Effect of latent variables on a binary (observed) outcome

[Leila Amorim]

Hi,

    We are running a model in blavaan, where all indicators for the latent variables are binary, and our outcome is also binary. We understand that blavaan considers the probit link function for our outcome (structural) model. 

      We are trying to obtain some measures to interpret our results:

a) Variance explained by each latent variable. Do you know if it is possible to decompose the total variance of the outcome by each of the covariates (including some latent variables) in such model?

b) Prediction of the outcome. We would like to get the predicted value of our binary outcome by fixing specific values for the covariates in the model. Is there a function in blavaan for that?

        I appreciate any thoughts and/or references to understand how to do that, if possible.

                  Thanks,

                          Leila

[Terrence Jorgensen]

a)  This does not make sense unless you have perfectly orthogonal predictors, as in an experimental design with balanced sample sizes in each condition.  The total R-squared is on the scale of the latent response, like McKelvey & Zavoina’s pseudo-R-squared:

https://stats.oarc.ucla.edu/other/mult-pkg/faq/general/faq-what-are-pseudo-r-squareds/

Calculating change in R-squared (or partial-eta-squared) when an effect is added is not straight-forward, even in the frequentist framework:

https://doi.org/10.3758/s13428-020-01532-y

b)  blavPredict() has a currently unused newdata= argument, so you might have to simply write a function that accepts a posterior sample and calculates the predicted value(s) you want, then apply it across posterior samples.  If the covariate-value combinations you are interested in actually exist in your data, then you can use blavPredict() and look for those rows, but it only returns predictions on the latent-response scale 

https://github.com/ecmerkle/blavaan/issues/13

Terrence D. Jorgensen

Assistant Professor, Methods and Statistics

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

http://www.uva.nl/profile/t.d.jorgensen

[Leila Amorim]

Dear Dr.Jorgensen,

     Many thanks for your answers. We really appreciate your comments.

     I just want to confirm an additional feature of blavaan:

(1) Can blavaan be used to run a Bayesian Path Analysis, where the outcome is binary and we would like to use probit or logit link functions? If so, could you please send us additional links/references for using such specifications in blavaan. 

                Best,

                     Leila

[Ed Merkle]

Leila,

In version 0.4-1, it should be possible to include a binary outcome in blavaan, using a probit link (and you don't get a choice of link function, it is automatically probit). This is new functionality, with some detail appearing here:

https://ecmerkle.github.io/blavaan/articles/ordinal.html

You would want to use the `ordered` argument to specify which variables in your model are binary/ordinal, just as you would in lavaan.

Ed

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[Leila Amorim]

Many thanks for your guidance!