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bctm_fun.R
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## This function fits Bayesian Conditional Transformation Models.
## Author: Manuel Carlan
bctm <- function(formula, family = c("gaussian", "logistic", "mev"), data, hyperparams=list(a=1, b=0.001), iterations = 2000, start=NULL,
warmup = iterations/2, burnin=iterations/2, cens=NULL, seed = NULL, intercept = TRUE, looic = TRUE,
nuts_settings=list(adapt_delta = 0.8, metric = NULL, step_size = NULL,
adapt_mass = TRUE, max_treedepth=12, init_buffer = 75, term_buffer = 50, window = 25)){
family <- match.arg(family)
f <- switch(as.character(family), `gaussian` = posterior_gauss,
`logistic` = posterior_logit, `mev` = posterior_mev )
ll <- switch(as.character(family), `gaussian` = ll_gauss,
`logistic` = ll_logit, `mev` = ll_mev )
grad <- switch(as.character(family), `gaussian` = gradf_gauss,
`logistic` = gradf_logit, `mev` = gradf_mev )
model <- bctm_setup(formula, data, intercept)
X <- as.matrix(model$X)
Xp <- as.matrix(model$Xp)
XtX <- as.matrix(t(X)%*%X)
p <- ncol(X)
exp_inds <- model$exp_inds
exp_ident <- (1:ncol(X))[c(rep(F, intercept), unlist(exp_inds))]
pen_ident <- model$pen_ident
pen_inds <- model$pen_inds
unpen_ident <- model$unpen_ident
# construct model precision matrix
Ks <- model$Ks
Ks_f <- unlist( model$Ks[pen_inds], recursive = F, use.names =F)
name_groups <-names(pen_ident)
labels <- model$labels
K_inds <- lapply(labels[pen_inds], function(x) which(x == name_groups))
names(Ks_f) <- names(pen_ident)
npen <- length(Ks_f)
ranks <- lapply(Ks_f, rankMatrix)
dpen_ind <- lapply(Ks, function(x) length(x) > 1)
spen_ind <- lapply(Ks, function(x) length(x) == 1)
S <- matrix(0, p - length(unlist(unpen_ident)) , p - length(unlist(unpen_ident)) )
# model ingredients
xx <- list(response = model$y, X = X, Xp = Xp, XtX = XtX, Xpt = t(Xp), K_inds = K_inds, p = p,
npen = length(Ks_f) , pen_ident = model$pen_ident, unpen_ident = model$unpen_ident, m_pen_ident = unlist(unique(pen_ident))-1,
ranks = lapply(Ks_f, rankMatrix), S = S, labels = model$labels, family = family,
exp_ident = exp_ident-1, n_coef = ncol(X), hyperparams = hyperparams, Ks_f = Ks_f)
if(!is.null(cens)){
cind <- as.logical(cens)
X1 <- X[cind,]
X2 <- X[!cind,]
Xp1 <- Xp[cind,]
Xp2 <- Xp[!cind,]
if(family != "logistic") stop("currently, censoring only with logistic reference distribution.")
f <- switch(as.character(family), `gaussian` = posterior_gauss_cens,
`logistic` = posterior_logit_cens, `mev` = posterior_mev_cens )
ll <- switch(as.character(family), `gaussian` = ll_gauss_cens,
`logistic` = ll_logit_cens, `mev` = ll_mev_cens )
grad <- switch(as.character(family), `gaussian` = gradf_gauss_cens,
`logistic` = gradf_logit_cens, `mev` = gradf_mev_cens )
xx$X1 <- X1
xx$X2 <- X2
xx$Xp1 <- Xp1
xx$Xp2 <- Xp2
}
if(is.null(start)) start <- rep(0,p)
# start <- -runif(p)
chain <-NUTS(n_iter = iterations, xx=xx, f = f, gr = grad, ll=ll, start=start, nuts_settings = nuts_settings, seed = seed)
betas <- chain$beta[burnin:iterations,]
colnames(betas) <- colnames(X)
# traplot(betas)
beta <- colMeans(betas)
bt <- beta
bt[exp_ident] <- exp(beta[exp_ident])
bt_samples <- betas
bt_samples[,exp_ident] <- exp(bt_samples[,exp_ident])
beta_tilde <- colMeans(bt_samples)
h <- X%*%beta_tilde
hp <- Xp%*%beta_tilde
distr = switch(family, gaussian = function(h) pnorm(h), logistic = function(h) plogis(h), mev = function(h) bctm_pmev(h))
dens = switch(family, gaussian = function(h, hp) dnorm(h)*hp, logistic = function(h, hp) dlogis(h)*hp, mev = function(h, hp) bctm_dmev(h)*hp)
fit <- data.frame(
h=h,
hp=hp,
distr=distr(h),
dens=dens(h,hp)
)
DIC <- {
Dbar <- -2 * mean(unlist(chain$log_liks[burnin:iterations]), na.rm = T)
Dhat <- -2 * sum(log(dens(h, hp)))
pD <- Dbar - Dhat
DIC <- pD + Dbar
round(c(DIC = DIC, pD = pD, Dbar = Dbar, Dhat = Dhat),3)
}
# log pointwise predicted density
llpd <- sum(log(rowMeans(dens(X%*%t(bt_samples), Xp%*%t(bt_samples)))))
WAIC1 <- {
pwaic1 <- 2*sum(log(rowMeans(dens(X%*%t(bt_samples), Xp%*%t(bt_samples)))) - rowMeans(log(dens(X%*%t(bt_samples), Xp%*%t(bt_samples)))))
WAIC1 <- -2*llpd + 2*pwaic1
round(c(WAIC1 = WAIC1, llpd = llpd, pwaic1 = pwaic1),3)
}
WAIC2 <- {
pwaic2 <- sum(apply(log(dens(X%*%t(bt_samples), Xp%*%t(bt_samples))), 1, var))
WAIC2 <- -2*llpd + 2*pwaic2
round(c(WAIC2 = WAIC2, llpd = llpd, pwaic2 = pwaic2), 3)
}
LOOIC <- ifelse(looic, suppressWarnings(loo::loo(t(log(dens(X%*%t(bt_samples), Xp%*%t(bt_samples)))))), NULL)
object <- list(y = model$y,
X = X,
Xp = Xp,
family = family,
hyper_parameters = xx$hyperparams,
formula = formula,
beta_tilde = beta_tilde,
fit = fit,
samples = chain,
funs = list(dens = dens, distr = distr),
IC = list(DIC = DIC,
WAIC1 = WAIC1,
WAIC2 = WAIC2,
LOOIC = LOOIC),
mcmc = list(iterations = iterations,
burnin = burnin),
model = list(label_inds = unlist(model$label_inds),
eff_inds = model$eff_ident,
exp_inds = exp_inds,
exp_ident = exp_ident,
specials = model$specials),
data = data,
predvars = model$predvar,
posterior_means = list(beta = colMeans(betas))
)
object
}