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Anouck Kluytmans
Sep 12, 2019, 9:11:50 AM9/12/19
to lavaan
I feel this should be a very simple question, but I'm unable to find answers that are applicable to a CFA model with correlated factors:
How can you obtain the total percentage of variance explained in the manifest variables by the factor model as a whole, based on a Lavaan cfa object?
Is it perhaps 1 minus one of the many fitMeasures() results?
The goal is to make statements like "this 3-factor model explains 60% of the total variance in the items". I know variance explained is not a fit measure, but I'd like to report this percentage to stay consistent with how a previous party reported EFA results for this dataset.
Many thanks in advance!
Nickname
Sep 13, 2019, 8:00:55 AM9/13/19
to lavaan
Anouck,
LISREL developers attempted something like this based on the determinants of the covariance matrix and the residual covariance matrix. You can find criticism in Chapter 6 of Leslie Hayduk's book LISREL: Issues, debates and strategies (1996, JHU Press). The basic problem is that it involves reducing a multivariate phenomenon, assuming you have more than one endogenous variable, to a single number. Imagine accounting for X% of the variance in two orthogonal outcome variables. Now imagine the same X% accounted for in two perfectly correlated variables. How should the total variance explained score reflect such differences?
As an alternative, consider reporting a summary of the individual R-square values. At minimum, report their range. Better yet, report a five number summary to describe their distribution.
Keith
------------------------
Keith A. Markus
John Jay College of Criminal Justice, CUNY
http://jjcweb.jjay.cuny.edu/kmarkus
Frontiers of Test Validity Theory: Measurement, Causation and Meaning.
http://www.routledge.com/books/details/9781841692203/
LISREL developers attempted something like this based on the determinants of the covariance matrix and the residual covariance matrix. You can find criticism in Chapter 6 of Leslie Hayduk's book LISREL: Issues, debates and strategies (1996, JHU Press). The basic problem is that it involves reducing a multivariate phenomenon, assuming you have more than one endogenous variable, to a single number. Imagine accounting for X% of the variance in two orthogonal outcome variables. Now imagine the same X% accounted for in two perfectly correlated variables. How should the total variance explained score reflect such differences?
As an alternative, consider reporting a summary of the individual R-square values. At minimum, report their range. Better yet, report a five number summary to describe their distribution.
# The Holzinger and Swineford (1939) example
HS.model <- ' visual =~ x1 + x2 + x3
textual =~ x4 + x5 + x6
speed =~ x7 + x8 + x9 '
fit <- lavaan(HS.model, data=HolzingerSwineford1939,
auto.var=TRUE, auto.fix.first=TRUE,
auto.cov.lv.x=TRUE)
fitRsquares <- lavInspect(fit, what='rsquare')
summary(fitRsquares)[-4]Keith
------------------------
Keith A. Markus
John Jay College of Criminal Justice, CUNY
http://jjcweb.jjay.cuny.edu/kmarkus
Frontiers of Test Validity Theory: Measurement, Causation and Meaning.
http://www.routledge.com/books/details/9781841692203/
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