Challenges in Bayesian Structural Equation Modeling

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Structural Equation Modeling (SEM) is a key framework in causal inference. As I’m diving deeper and deeper into these topics to teach them and, well, finally understand them, I was delighted to host Ed Merkle on the show.

A professor of psychological sciences at the University of Missouri, Ed discusses his work on Bayesian applications to psychometric models and model estimation, particularly in the context of Bayesian SEM. He explains the importance of BSEM in psychometrics and the challenges encountered in its estimation.

Ed also introduces his blavaan package in R, which enhances researchers' capabilities in BSEM and has been instrumental in the dissemination of these methods. Additionally, he explores the role of Bayesian methods in forecasting and crowdsourcing wisdom.

When he’s not thinking about stats and psychology, Ed can be found running, playing the piano, or playing 8-bit video games.

Our theme music is « Good Bayesian », by Baba Brinkman (feat MC Lars and Mega Ran). Check out his awesome work at https://bababrinkman.com/ !

Thank you to my Patrons for making this episode possible!

Yusuke Saito, Avi Bryant, Ero Carrera, Giuliano Cruz, Tim Gasser, James Wade, Tradd Salvo, William Benton, James Ahloy, Robin Taylor,, Chad Scherrer, Zwelithini Tunyiswa, Bertrand Wilden, James Thompson, Stephen Oates, Gian Luca Di Tanna, Jack Wells, Matthew Maldonado, Ian Costley, Ally Salim, Larry Gill, Ian Moran, Paul Oreto, Colin Caprani, Colin Carroll, Nathaniel Burbank, Michael Osthege, Rémi Louf, Clive Edelsten, Henri Wallen, Hugo Botha, Vinh Nguyen, Marcin Elantkowski, Adam C. Smith, Will Kurt, Andrew Moskowitz, Hector Munoz, Marco Gorelli, Simon Kessell, Bradley Rode, Patrick Kelley, Rick Anderson, Casper de Bruin, Philippe Labonde, Michael Hankin, Cameron Smith, Tomáš Frýda, Ryan Wesslen, Andreas Netti, Riley King, Yoshiyuki Hamajima, Sven De Maeyer, Michael DeCrescenzo, Fergal M, Mason Yahr, Naoya Kanai, Steven Rowland, Aubrey Clayton, Jeannine Sue, Omri Har Shemesh, Scott Anthony Robson, Robert Yolken, Or Duek, Pavel Dusek, Paul Cox, Andreas Kröpelin, Raphaël R, Nicolas Rode, Gabriel Stechschulte, Arkady, Kurt TeKolste, Gergely Juhasz, Marcus Nölke, Maggi Mackintosh, Grant Pezzolesi, Avram Aelony, Joshua Meehl, Javier Sabio, Kristian Higgins, Alex Jones, Gregorio Aguilar, Matt Rosinski, Bart Trudeau, Luis Fonseca, Dante Gates, Matt Niccolls, Maksim Kuznecov, Michael Thomas, Luke Gorrie, Cory Kiser and Julio.

Visit https://www.patreon.com/learnbayesstats to unlock exclusive Bayesian swag ;)

Takeaways:

- Bayesian SEM is a powerful framework in psychometrics that allows for the estimation of complex models involving multiple variables and causal relationships.

- Understanding the principles of Bayesian inference is crucial for effectively applying Bayesian SEM in psychological research.

- Informative priors play a key role in Bayesian modeling, providing valuable information and improving the accuracy of model estimates.

- Challenges in BSEM estimation include specifying appropriate prior distributions, dealing with unidentified parameters, and ensuring convergence of the model. Incorporating prior information is crucial in Bayesian modeling, especially when dealing with large models and imperfect data.

- The blavaan package enhances researchers' capabilities in Bayesian structural equation modeling, providing a user-friendly interface and compatibility with existing frequentist models.

- Bayesian methods offer advantages in forecasting and subjective probability by allowing for the characterization of uncertainty and providing a range of predictions.

- Interpreting Bayesian model results requires careful consideration of the entire posterior distribution, rather than focusing solely on point estimates.

- Latent variable models, also known as structural equation models, play a crucial role in psychometrics, allowing for the estimation of unobserved variables and their influence on observed variables.

- The speed of MCMC estimation and the need for a slower, more thoughtful workflow are common challenges in the Bayesian workflow.

- The future of Bayesian psychometrics may involve advancements in parallel computing and GPU-accelerated MCMC algorithms.

Chapters:

00:00 Introduction to the Conversation

02:17 Background and Work on Bayesian SEM

04:12 Topics of Focus: Structural Equation Models

05:16 Introduction to Bayesian Inference

09:30 Importance of Bayesian SEM in Psychometrics

10:28 Overview of Bayesian Structural Equation Modeling (BSEM)

12:22 Relationship between BSEM and Causal Inference

15:41 Advice for Learning BSEM

21:57 Challenges in BSEM Estimation

34:40 The Impact of Model Size and Data Quality

37:07 The Development of the Blavaan Package

42:16 Bayesian Methods in Forecasting and Subjective Probability

46:27 Interpreting Bayesian Model Results

51:13 Latent Variable Models in Psychometrics

56:23 Challenges in the Bayesian Workflow

01:01:13 The Future of Bayesian Psychometrics

Links from the show:

• Ed’s website: https://ecmerkle.github.io/
• Ed on Mastodon: https://mastodon.sdf.org/@edgarmerkle
• Ed on BlueSky: @edgarmerkle.bsky.social
• Ed on GitHub: https://github.com/ecmerkle
• blaavan R package: https://ecmerkle.github.io/blavaan/
• Resources on how to use blaavan: https://ecmerkle.github.io/blavaan/articles/resources.html
• Richard McElreath, Table 2 Fallacy: https://youtu.be/uanZZLlzKHw?si=vssrwJsvGO5HhH5H&t=4323

Transcript

This is an automatic transcript and may therefore contain errors. Please get in touch if you're willing to correct them.