R/blassoDC.R

In abnormally-distributed/Bayezilla: Bayesian Models With JAGS and Several Utilities for Data Exploration and Model Evaluation.

#' Bayesian Lasso with unpenalized design covariates
#'
#' The Bayesian LASSO of Park & Casella (2008), but with the allowance for a set of covariates that are not penalized. 
#' For example, you may wish to include variables such as age and gender in all models so that 
#' the coefficients for the other variables are penalized while controlling for these. This
#' is a common need in research. \cr
#' \cr
#' Note only the Gaussian likelihood is provided because the Bayesian LASSO requires conditioning
#' on the error variance, which GLM-families do not have. If you need to use the LASSO for a poisson or binomial regression, I suggest taking 
#' a look at \code{\link[Bayezilla]{extLASSODC}}\cr Alternatively, utilizing \code{\link[Bayezilla]{bridgeDC}} with kappa = 1
#' yields the New Bayesian LASSO, which is a re-parameterization of the Bayesian LASSO utilizing a scale mixture of
#' uniform distributions to obtain the Laplacian priors (Mallick & Yi, 2014).  \cr
#' 
#' \cr
#' Model Specification:
#' \cr
#' \if{html}{\figure{blassoDC.png}{}}
#' \if{latex}{\figure{blassoDC.png}{}}
#'
#' @param formula the model formula.
#' @param design.formula formula for the design covariates.
#' @param data a data frame.
#' @param log_lik Should the log likelihood be monitored? The default is FALSE.
#' @param iter How many post-warmup samples? Defaults to 10000.
#' @param warmup How many warmup samples? Defaults to 1000.
#' @param adapt How many adaptation steps? Defaults to 2000.
#' @param chains How many chains? Defaults to 4.
#' @param thin Thinning interval. Defaults to 1.
#' @param method Defaults to "parallel". For an alternative parallel option, choose "rjparallel" or.
#' Otherwise, "rjags" (single core run).
#' @param cl Use parallel::makeCluster(# clusters) to specify clusters for the parallel methods. 
#' Defaults to two cores.
#' @param ... Other arguments to run.jags.
#'
#' @references Park, T., & Casella, G. (2008). The Bayesian Lasso. Journal of the American Statistical Association, 
#' 103(482), 681-686. Retrieved from http://www.jstor.org/stable/27640090 \cr
#' \cr
#' Mallick, H., & Yi, N. (2014). A New Bayesian Lasso. Statistics and its interface, 7(4), 571–582. doi:10.4310/SII.2014.v7.n4.a12 \cr
#' 
#' @return
#' a runjags object
#' @export
#' 
#'
#' @examples
#' blassoDC()
blassoDC = function(formula, design.formula, data, log_lik = FALSE, iter=10000, warmup=1000, adapt=2000, chains=4, thin=1, method = "parallel", cl = makeCluster(2), ...){
  
  X = model.matrix(formula, data)[,-1]
  y = model.frame(formula, data)[,1]
  FX <- as.matrix(model.matrix(design.formula, data)[, -1])
  
  resids = y - as.vector(lmSolve(formula , data) %*% t(model.matrix(formula, data)))
  tau = prec(resids)
  
  if (family == "gaussian"){
    
  jags_blasso = "model{
  tau ~ dgamma(0.01, 0.01)
  sigma2 <- 1/tau
  lambda ~ dgamma(0.50 , 0.20)
  
  for (p in 1:P){
    eta[p] ~ dexp(lambda^2 / 2)
    omega[p] <- 1 / (sigma2 * eta[p])
    beta[p] ~ dnorm(0, omega[p])
  }
  
  for (f in 1:FP){
    design_beta[f] ~ dnorm(0, 1e-200)
  }
  
  Intercept ~ dnorm(0, 1e-10)
  
  for (i in 1:N){
    mu[i] <- Intercept + sum(beta[1:P] * X[i,1:P]) + sum(design_beta[1:FP] * FX[i,1:FP]) 
    y[i] ~ dnorm(mu[i], tau) 
    log_lik[i] <- logdensity.norm(y[i], mu[i], tau)
    ySim[i] ~ dnorm(mu[i], tau)
  }
  
  sigma <- sqrt(sigma2)
  Deviance <- -2 * sum(log_lik[1:N])
}"
  
  P <- ncol(X)
  FP <- ncol(FX)
  write_lines(jags_blasso, "jags_blasso.txt")
  jagsdata <- list(X = X, y = y, N = length(y), P = ncol(X), FP = FP, FX = FX)
  monitor <- c("Intercept", "beta", "design_beta", "sigma", "lambda", "Deviance", "eta", "ySim", "log_lik")
  if (log_lik == FALSE){
    monitor = monitor[-(length(monitor))]
  }
  inits <- lapply(1:chains, function(z) list("Intercept" = lmSolve(design.formula, data)[1], 
                                             "beta" = lmSolve(formula, data)[-1], 
                                             "design_beta" =  lmSolve(design.formula, data)[-1], 
                                             "eta" = rep(1, P), 
                                             "tau" = tau,
                                             "lambda" = sample(2:10, size = 1), 
                                             "ySim" = sample(y, length(y)),
                                             .RNG.name= "lecuyer::RngStream", 
                                             .RNG.seed= sample(1:10000, 1)))
  
  out = run.jags(model = "jags_blasso.txt", modules = c("bugs on", "glm on", "dic off"), monitor = monitor, data = jagsdata, inits = inits, burnin = warmup, sample = iter, thin = thin, adapt = adapt, method = method, cl = cl, summarise = FALSE, ...)
  file.remove("jags_blasso.txt")
  if (!is.null(cl)) {
    parallel::stopCluster(cl = cl)
  }
  return(out)
}


if (family == "binomial"){
  
  jags_blasso = "model{
    
  lambda ~ dgamma(0.50 , 0.20)
  
  for (i in 1:P){
    u[i] ~ dgamma( 2  , lambda )
    beta[i] ~ dunif(-1 * (sigma * u[i]), sigma * u[i])
  }
  
  Intercept ~ dnorm(0, 1e-10)
  
    
  for (f in 1:FP){
    design_beta[f] ~ dnorm(0, 1e-200)
  }
  
  
  for (i in 1:N){
      logit(psi[i]) <- Intercept + sum(beta[1:P] * X[i,1:P]) + sum(design_beta[1:FP] * FX[i,1:FP]) 
      y[i] ~ dbern(psi[i])
      log_lik[i] <- logdensity.bern(y[i], psi[i])
      ySim[i] ~ dbern(psi[i])
    }
  
  Deviance <- -2 * sum(log_lik[1:N])
}"
  
  FP <- ncol(FX)
  P <- ncol(X)
  write_lines(jags_blasso, "jags_blasso.txt")
  jagsdata <- list(X = X, y = y, N = length(y), P = ncol(X), sigma = sqrt(pow(mean(y), -1) * pow(1 - mean(y), -1)), FP = FP, FX = FX)
  monitor <- c("Intercept", "beta", "lambda", "Deviance", "ySim", "log_lik")
  if (log_lik == FALSE){
    monitor = monitor[-(length(monitor))]
  }
  inits <- lapply(1:chains, function(z) list("Intercept" = as.vector(coef(glmnet::glmnet(x = X, y = y, family = "binomial", lambda = 0.025, alpha = 0, standardize = FALSE))[1,1]), 
                                             "beta" = rep(0, P), 
                                             "design_beta" = as.vector(coef(glmnet::glmnet(x = FX, y = y, family = "binomial", lambda = 0, alpha = 0, standardize = FALSE))[-1,1]),
                                             "u" = rgamma(P, 2, 1), 
                                             "lambda" = sample(2:10, size = 1), 
                                             "ySim" = sample(y, length(y)),
                                             .RNG.name= "lecuyer::RngStream", 
                                             .RNG.seed= sample(1:10000, 1)))
  
  out = run.jags(model = "jags_blasso.txt", modules = c("bugs on", "glm on", "dic off"), monitor = monitor, data = jagsdata, inits = inits, burnin = warmup, sample = iter, thin = thin, adapt = adapt, method = method, cl = cl, summarise = FALSE, ...)
  file.remove("jags_blasso.txt")
  if (!is.null(cl)) {
    parallel::stopCluster(cl = cl)
  }
  return(out)
}


if (family == "poisson"){
  
  jags_blasso = "model{
    
  lambda ~ dgamma(0.50 , 0.20)
  
  for (i in 1:P){
    u[i] ~ dgamma( 2 , lambda )
    beta[i] ~ dunif(-1 * (sigma * u[i]), sigma * u[i])
  }
  
  Intercept ~ dnorm(0, 1e-10)
  
    
  for (f in 1:FP){
    design_beta[f] ~ dnorm(0, 1e-200)
  }
  
  for (i in 1:N){
    log(psi[i]) <- Intercept + sum(beta[1:P] * X[i,1:P]) + sum(design_beta[1:FP] * FX[i,1:FP]) 
    y[i] ~ dpois(psi[i])
    log_lik[i] <- logdensity.pois(y[i], psi[i])
    ySim[i] ~ dpois(psi[i])
}
              
  Deviance <- -2 * sum(log_lik[1:N])
}"
  
FP <- ncol(FX)
P <- ncol(X)
write_lines(jags_blasso, "jags_blasso.txt")
jagsdata <- list(X = X, y = y, N = length(y), P = ncol(X), sigma = sqrt(pow(mean(y) , -1)), FP = FP, FX = FX)
monitor <- c("Intercept", "beta", "lambda", "Deviance", "ySim", "log_lik")

if (log_lik == FALSE){
  monitor = monitor[-(length(monitor))]
}

inits <- lapply(1:chains, function(z) list("Intercept" = as.vector(coef(glmnet::glmnet(x = X, y = y, family = "poisson", lambda = 0.025, alpha = 0, standardize = FALSE))[1,1]),
                                           "design_beta" = as.vector(coef(glmnet::glmnet(x = FX, y = y, family = "poisson", lambda = 0, alpha = 0, standardize = FALSE))[-1,1]),
                                           "beta" = rep(0, P), 
                                           "u" = rgamma(P, 2, 1), 
                                           "lambda" = sample(2:10, size = 1), 
                                           "ySim" = sample(y, length(y)),
                                           .RNG.name= "lecuyer::RngStream", 
                                           .RNG.seed= sample(1:10000, 1)))

out = run.jags(model = "jags_blasso.txt", modules = c("bugs on", "glm on", "dic off"), monitor = monitor, data = jagsdata, inits = inits, burnin = warmup, sample = iter, thin = thin, adapt = adapt, method = method, cl = cl, summarise = FALSE, ...)
file.remove("jags_blasso.txt")
if (!is.null(cl)) {
  parallel::stopCluster(cl = cl)
}
return(out)
}

}