Variance Explained by a Latent Variable

[David Phillips]

Dear Lavaan community,

How would one estimate the variance of a particular variable that is explained by another variable in SEM?

Consider the political democracy example. How much of the variance in dem65 is explained by dem60, and how much is explained by ind60? Does this change if the structure of the latent variable relationship gets more complicated (e.g. latent variables as indicators for other latent variables)? 

Thanks,

David

[Mikko Rönkkö]

On 10 Nov 2016, at 12:07 , David Phillips <davidem...@gmail.com> wrote:

Dear Lavaan community,

How would one estimate the variance of a particular variable that is explained by another variable in SEM?

Consider the political democracy example. How much of the variance in dem65 is explained by dem60, and how much is explained by ind60?

If you want to get the share of variance explained uniquely by dem60 controlling for ind60, take the standardized estimates and square the regression paths.

Does this change if the structure of the latent variable relationship gets more complicated (e.g. latent variables as indicators for other latent variables)? 

No as long as the model is recursive.

Mikko

Thanks,

David

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[Terrence Jorgensen]

How would one estimate the variance of a particular variable that is explained by another variable in SEM?

It is implied by the model parameters.  You can request the (full, not residual) covariance matrix of latent variables from lavaan:

lavInspect(fit, "cov.lv")

lavInspect(fit, "cor.lv") # or correlation matrix

How much of the variance in dem65 is explained by dem60, and how much is explained by ind60?

You can request R-squared from lavaan as well

summary(fit, rsquare = TRUE)

parameterEstimates(fit, rsquare = TRUE)

Does this change if the structure of the latent variable relationship gets more complicated (e.g. latent variables as indicators for other latent variables)? 

Changing a regression equation by adding or removing predictors will always change R-squared, but the total variance of that variable should remain the same (as long as the measurement model remains constant).  The variance of a latent variable is set arbitrarily because it doesn't have an implicit scale (variables only have scales that we assign when we measure them), but if you change the definition of a latent variable by using different indicators, that can affect results because the latent variable will represent the shared variance among a different set of indicators.  For example, the amount of variance in dem65 that is explained by ind60 is inferred indirectly from the amount of shared variance between the common-variance among ind60 indicators and the common variance among dem65 indicators.

Your questions seem more about SEM than about software, so consider posting your question on the much larger forum SEMNET:

www2.gsu.edu/~mkteer/semnet.html

Terrence D. Jorgensen

Postdoctoral Researcher, Methods and Statistics

Research Institute for Child Development and Education, the University of Amsterdam

UvA web page: http://www.uva.nl/profile/t.d.jorgensen