Nothing
#' Generate fitted values from a estimated GAM
#'
#' @param object a fitted model. Currently only models fitted by [mgcv::gam()]
#' and [mgcv::bam()] are supported.
#' @param data optional data frame of covariate values for which fitted values
#' are to be returned.
#' @param scale character; what scale should the fitted values be returned on?
#' `"linear predictor"` is a synonym for `"link"` if you prefer that
#' terminology.
#' @param ci_level numeric; a value between 0 and 1 indicating the coverage of
#' the credible interval.
#' @param ... arguments passed to [mgcv::predict.gam()]. Note that `type`,
#' `newdata`, and `se.fit` are already used and passed on to
#' [mgcv::predict.gam()].
#'
#' @note For most families, regardless of the scale on which the fitted values
#' are returned, the `se` component of the returned object is on the *link*
#' (*linear predictor*) scale, not the response scale. An exception is the
#' `mgcv::ocat()` family, for which the `se` is on the response scale if
#' `scale = "response"`.
#'
#' @return A tibble (data frame) whose first *m* columns contain either the data
#' used to fit the model (if `data` was `NULL`), or the variables supplied to
#' `data`. Four further columns are added:
#'
#' * `fitted`: the fitted values on the specified scale,
#' * `se`: the standard error of the fitted values (always on the *link* scale),
#' * `lower`, `upper`: the limits of the credible interval on the fitted values,
#' on the specified scale.
#'
#' Models fitted with certain families will include additional variables
#'
#' * `mgcv::ocat()` models: when `scale = "repsonse"`, the returned object will
#' contain a `row` column and a `category` column, which indicate to which row
#' of the `data` each row of the returned object belongs. Additionally, there
#' will be `nrow(data) * n_categories` rows in the returned object; each row
#' is the predicted probability for a single category of the response.
#'
#' @export
#'
#' @examples
#' load_mgcv()
#' \dontshow{
#' op <- options(cli.unicode = FALSE, pillar.sigfig = 6)
#' }
#' sim_df <- data_sim("eg1", n = 400, dist = "normal", scale = 2, seed = 2)
#' m <- gam(y ~ s(x0) + s(x1) + s(x2) + s(x3), data = sim_df, method = "REML")
#' fv <- fitted_values(m)
#' fv
#' \dontshow{
#' options(op)
#' }
`fitted_values` <- function(object, ...) {
UseMethod("fitted_values")
}
#' @export
#' @rdname fitted_values
`fitted_values.gam` <- function(object,
data = NULL,
scale = c(
"response",
"link",
"linear predictor"
),
ci_level = 0.95, ...) {
# Handle everything up to and including the extended families, but not more
fn <- family_type(object)
if (inherits(family(object), "general.family")) {
allowed <- c(
"gaulss", "gammals", "gumbls", "gevlss", "shash", "ziplss",
"twlss"
)
if (!fn %in% allowed) {
stop("General likelihood GAMs not yet supported.")
}
}
scale <- match.arg(scale)
if (is.null(data)) {
data <- delete_response(object, model_frame = FALSE) %>%
as_tibble()
} else if (!is_tibble(data)) {
data <- as_tibble(data)
}
# handle special distributions that return more than vector fit & std. err.
# find the name of the function that produces fitted values for this family
fit_vals_fun <- get_fit_fun(fn)
extra_fns <- switch(fn,
"gumbls" = post_link_funs(location = exp, scale = exp),
"gammals" = post_link_funs(location = exp, scale = exp),
"gevlss" = post_link_funs(scale = exp),
"shash" = post_link_funs(scale = exp, kurtosis = exp),
"ziplss" = post_link_funs(
location = exp,
pi = inv_link(binomial("cloglog"))
),
"twlss" = post_link_funs(power = twlss_theta_2_power, scale = exp),
post_link_funs()
)
# compute fitted values
fit <- fit_vals_fun(object,
data = data, ci_level = ci_level,
scale = scale, extra_fns = extra_fns, ...
)
fit
}
#' @export
#' @rdname fitted_values
`fitted_values.gamm` <- function(object, ...) {
fitted_values(object$gam, ...)
}
#' @export
#' @rdname fitted_values
`fitted_values.scam` <- function(object, ...) {
fitted_values.gam(object, ...)
}
#' @importFrom rlang set_names .data
#' @importFrom dplyr bind_cols mutate across
#' @importFrom tibble as_tibble is_tibble
#' @importFrom tidyselect any_of
`fit_vals_default` <- function(
object, data, ci_level = 0.95,
scale = "response", ...) {
fit <- predict(object,
newdata = data, ..., type = "link",
se.fit = TRUE
) |>
as.data.frame() |>
rlang::set_names(c(".fitted", ".se")) |>
as_tibble()
# add .row *unless* it already exists
if (!".row" %in% names(data)) {
fit <- mutate(fit, .row = row_number())
}
fit <- bind_cols(data, fit) |>
relocate(".row", .before = 1L)
# create the confidence interval
crit <- coverage_normal(ci_level)
fit <- mutate(fit,
".lower_ci" = .data[[".fitted"]] - (crit * .data[[".se"]]),
".upper_ci" = .data[[".fitted"]] + (crit * .data[[".se"]])
)
# convert to the response scale if requested
if (identical(scale, "response")) {
fit <- fit |>
mutate(across(all_of(c(".fitted", ".lower_ci", ".upper_ci")),
.fns = inv_link(object)
))
}
fit
}
#' @importFrom dplyr mutate across case_match
#' @importFrom tidyr pivot_longer
#' @importFrom tibble as_tibble add_column
`fit_vals_general_lss` <- function(
object, data, ci_level = 0.95,
scale = "response", extra_fns = post_link_funs(), ...) {
crit <- coverage_normal(ci_level)
# get the fitted values for data
fv <- predict(object,
newdata = data, ..., type = "link",
se.fit = TRUE
)
std_err <- fv[[2L]]
fv <- fv[[1]]
colnames(std_err) <- colnames(fv) <- lss_parameters(object)
# convert fv to tibble then long format
fv <- fv |>
as_tibble() |>
mutate(.row = row_number()) |>
relocate(".row", .before = 1L) |>
tidyr::pivot_longer(!matches("\\.row"),
values_to = ".fitted",
names_to = ".parameter"
)
# convert fv to tibble then long format
std_err <- std_err |>
as_tibble() |>
mutate(.row = row_number()) |>
relocate(".row", .before = 1L) |>
tidyr::pivot_longer(!matches("\\.row"),
values_to = ".std_err",
names_to = ".parameter"
)
# bind .std_err to fv...
fit <- fv |>
add_column(.se = pull(std_err, ".std_err")) |>
# ...and compute interval
mutate(
.lower_ci = .data$.fitted + (crit * .data$.se),
.upper_ci = .data$.fitted - (crit * .data$.se)
)
# convert to the response scale if requested
if (identical(scale, "response")) {
il <- lss_links(object, inverse = TRUE)
fit <- fit |>
mutate(across(all_of(c(".fitted", ".lower_ci", ".upper_ci")),
.fns = ~ case_match(
.data$.parameter,
"location" ~ extra_fns[["location"]](il[["location"]](.x)),
"scale" ~ extra_fns[["scale"]](il[["scale"]](.x)),
"shape" ~ extra_fns[["shape"]](il[["shape"]](.x)),
"skewness" ~ extra_fns[["skewness"]](il[["skewness"]](.x)),
"kurtosis" ~ extra_fns[["kurtosis"]](il[["kurtosis"]](.x)),
"power" ~ extra_fns[["power"]](il[["power"]](.x)),
"pi" ~ extra_fns[["pi"]](il[["pi"]](.x))
)
))
}
fit
}
#' A list of transformation functions named for LSS parameters in a GAMLSS
#'
#' @keywords internal
post_link_funs <- function(
location = identity_fun,
scale = identity_fun,
shape = identity_fun,
skewness = identity_fun,
kurtosis = identity_fun,
power = identity_fun,
pi = identity_fun) {
list(
location = location, scale = scale, shape = shape, skewness = skewness,
kurtosis = kurtosis, power = power, pi = pi
)
}
#' General names of LSS parameters for each GAM family
#'
#' @keywords internal
lss_parameters <- function(object) {
fn <- family_type(object)
par_names <- switch(fn,
"gaulss" = c("location", "scale"),
"gammals" = c("location", "scale"),
"gumbls" = c("location", "scale"),
"gevlss" = c("location", "scale", "shape"),
"shash" = c("location", "scale", "skewness", "kurtosis"),
"ziplss" = c("location", "pi"),
"twlss" = c("location", "power", "scale"),
"location"
) # <- default, for most GAM families that's all there is
par_names
}
#' @importFrom purrr map
lss_links <- function(object, inverse = FALSE, which_eta = NULL) {
params <- lss_parameters(object)
param_nms <- c(
"location", "scale", "shape", "skewness", "kurtosis",
"power", "pi"
)
out <- rep(list(identity_fun), length(param_nms)) |>
setNames(param_nms)
funs <- purrr::map(params, .f = function(p, model, inverse, which_eta) {
extract_link(family(model),
parameter = p, inverse = inverse,
which_eta = which_eta
)
}, model = object, inverse = inverse, which_eta = which_eta) |>
setNames(params)
out[params] <- funs
out
}
# an identity function that simply returns input
identity_fun <- function(eta) {
eta
}
#' @importFrom dplyr mutate across case_match row_number
#' @importFrom tidyr pivot_longer
#' @importFrom tibble as_tibble add_column
`fit_vals_ziplss` <- function(
object, data, ci_level = 0.95,
scale = "response", extra_fns = post_link_funs(), ...) {
crit <- coverage_normal(ci_level)
# get the fitted values for data
fv <- predict(object,
newdata = data, ..., type = "link",
se.fit = TRUE
)
std_err <- fv[[2L]]
fv <- fv[[1]]
colnames(std_err) <- colnames(fv) <- lss_parameters(object)
# convert fv to tibble then long format
fv <- fv |>
as_tibble() |>
mutate(.row = row_number()) |>
relocate(".row", .before = 1L) |>
tidyr::pivot_longer(!matches("\\.row"),
values_to = ".fitted",
names_to = ".parameter"
)
# convert fv to tibble then long format
std_err <- std_err |>
as_tibble() |>
tidyr::pivot_longer(everything(),
values_to = ".std_err",
names_to = ".parameter"
)
# bind .std_err to fv...
fit <- fv |>
add_column(.se = pull(std_err, ".std_err")) |>
# ...and compute interval
mutate(
.lower_ci = .data$.fitted + (crit * .data$.se),
.upper_ci = .data$.fitted - (crit * .data$.se)
)
# convert to the response scale if requested
if (identical(scale, "response")) {
ilink_loc <- inv_link(object, parameter = "location")
ilink_pi <- inv_link(object, parameter = "pi")
fit <- fit |>
mutate(across(all_of(c(".fitted", ".lower_ci", ".upper_ci")),
.fns = ~ case_match(
.data$.parameter,
"location" ~ extra_fns[["location"]](ilink_loc(.x)),
"pi" ~ extra_fns[["pi"]](ilink_pi(.x))
)
))
}
fit
}
#' @importFrom dplyr mutate across case_match row_number
#' @importFrom tidyr pivot_longer
#' @importFrom tibble as_tibble add_column
`fit_vals_twlss` <- function(
object, data, ci_level = 0.95,
scale = "response", extra_fns = post_link_funs(), ...) {
crit <- coverage_normal(ci_level)
# get the fitted values for data
fv <- predict(object,
newdata = data, ..., type = "link",
se.fit = TRUE
)
std_err <- fv[[2L]]
fv <- fv[[1]]
colnames(std_err) <- colnames(fv) <- lss_parameters(object)
# convert fv to tibble then long format
fv <- fv |>
as_tibble() |>
mutate(.row = row_number()) |>
relocate(".row", .before = 1L) |>
tidyr::pivot_longer(!matches("\\.row"),
values_to = ".fitted",
names_to = ".parameter"
)
# convert fv to tibble then long format
std_err <- std_err |>
as_tibble() |>
tidyr::pivot_longer(everything(),
values_to = ".std_err",
names_to = ".parameter"
)
# bind .std_err to fv...
fit <- fv |>
add_column(.se = pull(std_err, ".std_err")) |>
# ...and compute interval
mutate(
.lower_ci = .data$.fitted + (crit * .data$.se),
.upper_ci = .data$.fitted - (crit * .data$.se)
)
# convert to the response scale if requested
if (identical(scale, "response")) {
il <- lss_links(object, inverse = TRUE)
bounds <- get_tw_bounds(object)
fit <- fit |>
mutate(across(all_of(c(".fitted", ".lower_ci", ".upper_ci")),
.fns = ~ case_match(
.data$.parameter,
"location" ~ extra_fns[["location"]](il[["location"]](.x)),
"power" ~ extra_fns[["power"]](il[["power"]](.x),
a = bounds[1], b = bounds[2]),
"scale" ~ extra_fns[["scale"]](il[["scale"]](.x))
)
))
}
fit
}
#' @importFrom dplyr bind_rows relocate
#' @importFrom tidyr expand_grid
#' @importFrom tibble tibble
`fit_vals_ocat` <- function(
object, data, ci_level = 0.95, scale = "response",
...) {
# if link (linear predictor) scale, we can just use `fit_vals_fun()`
if (scale %in% c("link", "linear predictor")) {
fit <- fit_vals_default(object,
data = data, ci_level = ci_level,
scale = "link", ...
)
} else {
# predict, needs to be response scale for ocat!
fv <- predict(object,
newdata = data, ..., type = "response",
se.fit = TRUE
)
crit <- coverage_normal(ci_level)
# extract information on how many thresholds, categories in the model
theta <- theta(object) # the estimated thresholds, first is always -1
n_cut <- length(theta) # how many thresholds...
n_cat <- n_cut + 1 # ...which implies this many categories
n_data <- NROW(data) # how many data are we predicting for
# \hat{pi} is the estimated probability of each class for each data
# \hat{pi} is given by fv$fit
# std. err. of \hat{pi} is given by fv$se.fit
# compute standard error of logit(\hat{pi}) via delta method
# this comes from Christensen RHB (2022), a vignette of ordinal
# package:
# https://cran.r-project.org/web/packages/ordinal/vignettes/clm_article.pdf
#
# se(logit(pi)) = se(pi) / (pi * (1 - pi))
se_lp <- fv$se.fit / (fv$fit * (1 - fv$fit))
# grab slightly better versions of plogis() & qlogis() from the binomial
# family
bin_fam <- binomial()
lfun <- link(bin_fam)
ifun <- inv_link(bin_fam)
# convert \hat{pi} to logit scale and form a Wald interval, then back
# transform the interval only (we already have \hat{pi})
fit_lp <- lfun(fv$fit) # logit(\hat{pi})
fit_lwr <- ifun(fit_lp - (crit * se_lp))
fit_upr <- ifun(fit_lp + (crit * se_lp))
# create the return object
fit <- tibble(
.row = rep(seq_len(n_data), times = n_cat),
.category = factor(rep(seq_len(n_cat), each = n_data)),
.fitted = as.numeric(fv$fit),
.se = as.numeric(fv$se.fit),
.lower_ci = as.numeric(fit_lwr),
.upper_ci = as.numeric(fit_upr)
)
# expand data so it is replicated once per category & add to the fitted
# values
fit <- expand_grid(category = seq_len(n_cat), data) |>
select(-c("category")) |>
bind_cols(fit) |>
relocate(".row", .before = 1)
}
fit
}
#' @importFrom dplyr case_when
`get_fit_fun` <- function(fam) {
# family <- family_type(object)
fam <- case_when(
grepl("^ordered_categorical", fam, ignore.case = TRUE) == TRUE ~ "ocat",
fam == "gaulss" ~ "general_lss",
fam == "gammals" ~ "general_lss",
fam == "gumbls" ~ "general_lss",
fam == "gevlss" ~ "general_lss",
fam == "shash" ~ "general_lss",
fam == "ziplss" ~ "ziplss",
fam == "twlss" ~ "twlss",
.default = "default"
)
get(paste0("fit_vals_", fam), mode = "function")
}
## my original code trying to follow Simon's ocat
# lp <- as.numeric(fv$fit)
# se <- as.numeric(fv$se.fit)
# upr <- lp + (crit * se)
# lwr <- lp - (crit * se)
# theta <- theta(object)
# n_cut <- length(theta)
# n_cat <- n_cut + 1
# n_data <- NROW(data)
# p_fit <- p_lwr <- p_upr <- matrix(0, nrow = n_data,
# ncol = n_cut + 2)
# # cumulative probability should sum to 1 over the latent
# # fill final column with 1 to reflect that
# p_fit[, n_cut + 2] <- p_lwr[, n_cut + 2] <- p_upr[, n_cut + 2] <- 1
# # function to give probability from latent
# `ocat_prob` <- function(lp, theta) {
# p <- theta - lp
# i <- p > 0
# p[i] <- 1 / (1 + exp(-p[i]))
# p[!i] <- exp(p[!i]) / (1 + exp(p[!i]))
# p
# }
# # fill in the matrix of cumulative probability
# for (j in seq_along(theta)) {
# p_fit[, j + 1] <- ocat_prob(lp, theta[j])
# p_lwr[, j + 1] <- ocat_prob(lwr, theta[j])
# p_upr[, j + 1] <- ocat_prob(upr, theta[j])
# }
# #browser()
# p_fit <- as.numeric(t(diff(t(p_fit))))
# p_lwr <- as.numeric(t(diff(t(p_lwr))))
# p_upr <- as.numeric(t(diff(t(p_upr))))
# fit <- tibble(row = rep(seq_len(n_data), times = n_cat),
# category = factor(rep(seq_len(n_cat), each = n_data)),
# fitted = p_fit,
# lower = p_lwr,
# upper = p_upr)
# # expand data so it is replicated once per category
# fit <- expand_grid(category = seq_len(n_cat), data) |>
# select(-c("category")) |>
# bind_cols(fit) |>
# relocate(row, .before = 1)
# fit
Any scripts or data that you put into this service are public.
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.