@roylevy.bsky.social
The weakness of “MUPPET B” is that estimating the relation between Y and C at the same stage as estimating the Xs on C leaves us vulnerable to interpretational confounding. “MUPPET A” precludes this, but takes longer (but the new R package speeds this up a bit relative to previous code) 5/5 end
February 8, 2026 at 4:09 PM
The weakness of “MUPPET B” is that estimating the relation between Y and C at the same stage as estimating the Xs on C leaves us vulnerable to interpretational confounding. “MUPPET A” precludes this, but takes longer (but the new R package speeds this up a bit relative to previous code) 5/5 end
Or we could combine the first two fragments in “MUPPET A” and we would have: (1) est. loadings for the Xs on C and relation between Y and C, and then (2) est. posteriors for C using only the Xs, dropping any potential influence of Y on our estimates of the C. Call this “MUPPET B” 4/n
February 8, 2026 at 4:09 PM
Or we could combine the first two fragments in “MUPPET A” and we would have: (1) est. loadings for the Xs on C and relation between Y and C, and then (2) est. posteriors for C using only the Xs, dropping any potential influence of Y on our estimates of the C. Call this “MUPPET B” 4/n
MUPPET now allows for the following in stages: (1) estimate loadings for the Xs on C. (2) est. relation between Y and C conditional on loadings from (1). (3) est. posteriors for C using only the Xs, dropping any potential influence of Y on our estimates of the C. Call this approach “MUPPET A” 3/n
February 8, 2026 at 4:07 PM
MUPPET now allows for the following in stages: (1) estimate loadings for the Xs on C. (2) est. relation between Y and C conditional on loadings from (1). (3) est. posteriors for C using only the Xs, dropping any potential influence of Y on our estimates of the C. Call this approach “MUPPET A” 3/n
So MUPPET passes along the posteriors for the loadings to estimate the next stage to estimate the structural relation, which works better (doi.org/10.1080/1070...). 2/n
Precluding Interpretational Confounding in Factor Analysis with a Covariate or Outcome via Measurement and Uncertainty Preserving Parametric Modeling
In latent variable models, interpretational confounding occurs when the inclusion of a covariate or outcome when fitting the model alters the results for the measurement model. Commonly used estima...
doi.org
February 8, 2026 at 4:04 PM
So MUPPET passes along the posteriors for the loadings to estimate the next stage to estimate the structural relation, which works better (doi.org/10.1080/1070...). 2/n
Not quite. Passing the posteriors for the latent variables to then estimate the relation between the latent variable and the outcome (C and Y in your example), yields biased estimates of that relation (doi.org/10.1037/met0...). 1/5
February 8, 2026 at 4:04 PM
Not quite. Passing the posteriors for the latent variables to then estimate the relation between the latent variable and the outcome (C and Y in your example), yields biased estimates of that relation (doi.org/10.1037/met0...). 1/5
Since my work (with @dmcneish.bsky.social) on addressing this exact issue came up, here's a working paper of the latest extensions of it: drive.google.com/drive/folder... and and associated R package and examples: roy-levy.github.io/muppet_pub/. Happy to discuss, & hope it helps.
MUPPET - Google Drive
drive.google.com
February 8, 2026 at 12:06 AM
Since my work (with @dmcneish.bsky.social) on addressing this exact issue came up, here's a working paper of the latest extensions of it: drive.google.com/drive/folder... and and associated R package and examples: roy-levy.github.io/muppet_pub/. Happy to discuss, & hope it helps.
So you're saying it was a bad thing that an esteemed scholar in the field fell asleep during a job talk I gave?
October 14, 2025 at 11:46 PM
So you're saying it was a bad thing that an esteemed scholar in the field fell asleep during a job talk I gave?