Oh, the Places You’ll Go: flexible modelling options available with brms

Bayesian workshop - STEP 2023

Scott James Perry

University of Alberta

I want you to know what’s out there



  • Be familiar with some options for models we didn’t talk about
  • Some resources that can help you

Distributional regression


  • Focus modelling the mean of a distribution
  • We can allow all parameters to vary by our predictors (fixed and random)



brm(bf(rt ~
         0 + group_factor,
       sigma ~
         0 + group_factor),
    data = LD_L2,
    ...
)

Robust regression using student-t

  • Too many outliers bumming you out?
  • student_t distribution assumings outliers more common

Finite Mixture models


  • We typically pick a single distribution
  • Models can have a composition of multiple distributions

Ordinal regression with varying scale parameters on latent distribution

  • Equal variance assumption dangerous in ordinal regression
  • Relaxing that assumption prevents errors (Liddell & Kruschke, 2018)



Other models


  • Zero-(One)-Inflated Beta Regression (e.g., slider data)
  • Drift-diffusion model (cognitive model for binary choices)
  • Multinomial regression (> 2 categories)
  • Poisson, Zero-inflated poisson (count data)
  • Generalized additive models
  • Gaussian process models
  • Bayesian networks (similar to SEM)

Beyond brms



Stan let’s you fit any mathematical model to data (in theory)



Where can I learn these stats?



“There is perhaps no better statistics textbook, ever, than Richard McElreath’s Statistical Rethinking” - (Winter, 2019, p.301)

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Books aimed at lingusits and cognitive scientists


An Introduction to Bayesian Data Analysis for Cognitive Science
Bruno Nicenboim, Daniel Schad, and Shravan Vasishth

Free at: https://vasishth.github.io/bayescogsci/book/

Bayesian Multilevel Models for Repeated Measures Data: A Conceptual and Practical Introduction in R
Santiago Barreda & Noah Silbert

Other readings

Gelman, A., & Hill, J. (2006). Data analysis using regression and multilevel/hierarchical models. Cambridge university press.

Gelman, A., Hill, J., & Vehtari, A. (2020). Regression and other stories. Cambridge University Press.

Kruschke, J. (2014). Doing Bayesian data analysis: A tutorial with R, JAGS, and Stan.

Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.