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brms: Bayesian Multilevel Models using Stan
Paul Bürkner 2018-04-09
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Why using Multilevel Models?
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brms: Bayesian Multilevel Models using Stan Paul Brkner 2018-04-09 - - PowerPoint PPT Presentation
brms: Bayesian Multilevel Models using Stan Paul Brkner 2018-04-09 - - PowerPoint PPT Presentation
brms: Bayesian Multilevel Models using Stan Paul Brkner 2018-04-09 1 Why using Multilevel Models? 2 Example: Effects of Sleep Deprivation on Reaction Times data ("sleepstudy", package = "lme4") head (sleepstudy, 10)
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Example: Effects of Sleep Deprivation on Reaction Times
data("sleepstudy", package = "lme4") head(sleepstudy, 10) Reaction Days Subject 249.5600 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
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Linear Regression vs. Multilevel Regression
250 300 350 0 1 2 3 4 5 6 7 8 9
Days Reaction
250 300 350 0 1 2 3 4 5 6 7 8 9
Days Reaction
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Regression Lines for Specific Subjects
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Why going Bayesian?
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The Posterior Distribution
b_Days sd_Subject__Days
4 8 12 16 5 10 15
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Why using Stan?
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Multilevel Models in Classical Statistics with lme4
fit <- lmer(Reaction ~ 1 + Days + (1 + Days|Subject), data = sleepstudy)
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Multilevel Models in Bayesian Statistics with brms
fit <- brm(Reaction ~ 1 + Days + (1 + Days|Subject), data = sleepstudy)
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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
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The idea of brms: Fitting all kinds of regression models within one framework
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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")
200 400 600 20 40 60
age time | cens(censored) sex
male female
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Example: Complex Non-Linear Relationships
−2 −1 1 −2 −1 1 2
X y
Latent mean function Realized data
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Modeling Non-Linear Relationships with Gaussian Processes
fitgp <- brm(y ~ gp(x), bdata) marginal_effects(fitgp, nsamples = 100, spaghetti = TRUE)
−4 −2 2 −2 −1 1 2
x y
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Modeling Non-Linear Relationships with Splines
fits <- brm(y ~ s(x), bdata) marginal_effects(fits, nsamples = 100, spaghetti = TRUE)
−4 −2 2 −2 −1 1 2
x y
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Example: Number of Fish Caught at a Camping Place
50 100 5 10 15 20 25
nfish count
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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")
1 2 3 4 1 2 3
child nfish
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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
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