brms: Bayesian Multilevel Models using Stan Paul Brkner 2018-04-09 - PowerPoint PPT Presentation

brms: Bayesian Multilevel Models using Stan Paul Bürkner 2018-04-09 1

Why using Multilevel Models? 2

Example: Effects of Sleep Deprivation on Reaction Times data ("sleepstudy", package = "lme4") head (sleepstudy, 10) Reaction Days Subject 249.5600 0 308 258.7047 1 308 250.8006 2 308 321.4398 3 308 356.8519 4 308 414.6901 5 308 382.2038 6 308 290.1486 7 308 430.5853 8 308 466.3535 9 308 3

Linear Regression vs. Multilevel Regression 350 350 Reaction Reaction 300 300 250 250 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 Days Days 4

Regression Lines for Specific Subjects 5

Why going Bayesian? 6

The Posterior Distribution b_Days sd_Subject__Days 4 8 12 16 5 10 15 7

Why using Stan? 8

Multilevel Models in Classical Statistics with lme4 fit <- lmer (Reaction ~ 1 + Days + (1 + Days | Subject), data = sleepstudy) 9

Multilevel Models in Bayesian Statistics with brms fit <- brm (Reaction ~ 1 + Days + (1 + Days | Subject), data = sleepstudy) 10

Post-Processing methods (class = "brmsfit") ## [1] add_ic add_loo add_waic as.array ## [5] as.data.frame as.matrix as.mcmc coef ## [9] control_params expose_functions family fitted ## [13] fixef formula hypothesis kfold ## [17] launch_shiny log_lik log_posterior logLik ## [21] loo LOO loo_linpred loo_predict ## [25] loo_predictive_interval marginal_effects marginal_smooths model.frame ## [29] neff_ratio ngrps nobs nsamples ## [33] nuts_params pairs parnames plot ## [37] posterior_predict posterior_samples pp_check pp_mixture ## [41] predict predictive_error print prior_samples ## [45] prior_summary ranef reloo residuals ## [49] rhat stancode standata stanplot ## [53] summary update VarCorr vcov ## [57] waic WAIC ## see '?methods' for accessing help and source code 11

The idea of brms : Fitting all kinds of regression models within one framework 12

Example: Censored Recurrance Times of Kidney Infections fitk <- brm (time | cens (censored) ~ age * sex + (1 | patient), data = kidney, family = weibull ()) marginal_effects (fitk, "age:sex") time | cens(censored) 600 sex 400 male female 200 0 20 40 60 13 age

Example: Complex Non-Linear Relationships 1 0 y −1 −2 −2 −1 0 1 2 X Latent mean function Realized data 14

Modeling Non-Linear Relationships with Gaussian Processes fitgp <- brm (y ~ gp (x), bdata) marginal_effects (fitgp, nsamples = 100, spaghetti = TRUE) 2 0 y −2 −4 −2 −1 0 1 2 x 15

Modeling Non-Linear Relationships with Splines fits <- brm (y ~ s (x), bdata) marginal_effects (fits, nsamples = 100, spaghetti = TRUE) 2 0 y −2 −4 −2 −1 0 1 2 x 16

Example: Number of Fish Caught at a Camping Place 100 count 50 0 0 5 10 15 20 25 nfish 17

Modeling Zero-Inflation form <- bf (nfish ~ persons + child + camper, zi ~ child) fit_zinb <- brm (form, zinb, zero_inflated_poisson ()) marginal_effects (fit_zinb, effects = "child") 4 3 nfish 2 1 0 0 1 2 3 child 18

Learn More about brms and Stan • Help within R: help("brms") • Overview of vignettes: vignette(package = "brms") • List of all methods: methods(class = "brmsfit") • Website of brms: https://github.com/paul-buerkner/brms • Website of Stan: http://mc-stan.org/ • Contact me: paul.buerkner@gmail.com • Twitter: @paulbuerkner 19