/r-bayes

name: r-bayes
description: Patterns for Bayesian inference in R using brms, including multilevel models, DAG validation, and marginal effects. Use when performing Bayesian analysis.

Core Packages

library(brms)
library(cmdstanr)
library(dagitty)
library(ggdag)
library(marginaleffects)
library(tidybayes)
library(bayesplot)

Directed Acyclic Graphs (DAGs)

Prior to causal inference, create and validate DAGs with dagitty and ggdag.

Define DAG Structure

dag <- dagitty('
dag {
  # Node positions for visualization
  exposure [pos="0,1"]
  mediator [pos="1,1"]
  outcome [pos="2,1"]
  confounder [pos="1,0"]

  # Edges (arrows)
  confounder -> exposure
  confounder -> outcome
  exposure -> mediator
  mediator -> outcome
  exposure -> outcome
}
')

Identify Adjustment Sets

# For direct effect
adjustmentSets(dag, exposure = "treatment", outcome = "outcome", effect = "direct")

# For total effect
adjustmentSets(dag, exposure = "treatment", outcome = "outcome", effect = "total")

Validate DAG Against Data

# Get implied conditional independencies
implied_cis <- impliedConditionalIndependencies(dag)

# Test against data
ci_results <- localTests(dag, data = analysis_data, type = "cis")

# Assess validation
ci_df <- as.data.frame(ci_results)
ci_df$independent <- ci_df$p.value > 0.05
pct_supported <- 100 * mean(ci_df$independent, na.rm = TRUE)

cat(sprintf("DAG support: %.1f%% of implied CIs hold\n", pct_supported))

Visualize DAG

dag_tidy <- tidy_dagitty(dag)

ggplot(dag_tidy, aes(x = x, y = y, xend = xend, yend = yend)) +
  geom_dag_edges(edge_colour = "grey50") +
  geom_dag_point(size = 20) +
  geom_dag_text(size = 3.5, color = "black") +
  theme_dag() +
  labs(title = "Causal DAG")

Bayesian Regression with brms

Standard Configuration

options(mc.cores = 4)

# Standard brms model call
model <- brm(
  formula = outcome ~ predictor1 + predictor2 + (1 | group_id),
  data = model_data,
  family = bernoulli(link = "logit"),  # For binary outcomes
  prior = priors,
  sample_prior = "yes",  # For prior-posterior comparison
  chains = 4,
  cores = 4,
  iter = 4000,
  warmup = 1000,
  control = list(
    adapt_delta = 0.95,
    max_treedepth = 15
  ),
  seed = 123,  # Set seed for reproducibility
  backend = "cmdstanr",
  file = "models/model_name",         # Cache compiled model
  file_refit = "on_change"            # Only refit if formula/data change
)

Priors

Store priors separately and define explicitly:

priors <- c(
  prior(normal(0, 2), class = "Intercept"),
  prior(normal(0, 1), class = "b"),                    # Fixed effects
  prior(exponential(1), class = "sd"),                 # Random effect SD
  prior(lkj(2), class = "cor")                         # Correlation priors
)

# Get default priors for a formula
get_prior(outcome ~ predictor + (1 | id), data = data, family = bernoulli())

Common Families

# Binary outcome
family = bernoulli(link = "logit")

# Count data
family = poisson(link = "log")
family = negbinomial(link = "log")

# Continuous
family = gaussian()
family = student()  # Robust to outliers

# Ordinal
family = cumulative(link = "logit")

Multilevel Models

Random Intercepts

# Random intercept per participant
outcome ~ predictors + (1 | participant_id)

Random Slopes

# Random intercept and slope for time
outcome ~ time + predictors + (1 + time | participant_id)

Crossed Random Effects

# Participants nested in groups, items crossed
response ~ predictors + (1 | participant_id) + (1 | item_id)

Within-Person Centering

For longitudinal data, separate between-person and within-person effects:

# Create person-centered variables
model_data <- data |>
  group_by(participant_id) |>
  mutate(
    # Between-person means (stable trait)
    predictor_mean = mean(predictor, na.rm = TRUE),

    # Within-person deviations (dynamic change)
    predictor_dev = predictor - predictor_mean,

    # Volatility (person-level SD)
    predictor_sd = sd(predictor, na.rm = TRUE)
  ) |>
  ungroup() |>
  # Standardize
  mutate(
    predictor_mean_z = scale(predictor_mean)[, 1],
    predictor_dev_z = scale(predictor_dev)[, 1]
  )

# Model with both components
model <- brm(
  outcome ~ predictor_mean_z + predictor_dev_z + (1 | participant_id),
  data = model_data,
  family = bernoulli()
)

Lagged Predictors for Temporal Precedence

# Create lagged predictors within person
model_data <- data |>
  group_by(participant_id) |>
  arrange(time) |>
  mutate(
    # Lagged values (from previous timepoint)
    predictor_lag = lag(predictor, order_by = time),
    predictor_dev_lag = lag(predictor_dev, order_by = time)
  ) |>
  ungroup()

# Test if t-1 predicts outcome at t (establishes temporal precedence)
model_lagged <- brm(
  outcome ~ predictor_dev_lag_z + predictor_mean_z + (1 | participant_id),
  ...
)

Extracting and Interpreting Results

Extract Posterior Samples

posterior <- as_draws_df(model)

# Access specific parameter
samples <- posterior$b_predictor_z

# Summary statistics
tibble(
  estimate = median(samples),
  lower_95 = quantile(samples, 0.025),
  upper_95 = quantile(samples, 0.975),
  lower_80 = quantile(samples, 0.10),
  upper_80 = quantile(samples, 0.90),
  prob_negative = mean(samples < 0),
  prob_positive = mean(samples > 0)
)

Odds Ratios (for logistic models)

# Convert log-odds to odds ratios
effects_df <- effects_df |>
  mutate(
    OR = exp(estimate),
    OR_lower = exp(lower_95),
    OR_upper = exp(upper_95)
  )

Posterior Probability of Direction

# P(effect is protective)
prob_protective <- mean(posterior$b_predictor < 0)

# P(effect is harmful)
prob_harmful <- mean(posterior$b_predictor > 0)

# P(|effect| > some threshold)
prob_meaningful <- mean(abs(posterior$b_predictor) > 0.1)

Compare Effect Magnitudes

# Test if within-person effect is larger than b