Marginalization and subsequent conditional sampling of latents in simple Structural Equation Models

[Mike Lawrence]

I'm not super well-versed in the underlying math of Structural Equation Models, more an end-user still, but the blavaan package for R employs a trick whereby for sampling purposes latent quantities are marginalized out (See Eqn 6 here) , with optional subsequent conditional sampling of the latent quantities from the posterior samples. Has anyone done/seen anything equivalent for SEMs in TFP?

[Christopher Suter]

We have a few util functions for dealing with normal distribution maths but nothing about SEMs in particular. What are the latents of interest here (that aren't marginalized), the residual covariances? 

On Wed, Apr 20, 2022 at 10:12 Mike Lawrence <mike....@gmail.com> wrote:

I'm not super well-versed in the underlying math of Structural Equation Models, more an end-user still, but the blavaan package for R employs a trick whereby for sampling purposes latent quantities are marginalized out (See Eqn 6 here) , with optional subsequent conditional sampling of the latent quantities from the posterior samples. Has anyone done/seen anything equivalent for SEMs in TFP?

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[Mike Lawrence]

A couple hours after posting here I found some decently readable Stan code [here](

https://gist.github.com/rmcelreath/68fb40bf7a3e73bf2623e10a5973216d) showing how to do the marginalization trick I’m referring to. It’s the latent quantity U I’m referring to. 

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Mike Lawrence, PhD

Co-founder & Research Scientist

Axem Neurotechnology

axemneuro.com

~ Certainty is (usually) folly ~