R/zsSpikeDC.R

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

#' Zellner-Siow g-prior Stochasitc Search Variable Selection with design covariates
#'
#' @description
#' The Zellner-Siow cauchy g-prior utilizes the inverse crossproduct to determine the proper scale of the coefficient priors 
#' by treating the inverse crossproduct of the model matrix as a covariance matrix for a multivariate normal prior distribution 
#' for the coefficients, which is scaled by the parameter "g". The logic is that variables which carry the most information will
#' consequently have a more dispersed prior, while variables that carry less information will have priors more concentrated about zero. 
#' While the joint prior is multivariate normal, the implied independent marginal priors are Cauchy distributions with 
#' squared-scale equal to g*sigma2. The approach here is to let g be a random variable estimated as part of the model, rather than
#' fixed values of g=N. This avoids several problems associated with fixed-g priors. For more information, see Liang et al. (2008). \cr
#' \cr
#' In addition, this function allows for a set of covariates that are held constant across all models.  
#' For example, you may wish to keep variables such as age and gender constant in order to control for them,
#' so that the selected variables are chosen in light of the effects of age and gender on the outcome variable. \cr
#' \cr
#' The probability that a variable has no effect is 1 - mean(delta_i), where delta_i is an indicator variable that takes on values of 1 for
#' inclusion and 0 for exclusion. Averaging the number of 1s over the MCMC iterations gives the posterior inclusion probability (pip), hence, 
#' 1-pip gives the posterior exclusion probability. The overall rate of inclusion for all variables is controlled by the hyperparameter 
#' "phi". Phi is given a beta(1,1) prior which gives uniform probability to the inclusion rate. \cr
#' \cr
#' The posterior means of the coefficients give the Bayesian Model Averaged estimates, which are the expected values of each 
#' parameter averaged over all sampled models (Hoeting et al., 1999). \cr
#' \cr
#' The model specification is given below. Note that the model formulae have been adjusted to reflect the fact that JAGS
#' parameterizes the normal and multivariate normal distributions by their precision, rater than (co)variance. For generalized
#' linear models plug-in pseudovariances are used.
#' \cr
#' \cr
#' Model Specification:
#' \cr
#' \if{html}{\figure{zsSpikeDC.png}{}}
#' \if{latex}{\figure{zsSpikeDC.png}{}}
#' \cr
#' \cr
#' Plugin Pseudo-Variances: \cr
#' \if{html}{\figure{pseudovar.png}{}}
#' \if{latex}{\figure{pseudovar.png}{}}
#' 
#' 
#' @references 
#' Zellner, A. & Siow S. (1980). Posterior odds ratio for selected regression hypotheses. In Bayesian statistics. Proc. 1st int. meeting (eds J. M. Bernardo, M. H. DeGroot, D. V. Lindley & A. F. M. Smith), 585–603. University Press, Valencia. \cr 
#' \cr
#' Zellner, A. (1986) On assessing prior distributions and Bayesian regression analysis with g-prior distributions. In P. K. Goel and A. Zellner, editors, Bayesian Inference and Decision Techniques: Essays in Honor of Bruno de Finetti, 233–243.  \cr
#' \cr
#' Kuo, L., & Mallick, B. (1998). Variable Selection for Regression Models. Sankhyā: The Indian Journal of Statistics, Series B, 60(1), 65-81. \cr
#' \cr
#' Hoeting, J. , Madigan, D., Raftery, A. & Volinsky, C. (1999). Bayesian model averaging: a tutorial. Statistical Science 14 382–417. \cr
#'
#' @param formula the model formula
#' @param design.formula formula for the design covariates.
#' @param data a data frame
#' @param family one of "gaussian", "binomial", or "poisson".
#' @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 "rjparallel". For an alternative parallel option, choose "parallel". 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.
#'
#' @return
#' A run.jags object.
#' @export
#'
#' @examples
#' zsSpikeDC()
#' 
zsSpikeDC = function(formula, design.formula, data, family = "gaussian",  log_lik = FALSE, 
                    iter = 10000, warmup=1000, adapt = 5000, chains=4, thin=1, method = "rjparallel", cl = makeCluster(2), ...)
{
  
data = as.data.frame(data)
y <- as.numeric(model.frame(formula, data)[, 1])
X <- as.matrix(model.matrix(formula, data)[,-1])
prior_cov = XtXinv(X)
FX <- as.matrix(model.matrix(design.formula, data)[, -1])
FP <- ncol(FX)

if (family == "gaussian"){
  
  jags_zs = "model{
              
              phi ~ dbeta(1, 1)
              tau ~ dscaled.gamma(.01, .01)
              g_inv ~ dgamma(.5, N * .5)
              g <- 1 / g_inv
              sigma <- sqrt(1/tau)
              
              for (j in 1:P){
                for (k in 1:P){
                  cov[j,k] = g * pow(sigma, 2) * prior_cov[j,k]
                }
              }
              
              omega <- inverse(cov) 
              theta[1:P] ~ dmnorm(rep(0,P), omega[1:P,1:P])
              for (i in 1:P){
                delta[i] ~ dbern(phi)
                beta[i] <- delta[i] * theta[i]
              }
              
              
              # Design Variable Coefficients
              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)
              }
              Deviance <- -2 * sum(log_lik[1:N])
              BIC <- (log(N) * (sum(delta[1:P])+FP)) + Deviance
          }"
  
  P = ncol(X)
  write_lines(jags_zs, "jags_zs.txt")
  jagsdata = list(X = X, y = y,  N = length(y), P = ncol(X), prior_cov = prior_cov, FP = FP, FX = FX)
  monitor = c("Intercept", "beta", "sigma", "g", "phi", "BIC" , "Deviance", "delta", "ySim" ,"log_lik")
  if (log_lik == FALSE){
    monitor = monitor[-(length(monitor))]
  }
  inits = lapply(1:chains, function(z) list("Intercept"= lmSolve(formula, data)[1], 
                                            "phi" = rbeta(1, 2, 2), 
                                            "delta" = rep(0, P), 
                                            "theta" = lmSolve(formula, data)[-1], 
                                            "tau" = 1, 
                                            "g_inv" = 1/length(y), 
                                            "ySim" = sample(y, length(y)),
                                            "design_beta" = rep(0, FP),
                                            .RNG.name= "lecuyer::RngStream", 
                                            .RNG.seed = sample(1:10000, 1)))
}

if (family == "binomial"){
  
  jags_zs = "model{
    
              phi ~ dbeta(1, 1)
              g_inv ~ dgamma(.5, N * .5)
              g <- 1 / g_inv
              
              for (j in 1:P){
                for (k in 1:P){
                  cov[j,k] = g * sigma2 * prior_cov[j,k]
                }
              }
              
              omega <- inverse(cov) 
              
              Intercept ~ dnorm(0, 1e-10)
              
              theta[1:P] ~ dmnorm(rep(0,P), omega[1:P,1:P])
              for (i in 1:P){
                delta[i] ~ dbern(phi)
                beta[i] <- delta[i] * theta[i]
              }
              
              # Design Variable Coefficients
              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])
             BIC <- (log(N) * (sum(delta[1:P])+FP)) + Deviance
          }"
  
  P = ncol(X)
  write_lines(jags_zs, "jags_zs.txt")
  jagsdata = list(X = X, y = y, N = length(y), P = ncol(X), prior_cov = prior_cov, sigma2 = pow(mean(y), -1) * pow(1 - mean(y), -1), FP = FP, FX = FX)
  monitor = c("Intercept", "beta", "g",  "phi",  "BIC" , "Deviance", "delta", "ySim", "log_lik")
  if (log_lik == FALSE){
    monitor = monitor[-(length(monitor))]
  }
  inits = lapply(1:chains, function(z) list("Intercept" = as.vector(coef(glm(formula, data, family = "binomial")))[1], 
                                            "phi" = rbeta(1, 2, 2), 
                                            "delta" = rep(0, P), 
                                            "theta" = as.vector(coef(glm(formula, data, family = "binomial")))[-1], 
                                            "g_inv" = 1/length(y), 
                                            "ySim" = sample(y, length(y)),
                                            "design_beta" = sample(c(0, 1), replace = TRUE, size = P),
                                            .RNG.name= "lecuyer::RngStream", 
                                            .RNG.seed= sample(1:10000, 1)))
}

if (family == "poisson"){
  
  jags_zs = "model{
    
              phi ~ dbeta(1, 1)

              g_inv ~ dgamma(.5, N * .5)
              g <- 1 / g_inv
              
              for (j in 1:P){
                for (k in 1:P){
                  cov[j,k] = g * sigma2 * prior_cov[j,k]
                }
              }
              
              omega <- inverse(cov) 
              
              Intercept ~ dnorm(0, 1e-10)
              
              theta[1:P] ~ dmnorm(rep(0,P), omega[1:P,1:P])
              
              for (i in 1:P){
                delta[i] ~ dbern(phi)
                beta[i] <- delta[i] * theta[i]
              }
              
              # Design Variable Coefficients
              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])
              BIC <- (log(N) * (sum(delta[1:P])+FP)) + Deviance
          }"
  
  write_lines(jags_zs, "jags_zs.txt")
  P = ncol(X)
  jagsdata = list(X = X, y = y, N = length(y),  P = ncol(X), prior_cov = prior_cov, sigma2 = pow(mean(y) , -1), FP = FP, FX = FX)
  monitor = c("Intercept", "beta", "g",  "phi", "BIC", "Deviance", "delta", "ySim", "log_lik")
  if (log_lik == FALSE){
    monitor = monitor[-(length(monitor))]
  }
  inits = lapply(1:chains, function(z) list("Intercept" = as.vector(coef(glm(formula, data, family = "poisson")))[1], 
                                            "g_inv" = 1/length(y), 
                                            "ySim" = sample(y, length(y)),
                                            .RNG.name= "lecuyer::RngStream", 
                                            .RNG.seed= sample(1:10000, 1),
                                            "phi" = rbeta(1, 2, 2), 
                                            "design_beta" = rep(0, FP),
                                            "delta" = rep(0, P), 
                                            "theta" = as.vector(coef(glm(formula, data, family = "poisson")))[-1]))
}


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