README.md
In josue-rodriguez/SSranef: Mixed-effects Models with Spike-and-Slab Priors
SSranef
SSranef is an R package for random effects selection that corresponds to
the models described in Rodriguez, Williams, and Rast (2021).
Specifically, ss_ranef_alpha() fits a random intercepts model with a
spike-and-slab prior on the random effects and ss_ranef_beta() fits a
model with both random intercepts and random slopes, with a
spike-and-slab prior on the random effects for the slope. The function
ss_ranef_mv() fits a multivariate mixed-effects models for two
outcomes and places a spike-and-slab prior on the random slope for each
outcome.
Installation
This package can be installed with
# install.packages("devtools")
devtools::install_github("josue-rodriguez/SSranef")
Example
Because SSranef uses JAGS as a backend, we must also load the rjags
package.
library(SSranef)
library(rjags)
#> Loading required package: coda
#> Linked to JAGS 4.3.0
#> Loaded modules: basemod,bugs
d <- lme4::sleepstudy
Alpha model
d$y <- c(scale(d$Reaction))
alpha <- ss_ranef_alpha(y = d$y, unit = d$Subject)
#> Compiling model graph
#> Resolving undeclared variables
#> Allocating nodes
#> Graph information:
#> Observed stochastic nodes: 180
#> Unobserved stochastic nodes: 39
#> Total graph size: 486
#>
#> Initializing model
posterior_summary(alpha, ci = 0.90, digits = 2)
#> Linear mixed model fit with SSranef
#> Call: ss_ranef_alpha(y = d$y, unit = d$Subject)
#>
#> Post.mean q05 q95
#> alpha 0.08 -0.08 0.24
#> sigma 0.79 0.72 0.87
#> tau 0.98 0.60 1.51
ranef_summary(alpha, ci = 0.95, digits = 2)
#> Linear mixed model fit with SSranef
#> Call: ss_ranef_alpha(y = d$y, unit = d$Subject)
#>
#> Post.mean q025 q975 PIP BF_10 BF_01
#> theta_308 0.58 0.00 1.14 0.87 6.94 0.14
#> theta_309 -1.43 -1.96 -0.91 1.00 Inf 0.00
#> theta_310 -1.18 -1.70 -0.67 1.00 Inf 0.00
#> theta_330 0.00 -0.28 0.31 0.22 0.28 3.55
#> theta_331 0.03 -0.20 0.44 0.24 0.32 3.15
#> theta_332 0.02 -0.24 0.42 0.24 0.32 3.12
#> theta_333 0.08 -0.11 0.61 0.30 0.42 2.36
#> theta_334 -0.03 -0.47 0.19 0.24 0.31 3.19
#> theta_335 -0.86 -1.39 -0.32 0.99 92.02 0.01
#> theta_337 1.19 0.70 1.69 1.00 Inf 0.00
#> theta_349 -0.27 -0.91 0.00 0.59 1.41 0.71
#> theta_350 0.06 -0.13 0.51 0.28 0.39 2.56
#> theta_351 -0.07 -0.56 0.13 0.30 0.42 2.39
#> theta_352 0.46 0.00 1.07 0.79 3.87 0.26
#> theta_369 0.02 -0.25 0.40 0.23 0.31 3.27
#> theta_370 -0.06 -0.56 0.13 0.27 0.37 2.68
#> theta_371 -0.03 -0.45 0.21 0.24 0.31 3.22
#> theta_372 0.09 -0.12 0.64 0.34 0.51 1.97
caterpillar_plot(alpha)
pip_plot(alpha)
Beta model
beta <- ss_ranef_beta(y = d$y, X = d$Days, unit = d$Subject)
#> Compiling model graph
#> Resolving undeclared variables
#> Allocating nodes
#> Graph information:
#> Observed stochastic nodes: 180
#> Unobserved stochastic nodes: 60
#> Total graph size: 1316
#>
#> Initializing model
posterior_summary(beta, digits = 2)
#> Linear mixed model fit with SSranef
#> Call: ss_ranef_beta(y = d$y, X = d$Days, unit = d$Subject)
#>
#> Post.mean q05 q95
#> alpha -0.84 -1.05 -0.62
#> beta 0.19 0.15 0.22
#> sigma 0.47 0.42 0.51
#> tau1 0.46 0.25 0.69
#> tau2 0.16 0.10 0.27
#> rho 0.18 -0.37 0.86
ranef_summary(beta, digits = 2)
#> Linear mixed model fit with SSranef
#> Call: ss_ranef_beta(y = d$y, X = d$Days, unit = d$Subject)
#>
#> Post.mean q05 q95 PIP BF_10 BF_01
#> theta1_308 0.02 -0.40 0.42 NA NA NA
#> theta1_309 -0.64 -1.09 -0.23 NA NA NA
#> theta1_310 -0.69 -1.19 -0.23 NA NA NA
#> theta1_330 0.30 -0.12 0.79 NA NA NA
#> theta1_331 0.28 -0.08 0.71 NA NA NA
#> theta1_332 0.14 -0.18 0.48 NA NA NA
#> theta1_333 0.28 -0.05 0.63 NA NA NA
#> theta1_334 -0.08 -0.42 0.25 NA NA NA
#> theta1_335 0.02 -0.38 0.43 NA NA NA
#> theta1_337 0.54 0.15 0.97 NA NA NA
#> theta1_349 -0.38 -0.73 -0.05 NA NA NA
#> theta1_350 -0.19 -0.65 0.23 NA NA NA
#> theta1_351 -0.04 -0.40 0.33 NA NA NA
#> theta1_352 0.46 0.03 0.88 NA NA NA
#> theta1_369 0.09 -0.24 0.44 NA NA NA
#> theta1_370 -0.35 -0.84 0.06 NA NA NA
#> theta1_371 -0.02 -0.35 0.33 NA NA NA
#> theta1_372 0.26 -0.08 0.61 NA NA NA
#> theta2_308 0.17 0.09 0.25 1.00 570.43 0.00
#> theta2_309 -0.17 -0.25 -0.08 0.99 73.07 0.01
#> theta2_310 -0.09 -0.19 0.00 0.79 3.67 0.27
#> theta2_330 -0.06 -0.16 0.00 0.64 1.78 0.56
#> theta2_331 -0.03 -0.12 0.00 0.44 0.77 1.30
#> theta2_332 0.00 -0.04 0.04 0.25 0.33 3.06
#> theta2_333 0.00 -0.03 0.03 0.25 0.33 3.07
#> theta2_334 0.01 -0.02 0.07 0.28 0.38 2.62
#> theta2_335 -0.20 -0.28 -0.12 1.00 Inf 0.00
#> theta2_337 0.17 0.09 0.25 1.00 306.69 0.00
#> theta2_349 0.01 -0.02 0.07 0.26 0.35 2.88
#> theta2_350 0.11 0.00 0.20 0.89 8.05 0.12
#> theta2_351 -0.02 -0.11 0.00 0.43 0.76 1.32
#> theta2_352 0.04 0.00 0.14 0.52 1.08 0.92
#> theta2_369 0.01 -0.01 0.06 0.26 0.35 2.87
#> theta2_370 0.06 0.00 0.17 0.67 2.03 0.49
#> theta2_371 -0.01 -0.07 0.02 0.27 0.36 2.75
#> theta2_372 0.01 -0.01 0.08 0.30 0.42 2.39
caterpillar_plot(beta)
pip_plot(beta)
Multivariate model
mv_data <- gen_mv_data(5, 5)
str(mv_data)
#> 'data.frame': 25 obs. of 4 variables:
#> $ y1: num 0.158 0.661 5.618 4.208 1.802 ...
#> $ y2: num 8.43 1.92 7.65 7.79 8.34 ...
#> $ x : num 1 0 1 1 1 1 0 1 1 1 ...
#> $ id: Factor w/ 5 levels "1","2","3","4",..: 1 1 1 1 1 2 2 2 2 2 ...
mv_model <- ss_ranef_mv(Y = cbind(mv_data$y1, mv_data$y2),
X = mv_data$x,
unit = mv_data$id,
burnin = 100,
iter = 500,
chains = 4)
#> Compiling model graph
#> Resolving undeclared variables
#> Allocating nodes
#> Graph information:
#> Observed stochastic nodes: 25
#> Unobserved stochastic nodes: 23
#> Total graph size: 338
#>
#> Initializing model
posterior_summary(mv_model)
#> Linear mixed model fit with SSranef
#> Call: ss_ranef_mv(Y = cbind(mv_data$y1, mv_data$y2), X = mv_data$x,
#> unit = mv_data$id, burnin = 100, iter = 500, chains = 4)
#>
#> Post.mean q05 q95
#> B_1_1 3.32 1.68 4.91
#> B_1_2 -0.85 -3.32 1.70
#> B_2_1 3.27 2.75 3.80
#> B_2_2 3.09 2.00 4.53
#> rb_1_2 0.14 -0.98 0.99
#> rb_1_3 0.19 -0.97 1.00
#> rb_1_4 -0.13 -0.99 0.99
#> rb_2_3 0.08 -0.98 0.99
#> rb_2_4 0.07 -0.99 0.99
#> rb_3_4 -0.02 -0.99 0.99
#> rw 0.20 -0.16 0.53
#> sigma_1 3.79 2.88 4.95
#> sigma_2 1.06 0.79 1.42
#> Tau_1_1 67.74 0.26 228.48
#> Tau_2_2 12.65 0.37 47.95
#> Tau_3_3 25.13 0.32 69.44
#> Tau_4_4 18.28 2.49 56.27
Priors
Priors can be passed on to either of the ss_ranef functions through a
named list and using JAGS code, e.g.,
# change prior for mean intercept
priors <- list(alpha = "alpha ~ dt(0, 1, 3)",
# for each jth unit, change prior probability of inclusion
gamma = "gamma[j] ~ dbern(0.75)")
fit <- ss_ranef_alpha(y = d$y, unit = d$Subject, priors = priors)
#> Compiling model graph
#> Resolving undeclared variables
#> Allocating nodes
#> Graph information:
#> Observed stochastic nodes: 180
#> Unobserved stochastic nodes: 39
#> Total graph size: 485
#>
#> Initializing model
ranef_summary(fit)
#> Linear mixed model fit with SSranef
#> Call: ss_ranef_alpha(y = d$y, unit = d$Subject, priors = priors)
#>
#> Post.mean q05 q95 PIP BF_10 BF_01
#> theta_308 0.62 0.06 1.06 0.96 24.16 0.04
#> theta_309 -1.37 -1.83 -0.93 1.00 Inf 0.00
#> theta_310 -1.13 -1.57 -0.69 1.00 Inf 0.00
#> theta_330 0.01 -0.31 0.36 0.51 1.03 0.97
#> theta_331 0.07 -0.21 0.49 0.55 1.22 0.82
#> theta_332 0.06 -0.23 0.44 0.53 1.11 0.90
#> theta_333 0.15 -0.11 0.59 0.61 1.57 0.64
#> theta_334 -0.05 -0.45 0.23 0.51 1.04 0.96
#> theta_335 -0.82 -1.25 -0.40 1.00 249.00 0.00
#> theta_337 1.19 0.77 1.62 1.00 Inf 0.00
#> theta_349 -0.34 -0.82 0.00 0.80 4.04 0.25
#> theta_350 0.12 -0.14 0.56 0.57 1.34 0.75
#> theta_351 -0.11 -0.56 0.16 0.57 1.32 0.76
#> theta_352 0.53 0.00 0.99 0.91 10.63 0.09
#> theta_369 0.04 -0.24 0.42 0.50 1.00 1.00
#> theta_370 -0.10 -0.54 0.16 0.55 1.21 0.83
#> theta_371 -0.06 -0.46 0.23 0.52 1.08 0.92
#> theta_372 0.18 -0.10 0.65 0.66 1.90 0.53
Building on top of SSranef models
The code for each model can also be extracted to make more extensive
modifications or build more complex models
jags_model_text <- fit$model_text
cat(jags_model_text)
#> model{
#> for (i in 1:N) {
#> # likelihood
#> y[i] ~ dnorm(alpha_j[unit[i]], precision)
#> }
#> for (j in 1:J) {
#> gamma[j] ~ dbern(0.75)
#> # non-centered parameterization
#> alpha_raw[j] ~ dnorm(0, 1)
#> theta[j] <- tau * alpha_raw[j] * gamma[j]
#> alpha_j[j] <- alpha + theta[j]
#> lambda[j] <- (tau^2 / (tau^2 + sigma^2/n_j[j])) * gamma[j]
#> }
#> alpha ~ dt(0, 1, 3)
#> tau ~ dt(0, 1, 3)T(0, )
#> precision <- pow(sigma, -2)
#> sigma ~ dt(0, 1, 3)T(0, )
#> }
References
Rodriguez, Josue E, Donald R Williams, and Philippe Rast. 2021. “Who Is
and Is Not" Average’"? Random Effects Selection with Spike-and-Slab
Priors.” .
josue-rodriguez/SSranef documentation built on March 23, 2022, 3:27 p.m.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
SSranef
SSranef is an R package for random effects selection that corresponds to
the models described in Rodriguez, Williams, and Rast (2021).
Specifically, ss_ranef_alpha() fits a random intercepts model with a
spike-and-slab prior on the random effects and ss_ranef_beta() fits a
model with both random intercepts and random slopes, with a
spike-and-slab prior on the random effects for the slope. The function
ss_ranef_mv() fits a multivariate mixed-effects models for two
outcomes and places a spike-and-slab prior on the random slope for each
outcome.
Installation
This package can be installed with
# install.packages("devtools")
devtools::install_github("josue-rodriguez/SSranef")
Example
Because SSranef uses JAGS as a backend, we must also load the rjags
package.
library(SSranef)
library(rjags)
#> Loading required package: coda
#> Linked to JAGS 4.3.0
#> Loaded modules: basemod,bugs
d <- lme4::sleepstudy
Alpha model
d$y <- c(scale(d$Reaction))
alpha <- ss_ranef_alpha(y = d$y, unit = d$Subject)
#> Compiling model graph
#> Resolving undeclared variables
#> Allocating nodes
#> Graph information:
#> Observed stochastic nodes: 180
#> Unobserved stochastic nodes: 39
#> Total graph size: 486
#>
#> Initializing model
posterior_summary(alpha, ci = 0.90, digits = 2)
#> Linear mixed model fit with SSranef
#> Call: ss_ranef_alpha(y = d$y, unit = d$Subject)
#>
#> Post.mean q05 q95
#> alpha 0.08 -0.08 0.24
#> sigma 0.79 0.72 0.87
#> tau 0.98 0.60 1.51
ranef_summary(alpha, ci = 0.95, digits = 2)
#> Linear mixed model fit with SSranef
#> Call: ss_ranef_alpha(y = d$y, unit = d$Subject)
#>
#> Post.mean q025 q975 PIP BF_10 BF_01
#> theta_308 0.58 0.00 1.14 0.87 6.94 0.14
#> theta_309 -1.43 -1.96 -0.91 1.00 Inf 0.00
#> theta_310 -1.18 -1.70 -0.67 1.00 Inf 0.00
#> theta_330 0.00 -0.28 0.31 0.22 0.28 3.55
#> theta_331 0.03 -0.20 0.44 0.24 0.32 3.15
#> theta_332 0.02 -0.24 0.42 0.24 0.32 3.12
#> theta_333 0.08 -0.11 0.61 0.30 0.42 2.36
#> theta_334 -0.03 -0.47 0.19 0.24 0.31 3.19
#> theta_335 -0.86 -1.39 -0.32 0.99 92.02 0.01
#> theta_337 1.19 0.70 1.69 1.00 Inf 0.00
#> theta_349 -0.27 -0.91 0.00 0.59 1.41 0.71
#> theta_350 0.06 -0.13 0.51 0.28 0.39 2.56
#> theta_351 -0.07 -0.56 0.13 0.30 0.42 2.39
#> theta_352 0.46 0.00 1.07 0.79 3.87 0.26
#> theta_369 0.02 -0.25 0.40 0.23 0.31 3.27
#> theta_370 -0.06 -0.56 0.13 0.27 0.37 2.68
#> theta_371 -0.03 -0.45 0.21 0.24 0.31 3.22
#> theta_372 0.09 -0.12 0.64 0.34 0.51 1.97
caterpillar_plot(alpha)
pip_plot(alpha)
Beta model
beta <- ss_ranef_beta(y = d$y, X = d$Days, unit = d$Subject)
#> Compiling model graph
#> Resolving undeclared variables
#> Allocating nodes
#> Graph information:
#> Observed stochastic nodes: 180
#> Unobserved stochastic nodes: 60
#> Total graph size: 1316
#>
#> Initializing model
posterior_summary(beta, digits = 2)
#> Linear mixed model fit with SSranef
#> Call: ss_ranef_beta(y = d$y, X = d$Days, unit = d$Subject)
#>
#> Post.mean q05 q95
#> alpha -0.84 -1.05 -0.62
#> beta 0.19 0.15 0.22
#> sigma 0.47 0.42 0.51
#> tau1 0.46 0.25 0.69
#> tau2 0.16 0.10 0.27
#> rho 0.18 -0.37 0.86
ranef_summary(beta, digits = 2)
#> Linear mixed model fit with SSranef
#> Call: ss_ranef_beta(y = d$y, X = d$Days, unit = d$Subject)
#>
#> Post.mean q05 q95 PIP BF_10 BF_01
#> theta1_308 0.02 -0.40 0.42 NA NA NA
#> theta1_309 -0.64 -1.09 -0.23 NA NA NA
#> theta1_310 -0.69 -1.19 -0.23 NA NA NA
#> theta1_330 0.30 -0.12 0.79 NA NA NA
#> theta1_331 0.28 -0.08 0.71 NA NA NA
#> theta1_332 0.14 -0.18 0.48 NA NA NA
#> theta1_333 0.28 -0.05 0.63 NA NA NA
#> theta1_334 -0.08 -0.42 0.25 NA NA NA
#> theta1_335 0.02 -0.38 0.43 NA NA NA
#> theta1_337 0.54 0.15 0.97 NA NA NA
#> theta1_349 -0.38 -0.73 -0.05 NA NA NA
#> theta1_350 -0.19 -0.65 0.23 NA NA NA
#> theta1_351 -0.04 -0.40 0.33 NA NA NA
#> theta1_352 0.46 0.03 0.88 NA NA NA
#> theta1_369 0.09 -0.24 0.44 NA NA NA
#> theta1_370 -0.35 -0.84 0.06 NA NA NA
#> theta1_371 -0.02 -0.35 0.33 NA NA NA
#> theta1_372 0.26 -0.08 0.61 NA NA NA
#> theta2_308 0.17 0.09 0.25 1.00 570.43 0.00
#> theta2_309 -0.17 -0.25 -0.08 0.99 73.07 0.01
#> theta2_310 -0.09 -0.19 0.00 0.79 3.67 0.27
#> theta2_330 -0.06 -0.16 0.00 0.64 1.78 0.56
#> theta2_331 -0.03 -0.12 0.00 0.44 0.77 1.30
#> theta2_332 0.00 -0.04 0.04 0.25 0.33 3.06
#> theta2_333 0.00 -0.03 0.03 0.25 0.33 3.07
#> theta2_334 0.01 -0.02 0.07 0.28 0.38 2.62
#> theta2_335 -0.20 -0.28 -0.12 1.00 Inf 0.00
#> theta2_337 0.17 0.09 0.25 1.00 306.69 0.00
#> theta2_349 0.01 -0.02 0.07 0.26 0.35 2.88
#> theta2_350 0.11 0.00 0.20 0.89 8.05 0.12
#> theta2_351 -0.02 -0.11 0.00 0.43 0.76 1.32
#> theta2_352 0.04 0.00 0.14 0.52 1.08 0.92
#> theta2_369 0.01 -0.01 0.06 0.26 0.35 2.87
#> theta2_370 0.06 0.00 0.17 0.67 2.03 0.49
#> theta2_371 -0.01 -0.07 0.02 0.27 0.36 2.75
#> theta2_372 0.01 -0.01 0.08 0.30 0.42 2.39
caterpillar_plot(beta)
pip_plot(beta)
Multivariate model
mv_data <- gen_mv_data(5, 5)
str(mv_data)
#> 'data.frame': 25 obs. of 4 variables:
#> $ y1: num 0.158 0.661 5.618 4.208 1.802 ...
#> $ y2: num 8.43 1.92 7.65 7.79 8.34 ...
#> $ x : num 1 0 1 1 1 1 0 1 1 1 ...
#> $ id: Factor w/ 5 levels "1","2","3","4",..: 1 1 1 1 1 2 2 2 2 2 ...
mv_model <- ss_ranef_mv(Y = cbind(mv_data$y1, mv_data$y2),
X = mv_data$x,
unit = mv_data$id,
burnin = 100,
iter = 500,
chains = 4)
#> Compiling model graph
#> Resolving undeclared variables
#> Allocating nodes
#> Graph information:
#> Observed stochastic nodes: 25
#> Unobserved stochastic nodes: 23
#> Total graph size: 338
#>
#> Initializing model
posterior_summary(mv_model)
#> Linear mixed model fit with SSranef
#> Call: ss_ranef_mv(Y = cbind(mv_data$y1, mv_data$y2), X = mv_data$x,
#> unit = mv_data$id, burnin = 100, iter = 500, chains = 4)
#>
#> Post.mean q05 q95
#> B_1_1 3.32 1.68 4.91
#> B_1_2 -0.85 -3.32 1.70
#> B_2_1 3.27 2.75 3.80
#> B_2_2 3.09 2.00 4.53
#> rb_1_2 0.14 -0.98 0.99
#> rb_1_3 0.19 -0.97 1.00
#> rb_1_4 -0.13 -0.99 0.99
#> rb_2_3 0.08 -0.98 0.99
#> rb_2_4 0.07 -0.99 0.99
#> rb_3_4 -0.02 -0.99 0.99
#> rw 0.20 -0.16 0.53
#> sigma_1 3.79 2.88 4.95
#> sigma_2 1.06 0.79 1.42
#> Tau_1_1 67.74 0.26 228.48
#> Tau_2_2 12.65 0.37 47.95
#> Tau_3_3 25.13 0.32 69.44
#> Tau_4_4 18.28 2.49 56.27
Priors
Priors can be passed on to either of the ss_ranef functions through a
named list and using JAGS code, e.g.,
# change prior for mean intercept
priors <- list(alpha = "alpha ~ dt(0, 1, 3)",
# for each jth unit, change prior probability of inclusion
gamma = "gamma[j] ~ dbern(0.75)")
fit <- ss_ranef_alpha(y = d$y, unit = d$Subject, priors = priors)
#> Compiling model graph
#> Resolving undeclared variables
#> Allocating nodes
#> Graph information:
#> Observed stochastic nodes: 180
#> Unobserved stochastic nodes: 39
#> Total graph size: 485
#>
#> Initializing model
ranef_summary(fit)
#> Linear mixed model fit with SSranef
#> Call: ss_ranef_alpha(y = d$y, unit = d$Subject, priors = priors)
#>
#> Post.mean q05 q95 PIP BF_10 BF_01
#> theta_308 0.62 0.06 1.06 0.96 24.16 0.04
#> theta_309 -1.37 -1.83 -0.93 1.00 Inf 0.00
#> theta_310 -1.13 -1.57 -0.69 1.00 Inf 0.00
#> theta_330 0.01 -0.31 0.36 0.51 1.03 0.97
#> theta_331 0.07 -0.21 0.49 0.55 1.22 0.82
#> theta_332 0.06 -0.23 0.44 0.53 1.11 0.90
#> theta_333 0.15 -0.11 0.59 0.61 1.57 0.64
#> theta_334 -0.05 -0.45 0.23 0.51 1.04 0.96
#> theta_335 -0.82 -1.25 -0.40 1.00 249.00 0.00
#> theta_337 1.19 0.77 1.62 1.00 Inf 0.00
#> theta_349 -0.34 -0.82 0.00 0.80 4.04 0.25
#> theta_350 0.12 -0.14 0.56 0.57 1.34 0.75
#> theta_351 -0.11 -0.56 0.16 0.57 1.32 0.76
#> theta_352 0.53 0.00 0.99 0.91 10.63 0.09
#> theta_369 0.04 -0.24 0.42 0.50 1.00 1.00
#> theta_370 -0.10 -0.54 0.16 0.55 1.21 0.83
#> theta_371 -0.06 -0.46 0.23 0.52 1.08 0.92
#> theta_372 0.18 -0.10 0.65 0.66 1.90 0.53
Building on top of SSranef models
The code for each model can also be extracted to make more extensive modifications or build more complex models
jags_model_text <- fit$model_text
cat(jags_model_text)
#> model{
#> for (i in 1:N) {
#> # likelihood
#> y[i] ~ dnorm(alpha_j[unit[i]], precision)
#> }
#> for (j in 1:J) {
#> gamma[j] ~ dbern(0.75)
#> # non-centered parameterization
#> alpha_raw[j] ~ dnorm(0, 1)
#> theta[j] <- tau * alpha_raw[j] * gamma[j]
#> alpha_j[j] <- alpha + theta[j]
#> lambda[j] <- (tau^2 / (tau^2 + sigma^2/n_j[j])) * gamma[j]
#> }
#> alpha ~ dt(0, 1, 3)
#> tau ~ dt(0, 1, 3)T(0, )
#> precision <- pow(sigma, -2)
#> sigma ~ dt(0, 1, 3)T(0, )
#> }
References
Rodriguez, Josue E, Donald R Williams, and Philippe Rast. 2021. “Who Is
and Is Not" Average’"? Random Effects Selection with Spike-and-Slab
Priors.” .
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Embedding an R snippet on your website
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.