are quiet hard to identify. Right now there are already problems of identification when i test for strong invariance.
Fatemeh Khozaei Thanks for the link. I will have a look.
Kind regards,
Max
Maximilian,
constraints are not set between factors but for sets of parameters. For instance, a 2-indicator latent can be specified by restricting both loadings to be equal (hence, to 1, as one is the marker) or by restricting both error variances to be equal. This, however, does not show whether the factor has any realistic appropriateness (an issue, the still positivist psychology asks too seldomly).
Hence you can do this with your model but a better way would be to add further predictors and/or outcomes of the higher-order factor and to avoid to do only-factor models. This is a perspective also valid for simple CFAs.
Good luck
Holger
- Badges
- Science topic
- Similar topics
- Thesis Research