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families.R
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families.R
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#' Supported mvgam families
#' @importFrom stats make.link dgamma pgamma rgamma qnorm plnorm runif pbeta dlnorm dpois
#' @importFrom stats pnorm ppois plogis gaussian poisson Gamma dnbinom rnbinom dnorm dbeta
#' @importFrom stats binomial rbinom pbinom dbinom qbinom qlogis
#' @importFrom brms lognormal student bernoulli rstudent_t qstudent_t dstudent_t pstudent_t dbeta_binomial rbeta_binomial pbeta_binomial
#' @param link a specification for the family link function. At present these cannot
#' be changed
#' @details \code{mvgam} currently supports the following standard observation families:
#'\itemize{
#' \item \code{\link[stats]{gaussian}} with identity link, for real-valued data
#' \item \code{\link[stats]{poisson}} with log-link, for count data
#' \item \code{\link[stats]{Gamma}} with log-link, for non-negative real-valued data
#' \item \code{\link[stats]{binomial}} with logit-link, for count data when the number
#' of trials is known (and must be supplied)
#' }
#'
#'In addition, the following extended families from the \code{mgcv} and \code{brms} packages are supported:
#'\itemize{
#' \item \code{\link[mgcv]{betar}} with logit-link, for proportional data on `(0,1)`
#' \item \code{\link[mgcv]{nb}} with log-link, for count data
#' \item \code{\link[brms]{lognormal}} with identity-link, for non-negative real-valued data
#' \item \code{\link[brms]{bernoulli}} with logit-link, for binary data
#' }
#'
#'Finally, \code{mvgam} supports the three extended families described here:
#'\itemize{
#' \item \code{tweedie} with log-link, for count data (power parameter `p` fixed at `1.5`)
#' \item `student_t()` (or \code{\link[brms]{student}}) with identity-link, for real-valued data
#' \item \code{nmix} for count data with imperfect detection modeled via a
#' State-Space N-Mixture model. The latent states are Poisson (with log link), capturing the 'true' latent
#' abundance, while the observation process is Binomial to account for imperfect detection. The
#' observation \code{formula} in these models is used to set up a linear predictor for the detection
#' probability (with logit link). See the example below for a more detailed worked explanation
#' of the `nmix()` family
#' }
#' Only `poisson()`, `nb()`, and `tweedie()` are available if
#' using `JAGS`. All families, apart from `tweedie()`, are supported if
#' using `Stan`.
#' @name mvgam_families
#' @return Objects of class `family`
#' @details Note that currently it is not possible to change the default link
#' functions in `mvgam`, so any call to change these will be silently ignored
#' @author Nicholas J Clark
#'
NULL
#' @rdname mvgam_families
#' @export
tweedie = function(link = 'log'){
linktemp <- make.link('log')
structure(list(family = "tweedie", link = 'log', linkfun = linktemp$linkfun,
linkinv = linktemp$linkinv, mu.eta = linktemp$mu.eta,
valideta = linktemp$valideta),
class = c("extended.family", "family"))
}
#' @rdname mvgam_families
#' @export
student_t = function(link = 'identity'){
linktemp <- make.link('identity')
structure(list(family = "student", link = 'identity', linkfun = linktemp$linkfun,
linkinv = linktemp$linkinv, mu.eta = linktemp$mu.eta,
valideta = linktemp$valideta),
class = c("extended.family", "family"))
}
#' @rdname mvgam_families
#' @examples
#' \dontrun{
#' # Example showing how to set up N-mixture models
#' set.seed(999)
#'# Simulate observations for species 1, which shows a declining trend and 0.7 detection probability
#'data.frame(site = 1,
#' # five replicates per year; six years
#' replicate = rep(1:5, 6),
#' time = sort(rep(1:6, 5)),
#' species = 'sp_1',
#' # true abundance declines nonlinearly
#' truth = c(rep(28, 5),
#' rep(26, 5),
#' rep(23, 5),
#' rep(16, 5),
#' rep(14, 5),
#' rep(14, 5)),
#' # observations are taken with detection prob = 0.7
#' obs = c(rbinom(5, 28, 0.7),
#' rbinom(5, 26, 0.7),
#' rbinom(5, 23, 0.7),
#' rbinom(5, 15, 0.7),
#' rbinom(5, 14, 0.7),
#' rbinom(5, 14, 0.7))) %>%
#' # add 'series' information, which is an identifier of site, replicate and species
#' dplyr::mutate(series = paste0('site_', site,
#' '_', species,
#' '_rep_', replicate),
#' time = as.numeric(time),
#' # add a 'cap' variable that defines the maximum latent N to
#' # marginalize over when estimating latent abundance; in other words
#' # how large do we realistically think the true abundance could be?
#' cap = 80) %>%
#' dplyr::select(- replicate) -> testdat
#'
#'# Now add another species that has a different temporal trend and a smaller
#'# detection probability (0.45 for this species)
#'testdat = testdat %>%
#' dplyr::bind_rows(data.frame(site = 1,
#' replicate = rep(1:5, 6),
#' time = sort(rep(1:6, 5)),
#' species = 'sp_2',
#' truth = c(rep(4, 5),
#' rep(7, 5),
#' rep(15, 5),
#' rep(16, 5),
#' rep(19, 5),
#' rep(18, 5)),
#' obs = c(rbinom(5, 4, 0.45),
#' rbinom(5, 7, 0.45),
#' rbinom(5, 15, 0.45),
#' rbinom(5, 16, 0.45),
#' rbinom(5, 19, 0.45),
#' rbinom(5, 18, 0.45))) %>%
#' dplyr::mutate(series = paste0('site_', site,
#' '_', species,
#' '_rep_', replicate),
#' time = as.numeric(time),
#' cap = 50) %>%
#' dplyr::select(-replicate))
#'
#' # series identifiers
#' testdat$species <- factor(testdat$species,
#' levels = unique(testdat$species))
#' testdat$series <- factor(testdat$series,
#' levels = unique(testdat$series))
#'
#' # The trend_map to state how replicates are structured
#' testdat %>%
#' # each unique combination of site*species is a separate process
#'dplyr::mutate(trend = as.numeric(factor(paste0(site, species)))) %>%
#' dplyr::select(trend, series) %>%
#' dplyr::distinct() -> trend_map
#'trend_map
#'
#' # Fit a model
#' mod <- mvgam(
#' # the observation formula sets up linear predictors for
#' # detection probability on the logit scale
#' formula = obs ~ species - 1,
#'
#' # the trend_formula sets up the linear predictors for
#' # the latent abundance processes on the log scale
#' trend_formula = ~ s(time, by = trend, k = 4) + species,
#'
#' # the trend_map takes care of the mapping
#' trend_map = trend_map,
#'
#' # nmix() family and data
#' family = nmix(),
#' data = testdat,
#'
#' # priors can be set in the usual way
#' priors = c(prior(std_normal(), class = b),
#' prior(normal(1, 1.5), class = Intercept_trend)),
#' burnin = 300,
#' samples = 300,
#' chains = 2)
#'
#' # The usual diagnostics
#' summary(mod)
#'
#' # Plotting conditional effects
#' library(ggplot2)
#' plot_predictions(mod, condition = 'species',
#' type = 'detection') +
#' ylab('Pr(detection)') +
#' ylim(c(0, 1)) +
#' theme_classic() +
#' theme(legend.position = 'none')
#'
#' # Example showcasing how cbind() is needed for Binomial observations
#' # Simulate two time series of Binomial trials
#' trials <- sample(c(20:25), 50, replace = TRUE)
#' x <- rnorm(50)
#' detprob1 <- plogis(-0.5 + 0.9*x)
#' detprob2 <- plogis(-0.1 -0.7*x)
#' dat <- rbind(data.frame(y = rbinom(n = 50, size = trials, prob = detprob1),
#' time = 1:50,
#' series = 'series1',
#' x = x,
#' ntrials = trials),
#' data.frame(y = rbinom(n = 50, size = trials, prob = detprob2),
#' time = 1:50,
#' series = 'series2',
#' x = x,
#' ntrials = trials))
#' dat <- dplyr::mutate(dat, series = as.factor(series))
#' dat <- dplyr::arrange(dat, time, series)
#'
#' # Fit a model using the binomial() family; must specify observations
#' # and number of trials in the cbind() wrapper
#' mod <- mvgam(cbind(y, ntrials) ~ series + s(x, by = series),
#' family = binomial(),
#' data = dat)
#' summary(mod)
#' }
#' @export
nmix = function(link = 'log'){
linktemp <- make.link('log')
structure(list(family = "nmix", link = 'log', linkfun = linktemp$linkfun,
linkinv = linktemp$linkinv, mu.eta = linktemp$mu.eta,
valideta = linktemp$valideta),
class = c("extended.family", "family"))
}
#### Non-exported functions for performing family-specific tasks ####
#' Family options in character format
#' @noRd
family_char_choices = function(){
c('negative binomial',
"poisson",
"binomial",
'beta_binomial',
"bernoulli",
"nmix",
"tweedie",
"beta",
"gaussian",
"lognormal",
"student",
"Gamma")
}
# Convert location / precision parameters to shape parameters for the beta distribution
# Original author: Andrew Heiss (https://www.andrewheiss.com/blog/2021/11/08/beta-regression-guide/)
#' @noRd
beta_shapes = function(mu, phi) {
return(list(shape1 = mu * phi,
shape2 = (1 - mu) * phi))
}
# Calculate all possible Poisson log-densities for N-mixture simulation
#' @noRd
pois_dens = function(min_cap, max_cap, lambdas){
# Identify which indices share the exact same lambda AND
# k value so that we only need to run dpois once for each group
data.frame(lambdas,
min_cap,
max_cap) %>%
dplyr::group_by(lambdas) %>%
dplyr::summarise(min_cap = min(min_cap, na.rm = TRUE),
max_cap = max(max_cap, na.rm = TRUE)) -> group_inds
l <- mapply(`:`, group_inds$min_cap, group_inds$max_cap)
data.frame(k = unlist(l),
lambda = group_inds$lambdas[rep(1:nrow(group_inds),
lengths(l))]) %>%
dplyr::mutate(pois_dens = dpois(k,
lambda,
log = TRUE)) -> all_ks
return(all_ks)
}
#' Generic prediction function
#' @importFrom stats predict
#' @param Xp A `mgcv` linear predictor matrix
#' @param family \code{character}. The `family` slot of the model's family argument
#' @param betas Vector of regression coefficients of length `NCOL(Xp)`
#' @param latent_lambdas Optional vector of latent abundance estimates, only used for N-Mixture models
#' @param cap Optional vector of latent abundance maximum capacities, only used for N-Mixture models
#' @param type Either `link`, `expected`, `response`, `variance`,
#' `latent_N` (only applies to N-mixture distributions) or
#' `detection` (only applies to N-mixture distributions)
#' @param family_pars Additional arguments for each specific observation process (i.e.
#' overdispersion parameter if `family == "nb"`)
#' @param density logical. Rather than calculating a prediction, evaluate the log-likelihood.
#' Use this option when particle filtering
#' @param truth Observation to use for evaluating the likelihood (if `density == TRUE`)
#' @details A generic prediction function that will make it easier to add new
#' response distributions in future. Use `type = variance` for computing family-level
#' variance as a function of the mean
#' @noRd
mvgam_predict = function(Xp,
family,
betas,
latent_lambdas,
cap,
min_cap,
type = 'link',
family_pars,
density = FALSE,
truth = NULL){
if(type == 'latent_N' & family != 'nmix'){
stop('"latent_N" type only available for N-mixture models',
call. = FALSE)
}
if(type == 'detection' & family != 'nmix'){
stop('"detection" type only available for N-mixture models',
call. = FALSE)
}
# Poisson-Binomial N-Mixture (requires family parameter
# 'cap' as well as 'latent_lambdas' argument)
if(family == 'nmix'){
insight::check_if_installed("extraDistr",
reason = 'to simulate from N-Mixture distributions')
insight::check_if_installed("wrswoR",
reason = 'to simulate from N-Mixture distributions')
# Calculate detection probability and convert to probability scale
p <- as.vector((matrix(Xp, ncol = NCOL(Xp)) %*%
betas) + attr(Xp, 'model.offset'))
p <- plogis(p)
# Latent mean of State vector
lambdas <- as.vector(latent_lambdas)
# User-specified cap on latent abundance
cap <- as.vector(cap)
if(type == 'detection'){
out <- p
} else if(type == 'link'){
# 'link' predictions are expectations of the latent abundance
out <- lambdas
if(density){
out <- unlist(lapply(seq_along(truth), function(i){
if(is.na(truth[i])){
output <- NA
} else {
ks <- truth[i]:cap[i]
lik_binom <- dbinom(truth[i], size = ks,
prob = p[i], log = TRUE)
lik_poisson <- dpois(x = ks,
lambda = lambdas[i], log = TRUE)
loglik <- lik_binom + lik_poisson
output <- log_sum_exp(loglik)
}
output
}), use.names = FALSE)
}
} else if(type == 'latent_N'){
if(missing(min_cap)) min_cap <- 0
min_cap <- as.vector(min_cap)
if(missing(truth)){
out <- extraDistr::rtpois(n = length(lambdas),
lambda = lambdas,
a = min_cap,
b = cap)
} else {
# If true observed N is supplied, we can calculate the
# most likely latent N given the covariates and the estimated
# detection probability
out <- unlist(lapply(seq_along(truth), function(i){
if(is.na(truth[i])){
output <- NA
} else {
ks <- min_cap[[i]]:cap[[i]]
lik <- exp(dbinom(truth[[i]], size = ks,
prob = p[[i]], log = TRUE) +
dpois(x = ks,
lambda = lambdas[i], log = TRUE))
probs <- lik / sum(lik)
probs[!is.finite(probs)] <- 0
output <- ks[wrswoR::sample_int_ccrank(length(ks),
size = 1L,
prob = probs)]
}
output
}), use.names = FALSE)
}
} else if(type == 'response'){
xpred <- extraDistr::rtpois(n = length(lambdas),
lambda = lambdas,
b = cap)
out <- rbinom(length(lambdas), size = xpred, prob = p)
} else if(type == 'variance'){
xpred <- extraDistr::rtpois(n = length(lambdas),
lambda = lambdas,
b = cap)
# Variance of a Binomial distribution using the
# weights convention from stats::glm()
mu <- p / xpred
out <- mu * (1 - mu)
} else {
# Expectations
xpred <- extraDistr::rtpois(n = length(lambdas),
lambda = lambdas,
b = cap)
out <- xpred * p
}
}
# Gaussian observations (requires family parameter 'sigma_obs')
if(family == 'gaussian'){
if(type %in% c('link', 'expected')){
out <- as.vector((matrix(Xp, ncol = NCOL(Xp)) %*%
betas) + attr(Xp, 'model.offset'))
if(density){
out <- dnorm(truth, mean = out,
sd = as.vector(family_pars$sigma_obs),
log = TRUE)
}
} else if(type == 'variance') {
out <- rep.int(1, NROW(Xp))
} else {
out <- rnorm(n = NROW(Xp),
mean = ((matrix(Xp, ncol = NCOL(Xp)) %*%
betas)) +
attr(Xp, 'model.offset'),
sd = as.vector(family_pars$sigma_obs))
}
}
# LogNormal observations (requires family parameter 'sigma_obs')
if(family == 'lognormal'){
if(type == 'link'){
out <- as.vector((matrix(Xp, ncol = NCOL(Xp)) %*%
betas) + attr(Xp, 'model.offset'))
if(density){
out <- dlnorm(truth, meanlog = out,
sdlog = as.vector(family_pars$sigma_obs),
log = TRUE)
}
} else if(type == 'response'){
out <- rlnorm(n = NROW(Xp),
meanlog = ((matrix(Xp, ncol = NCOL(Xp)) %*%
betas)) +
attr(Xp, 'model.offset'),
sdlog = as.vector(family_pars$sigma_obs))
} else if(type == 'variance'){
mu <- ((matrix(Xp, ncol = NCOL(Xp)) %*%
betas)) + attr(Xp, 'model.offset')
sd <- as.vector(family_pars$sigma_obs)
out <- (exp((sd) ^ 2) - 1) * exp((2 * mu + sd ^ 2))
} else {
mu <- as.vector((matrix(Xp, ncol = NCOL(Xp)) %*%
betas) + attr(Xp, 'model.offset'))
out <- exp(mu + (as.vector(family_pars$sigma_obs)^2 / 2))
}
}
# Student-T observations (requires family parameters 'nu', 'sigma_obs')
if(family == 'student'){
if(type %in% c('link', 'expected')){
out <- as.vector((matrix(Xp, ncol = NCOL(Xp)) %*%
betas) + attr(Xp, 'model.offset'))
if(density){
out <- dstudent_t(truth,
df = as.vector(family_pars$nu),
mu = out,
sigma = as.vector(family_pars$sigma_obs),
log = TRUE)
}
} else if(type == 'variance') {
out <- as.vector(family_pars$sigma_obs)^2 *
as.vector(family_pars$nu) /
pmax(1.01, (as.vector(family_pars$nu) - 2))
} else {
out <- rstudent_t(n = NROW(Xp),
df = family_pars$nu,
mu = ((matrix(Xp, ncol = NCOL(Xp)) %*%
betas)) +
attr(Xp, 'model.offset'),
sigma = as.vector(family_pars$sigma_obs))
}
}
# Poisson observations
if(family == 'poisson'){
if(type == 'link'){
out <- as.vector((matrix(Xp, ncol = NCOL(Xp)) %*%
betas) + attr(Xp, 'model.offset'))
if(density){
out <- dpois(truth, lambda = exp(out),
log = TRUE)
}
} else if(type == 'response'){
out <- rpois(n = NROW(Xp),
lambda = exp(((matrix(Xp, ncol = NCOL(Xp)) %*%
betas)) +
attr(Xp, 'model.offset')))
} else if(type == 'variance'){
out <- exp(as.vector((matrix(Xp, ncol = NCOL(Xp)) %*%
betas) + attr(Xp, 'model.offset')))
} else {
out <- exp(as.vector(((matrix(Xp, ncol = NCOL(Xp)) %*%
betas)) +
attr(Xp, 'model.offset')))
}
}
# Bernoulli observations
if(family == 'bernoulli'){
if(type == 'link'){
out <- as.vector((matrix(Xp, ncol = NCOL(Xp)) %*%
betas) + attr(Xp, 'model.offset'))
if(density){
out <- dbinom(truth,
prob = plogis(out),
size = 1,
log = TRUE)
}
} else if(type == 'response'){
out <- rbinom(n = NROW(Xp),
prob = plogis(((matrix(Xp, ncol = NCOL(Xp)) %*%
betas)) +
attr(Xp, 'model.offset')),
size = 1)
} else if(type == 'variance'){
mu <- plogis(as.vector((matrix(Xp, ncol = NCOL(Xp)) %*%
betas) + attr(Xp, 'model.offset')))
out <- mu * (1 - mu)
} else {
out <- plogis(((matrix(Xp, ncol = NCOL(Xp)) %*%
betas)) +
attr(Xp, 'model.offset'))
}
}
# Binomial observations (requires argument 'trials')
if(family == 'binomial'){
if(type == 'link'){
out <- as.vector((matrix(Xp, ncol = NCOL(Xp)) %*%
betas) + attr(Xp, 'model.offset'))
if(density){
out <- dbinom(truth,
prob = plogis(out),
size = as.vector(family_pars$trials),
log = TRUE)
}
} else if(type == 'response'){
out <- rbinom(n = NROW(Xp),
prob = plogis(((matrix(Xp, ncol = NCOL(Xp)) %*%
betas)) +
attr(Xp, 'model.offset')),
size = as.vector(family_pars$trials))
} else if(type == 'variance'){
mu <- plogis(as.vector((matrix(Xp, ncol = NCOL(Xp)) %*%
betas) + attr(Xp, 'model.offset'))) /
as.vector(family_pars$trials)
out <- mu * (1 - mu)
} else {
out <- plogis(((matrix(Xp, ncol = NCOL(Xp)) %*%
betas)) +
attr(Xp, 'model.offset')) *
as.vector(family_pars$trials)
}
}
# Beta_Binomial observations (requires arguments 'trials' and 'phi')
if(family == 'beta_binomial'){
if(type == 'link'){
out <- as.vector((matrix(Xp, ncol = NCOL(Xp)) %*%
betas) + attr(Xp, 'model.offset'))
if(density){
out <- dbeta_binomial(truth,
mu = plogis(out),
phi = as.vector(family_pars$phi),
size = as.vector(family_pars$trials),
log = TRUE)
}
} else if(type == 'response'){
out <- rbeta_binomial(n = NROW(Xp),
mu = plogis(((matrix(Xp, ncol = NCOL(Xp)) %*%
betas)) +
attr(Xp, 'model.offset')),
phi = as.vector(family_pars$phi),
size = as.vector(family_pars$trials))
} else if(type == 'variance'){
mu <- plogis(as.vector((matrix(Xp, ncol = NCOL(Xp)) %*%
betas) + attr(Xp, 'model.offset')))
# https://en.wikipedia.org/wiki/Beta-binomial_distribution
alpha <- mu * as.vector(family_pars$phi)
beta <- (1 - mu) * as.vector(family_pars$phi)
p <- 1 / (alpha + beta + 1)
n <- as.vector(family_pars$trials)
out <- ((n * p) * (1 - p)) * ((alpha + beta + n) / (alpha + beta + 1))
} else {
out <- plogis(((matrix(Xp, ncol = NCOL(Xp)) %*%
betas)) +
attr(Xp, 'model.offset')) *
as.vector(family_pars$trials)
}
}
# Negative Binomial observations (requires argument 'phi')
if(family == 'negative binomial'){
if(type == 'link'){
out <- as.vector((matrix(Xp, ncol = NCOL(Xp)) %*%
betas) + attr(Xp, 'model.offset'))
if(density){
out <- dnbinom(truth, mu = exp(out),
size = as.vector(family_pars$phi),
log = TRUE)
}
} else if(type == 'response'){
out <- rnbinom(n = NROW(Xp),
mu = exp(((matrix(Xp, ncol = NCOL(Xp)) %*%
betas)) +
attr(Xp, 'model.offset')),
size = as.vector(family_pars$phi))
} else if(type == 'variance'){
mu <- exp(as.vector((matrix(Xp, ncol = NCOL(Xp)) %*%
betas) + attr(Xp, 'model.offset')))
out <- mu + mu^2 / as.vector(family_pars$phi)
} else {
out <- exp(((matrix(Xp, ncol = NCOL(Xp)) %*%
betas)) +
attr(Xp, 'model.offset'))
}
}
# Beta observations (requires argument 'phi')
if(family == 'beta'){
shape_pars <- beta_shapes(mu = plogis(as.vector((matrix(Xp, ncol = NCOL(Xp)) %*%
betas) + attr(Xp, 'model.offset'))),
phi = as.vector(family_pars$phi))
if(type == 'link'){
out <- as.vector((matrix(Xp, ncol = NCOL(Xp)) %*%
betas) + attr(Xp, 'model.offset'))
if(density){
out <- dbeta(truth,
shape1 = shape_pars$shape1,
shape2 = shape_pars$shape2,
log = TRUE)
}
} else if(type == 'response'){
out <- rbeta(n = NROW(Xp),
shape1 = shape_pars$shape1,
shape2 = shape_pars$shape2)
} else if(type == 'variance'){
mu <- plogis(as.vector((matrix(Xp, ncol = NCOL(Xp)) %*%
betas) + attr(Xp, 'model.offset')))
out <- mu * (1 - mu) / (1 + as.vector(family_pars$phi))
} else {
out <- plogis(as.vector((matrix(Xp, ncol = NCOL(Xp)) %*%
betas) + attr(Xp, 'model.offset')))
}
}
# Gamma observations (requires argument 'shape')
if(family == 'Gamma'){
if(type == 'link'){
out <- as.vector((matrix(Xp, ncol = NCOL(Xp)) %*%
betas) + attr(Xp, 'model.offset'))
if(density){
out <- dgamma(truth,
rate = as.vector(family_pars$shape) / exp(out),
shape = as.vector(family_pars$shape),
log = TRUE)
}
} else if(type == 'response'){
out <- rgamma(n = NROW(Xp),
rate = as.vector(family_pars$shape) /
exp(as.vector((matrix(Xp, ncol = NCOL(Xp)) %*%
betas) + attr(Xp, 'model.offset'))),
shape = as.vector(family_pars$shape))
} else if(type == 'variance'){
out <- as.vector((matrix(Xp, ncol = NCOL(Xp)) %*%
betas) + attr(Xp, 'model.offset')) ^ 2
} else {
out <- as.vector(family_pars$shape) /
(as.vector(family_pars$shape) / exp(as.vector((matrix(Xp, ncol = NCOL(Xp)) %*%
betas) + attr(Xp, 'model.offset'))))
}
}
# Tweedie observations (requires argument 'phi')
if(family == 'tweedie'){
if(type == 'link'){
out <- as.vector((matrix(Xp, ncol = NCOL(Xp)) %*%
betas) + attr(Xp, 'model.offset'))
if(density){
out <- mgcv::ldTweedie(y = truth,
mu = exp(out),
# Power parameter is fixed
p = 1.5,
phi = as.vector(family_pars$phi),
all.derivs = F)[,1]
}
} else if(type == 'response'){
out <- rpois(n = NROW(Xp),
lambda = mgcv::rTweedie(
mu = exp(((matrix(Xp, ncol = NCOL(Xp)) %*%
betas)) +
attr(Xp, 'model.offset')),
# Power parameter is fixed
p = 1.5,
phi = as.vector(family_pars$phi)))
} else if(type == 'variance'){
out <- (exp(((matrix(Xp, ncol = NCOL(Xp)) %*%
betas)) +
attr(Xp, 'model.offset')) ^ 1.5) *
as.vector(family_pars$phi)
} else {
out <- exp(((matrix(Xp, ncol = NCOL(Xp)) %*%
betas)) +
attr(Xp, 'model.offset'))
}
}
return(out)
}
#' Set which family to use when calculating default intercept priors
#' in brms
#' @noRd
family_to_brmsfam = function(family){
if(family$family == 'beta'){
brms::Beta()
} else if(family$family == 'Beta regression'){
brms::Beta()
} else if(family$family == 'student'){
brms::student()
} else if(family$family %in% c('tweedie','negative binomial')){
brms::negbinomial()
} else if(family$family == 'Gamma'){
Gamma(link = 'log')
} else {
family
}
}
#' Set which family to use when setting up the gam object
#' Stick to Gaussian where possible to ensure the initial setup
#' doesn't fail
#' @noRd
family_to_mgcvfam = function(family){
if(family$family == 'beta'){
mgcv::betar()
} else if(family$family == 'student'){
gaussian()
} else if(family$family %in% c('gamma', 'Gamma', 'lognormal')){
gaussian()
} else if(family$family == 'tweedie'){
mgcv::Tweedie(p = 1.5, link = 'log')
} else if(family$family == 'nmix'){
poisson()
} else if(family$family %in% c('bernoulli', 'beta_binomial')){
binomial()
} else {
family
}
}
#' Set which family to use when setting up the jagam object
#' @noRd
family_to_jagamfam = function(family){
if(family %in% c('gaussian', 'student')){
gaussian()
} else {
poisson()
}
}
#' Define links used for the mean
#' @noRd
family_links = function(family){
if(family %in% c('gaussian', 'lognormal', 'student')){
out <- 'identity'
}
if(family %in% c('Gamma', 'poisson',
'negative binomial',
'tweedie', 'nmix')){
out <- 'log'
}
if(family %in% c('beta',
'binomial',
'bernoulli',
'beta_binomial')){
out <- 'logit'
}
out
}
#' @noRd
family_invlinks = function(family){
if(family %in% c('gaussian', 'lognormal', 'student')){
out <- function(x) { x }
}
if(family %in% c('Gamma', 'poisson', 'negative binomial', 'tweedie')){
out <- function(x) { exp(x) }
}
if(family %in% c('beta', 'binomial', 'bernoulli',
'beta_binomial')){
out <- function(x) { plogis(x) }
}
out
}
#' Parameters to monitor / extract depending on the observation family
#' @noRd
family_par_names = function(family){
if(family %in% c('gaussian',
'lognormal')){
out <- c('sigma_obs')
}
if(family == 'student'){
out <- c('sigma_obs', 'nu')
}
if(family == 'Gamma'){
out <- c('shape')
}
if(family %in% c('beta',
'beta_binomial',
'negative binomial',
'tweedie')){
out <- c('phi')
}
if(family %in% c('poisson',
'binomial',
'bernoulli')){
out <- c()
}
if(family == 'nmix'){
out <- c('p')
}
return(out)
}
#' Define which parameters to monitor / extract
#' @noRd
extract_family_pars = function(object, newdata = NULL){
# Get names of parameters to extract
pars_to_extract <- family_par_names(object$family)
# Extract into a named list
if(length(pars_to_extract) > 0){
out <- vector(mode = 'list')
for(i in 1:length(pars_to_extract)){
out[[i]] <- mcmc_chains(object$model_output,
params = pars_to_extract[i])
if(NCOL(out[[i]]) == 1){
out[[i]] <- as.vector(out[[i]])
}
}
} else {
out <- list()
}
names(out) <- pars_to_extract
# Return list of extracted posterior parameter samples
out
}
#' Family-specific prior information
#' @noRd
family_prior_info = function(family, use_stan, data){
if(family == 'gaussian'){
prior_df <- data.frame(param_name = c('vector<lower=0>[n_series] sigma_obs;'),
param_length = length(unique(data$series)),
param_info = c('observation error sd'),
prior = c('sigma_obs ~ student_t(3, 0, 2);'),
example_change = c(
paste0(
'sigma_obs ~ normal(',
round(runif(min = -1, max = 1, n = 1), 2),
', ',
round(runif(min = 0.1, max = 1, n = 1), 2),
');'
)))
}
if(family == 'lognormal'){
prior_df <- data.frame(param_name = c('vector<lower=0>[n_series] sigma_obs;'),
param_length = length(unique(data$series)),
param_info = c('log(observation error sd)'),
prior = c('sigma_obs ~ student_t(3, 0, 1);'),
example_change = c(
paste0(
'sigma_obs ~ normal(',
round(runif(min = -1, max = 1, n = 1), 2),
', ',
round(runif(min = 0.1, max = 1, n = 1), 2),
');'
)))
}
if(family == 'student'){
prior_df <- data.frame(param_name = c('vector<lower=0>[n_series] sigma_obs;',
'vector<lower=0>[n_series] nu;'),
param_length = rep(length(unique(data$series)),
2),
param_info = c('observation error sd',
'observation degrees of freedom'),
prior = c('sigma_obs ~ student_t(3, 0, 2);',
'nu ~ gamma(2, 0.1);'),
example_change = c(
paste0(
'sigma_obs ~ normal(',
round(runif(min = -1, max = 1, n = 1), 2),
', ',
round(runif(min = 0.1, max = 1, n = 1), 2),
');'
),
paste0(
'nu ~ normal(',
round(runif(min = -1, max = 1, n = 1), 2),
', ',
round(runif(min = 0.1, max = 1, n = 1), 2),
');'
)))
}
if(family == 'beta'){
prior_df <- data.frame(param_name = c('vector<lower=0>[n_series] phi;'),
param_length = length(unique(data$series)),
param_info = c('Beta precision parameter'),
prior = c('phi ~ gamma(0.01, 0.01);'),
example_change = c(
paste0(
'phi ~ normal(',
round(runif(min = -1, max = 1, n = 1), 2),
', ',
round(runif(min = 0.1, max = 1, n = 1), 2),
');'
)))
}
if(family == 'beta_binomial'){
prior_df <- data.frame(param_name = c('vector<lower=0>[n_series] phi;'),
param_length = length(unique(data$series)),
param_info = c('Beta Binomial precision parameter'),
prior = c('phi ~ gamma(0.01, 0.01);'),
example_change = c(
paste0(
'phi ~ normal(',
round(runif(min = -1, max = 1, n = 1), 2),
', ',
round(runif(min = 0.1, max = 1, n = 1), 2),
');'
)))
}
if(family == 'Gamma'){
prior_df <- data.frame(param_name = c('vector<lower=0>[n_series] shape;'),
param_length = length(unique(data$series)),
param_info = c('Gamma shape parameter'),
prior = c('shape ~ gamma(0.01, 0.01);'),
example_change = c(
paste0(
'shape ~ normal(',
round(runif(min = -1, max = 1, n = 1), 2),
', ',
round(runif(min = 0.1, max = 1, n = 1), 2),
');'
)))
}
if(family == 'negative binomial'){
if(use_stan){
prior_df <- data.frame(param_name = c('vector<lower=0>[n_series] phi_inv;'),
param_length = length(unique(data$series)),
param_info = c('inverse of NB dispsersion'),
prior = c('phi_inv ~ student_t(3, 0, 0.1);'),
example_change = c(
paste0(
'phi_inv ~ normal(',
round(runif(min = -1, max = 1, n = 1), 2),
', ',
round(runif(min = 0.1, max = 1, n = 1), 2),