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zero_inflated_cumulative.R
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library(brms)
library(cmdstanr)
library(posterior)
library(magrittr)
library(tidyverse)
library(here)
source("helper_functions_from_brms.R")
# needed functions fro custom family
stan_funs <- "
real zero_inflated_cumulative_lpmf(int y, real mu, real zi, vector c, int vint1) {
if (y == vint1) {
return log_sum_exp(bernoulli_lpmf(1 | zi),
bernoulli_lpmf(0 | zi) +
ordered_logistic_lpmf(y | logit(mu), c));
} else {
return bernoulli_lpmf(0 | zi) +
ordered_logistic_lpmf(y | logit(mu), c);
}
}
"
zero_inflated_cumulative <-
# Create a custom family that is logit if y = DK, cumulative if not
custom_family("zero_inflated_cumulative",
dpars = c("mu", "zi"),
links = c("logit", "logit"),
specials = "ordinal",
type = "int",
vars = "vint1[n]",
threshold = "flexible")
log_lik_zero_inflated_cumulative <- function(i, prep) {
mu <- logit(get_dpar(prep, "mu", i = i))
theta <- get_dpar(prep, "zi", i = i)
thres <- subset_thres(prep, i)
nthres <- NCOL(thres)
eta <- thres - mu
y <- prep$data$Y[i]
zi <- prep$data$vint1[i]
if (y == 1L & y == zi) {
out <- log_cdf(eta[, 1L], prep$family$link) +
dbinom(1, size = 1, prob = theta, log = TRUE)
} else if (y == 1L) {
out <- log_cdf(eta[, 1L], prep$family$link) +
dbinom(0, size = 1, prob = theta, log = TRUE)
} else if (y == nthres + 1L & y == zi) {
out <- log_ccdf(eta[, y - 1L], prep$family$link) +
dbinom(1, size = 1, prob = theta, log = TRUE)
} else if (y == nthres + 1L) {
out <- log_ccdf(eta[, y - 1L], prep$family$link) +
dbinom(0, size = 1, prob = theta, log = TRUE)
} else if (y == zi) {
out <- log_diff_exp(
log_cdf(eta[, y], prep$family$link),
log_cdf(eta[, y - 1L], prep$family$link)
) + dbinom(1, size = 1, prob = theta, log = TRUE)
} else {
out <- log_diff_exp(
log_cdf(eta[, y], prep$family$link),
log_cdf(eta[, y - 1L], prep$family$link)
) + dbinom(0, size = 1, prob = theta, log = TRUE)
}
log_lik_weight(out, i = i, prep = prep)
}
# Gotta work on this
posterior_predict_zero_inflated_cumulative <- function(i, prep, ...) {
mu <- brms::get_dpar(prep, "mu", i = i)
theta <- brms::get_dpar(prep, "zi", i = i)
thres <- subset_thres(prep)
nthres <- NCOL(thres)
ndraws <- prep$ndraws
ZI <- prep$data$vint1
p <- pordinal(
seq_len(nthres + 1),
eta = logit(mu),
disc = 1,
thres = thres,
family = "cumulative",
link = "logit"
)
draws <- first_greater(p, target = runif(prep$ndraws, min = 0, max = 1))
theta_draws <- runif(ndraws, 0, 1)
draws[theta_draws < theta] <- ZI[1]
return(draws)
}
#and gotta work on this
posterior_epred_zero_inflated_cumulative <- function(prep) {
#dens <- get(paste0("d", "cumulative"), mode = "function")
# the linear scale has one column less than the response scale
adjust <- ifelse(prep$family$link == "identity", 0, 1)
#ncat_max <- max(prep$data$nthres) + adjust
ncat_max <- NCOL(prep$thres$thres) + adjust
#nact_min <- min(prep$data$nthres) + adjust
#init_mat <- matrix(ifelse(prep$family$link == "identity", NA, 0),
# nrow = prep$ndraws,
# ncol = ncat_max - nact_min)
args <- list(link = prep$family$link)
out <- vector("list", prep$nobs)
ZI <- prep$data$vint1[1]
#for (i in seq_along(out)) {
for (i in seq_along(out)) {
args_i <- args
args_i$eta <- logit(slice_col(get_dpar(prep, "mu", i)))
#args_i$disc <- slice_col(get_dpar(prep, "disc", i))
args_i$disc <- 1
args_i$thres <- subset_thres(prep, i)
ncat_i <- NCOL(args_i$thres) + adjust
args_i$x <- seq_len(ncat_i)
out[[i]] <- do_call(dcumulative, args_i)
zi <- get_dpar(prep, "zi", i)
out[[i]] <- out[[i]] * (1 - zi)
out[[i]][,ZI] <- out[[i]][,ZI] + zi
# this section not needed right now because we cannot use thresh
# But can leave as is because
#if (ncat_i < ncat_max) {
# sel <- seq_len(ncat_max - ncat_i)
# out[[i]] <- cbind(out[[i]], init_mat[, sel])
#}
}
out <- abind(out, along = 3)
out <- aperm(out, perm = c(1, 3, 2))
dimnames(out)[[3]] <- seq_len(ncat_max)
return(out)
}
#### Simulate some data for testing ####
N <- 10000
N_zi <- 1000
P <- 5
cutpoints <- c(1, -1)
y_zi <- rep(0, N)
set.seed(143140914)
X <- matrix(runif(N * P), N, P)
betas <- c(-.15, -.5, 3, .5, -1)
gammas <- c(3, -2, -2, -1, -.5)
p2 <- plogis(cutpoints[1] + X %*% betas)
p3 <- plogis(cutpoints[2] + X %*% betas)
p1 <- 1 - p2
p2 <- p2 - p3
for(i in 1:N){
y_zi[i] <- sample(1:3,
size = 1,
prob = c(p1[i], p2[i], p3[i]))
}
# Simulate non-response bias
p <- plogis(X %*% gammas)
dk <- rbinom(N, 1, p)
y_zi[dk == 1] = 2
df_zi <- data.frame(y = y_zi, X)
out_sim_zi <- brm(bf(y | vint(2) ~ X1 + X2 + X3 + X4 + X5,
zi ~ 0 + X1 + X2 + X3 + X4 + X5),
prior = c(prior(normal(0, 2), class = b)),
data = df_zi,
family = zero_inflated_cumulative,
stan_funs = stan_funs,
cores = 4,
chains = 4,
iter = 2000,
warmup = 1000,
backend = "cmdstanr")
summary(out_sim_zi)
pp_check(out_sim_zi, type = "bars")
# test with real data
# with this data it doesn't return the proper values. I am not sure why.
merkel <- read.csv("https://raw.githubusercontent.com/octmedina/zi-ordinal/main/merkel_data.csv")
merkel$confid_merkel[merkel$confid_merkel == 0] <- 3
out_merkel_zi <- brm(bf(confid_merkel | vint(3) ~ edu + race + income + party,
#disc ~ 1 + edu,
zi ~ 1 + edu + race + income + party),
data = merkel,
family = zero_inflated_cumulative,
stan_funs = stan_funs,
prior = c(prior(normal(0, 2), class = b),
prior(normal(0, 2), class = Intercept, dpar = zi)),
cores = 4,
chains = 4,
iter = 3000,
warmup = 2000,
backend = "cmdstanr",
control = list(adapt_delta = 0.99))
loo(out_merkel_zi)
pp_check(out_merkel_zi, type = "bars", ndraws = 50)
summary(out_merkel_zi)