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bsts.R
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bsts.R
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# Copyright 2018 Google LLC. All Rights Reserved.
#
# This library is free software; you can redistribute it and/or
# modify it under the terms of the GNU Lesser General Public
# License as published by the Free Software Foundation; either
# version 2.1 of the License, or (at your option) any later version.
#
# This library is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
# Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public
# License along with this library; if not, write to the Free Software
# Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA
## This file implements the main bsts function and most of its methods
## (plot, print, summary).
##
## Two common use cases:
## bsts(y ~ formula, data = my.data, state.specification = ss)
## bsts(y, state.specification = ss)
##
## Then we can plot.bsts, predict.bsts, etc. Of course, they will
## need different argument lists depending on the presence/absence of
## predictors.
bsts <- function(formula,
state.specification,
family = c("gaussian", "logit", "poisson", "student"),
data,
prior = NULL,
contrasts = NULL,
na.action = na.pass,
niter,
ping = niter / 10,
model.options = BstsOptions(),
timestamps = NULL,
seed = NULL,
...) {
## Uses MCMC to sample from the posterior distribution of a Bayesian
## structural time series model. This function can be used either
## with or without contemporaneous predictor variables (in a time
## series regression).
##
## If predictor variables are present, the regression coefficients
## are fixed (as opposed to time varying, though time varying
## coefficients might be added as part of a state variable). The
## predictors and response in the formula are contemporaneous, so if
## you want lags and differences you need to put them in the
## predictor matrix yourself.
##
## If no predictor variables are used, then the model is an ordinary
## state space time series model.
##
## Args:
## formula: A formula describing the regression portion of the relationship
## between y and X. See the Details section below about options for y in
## Poisson or logit models. If no regressors are desired then the formula
## can be replaced by a numeric vector giving the time series to be
## modeled. Missing values are not allowed in predictor variables but
## they are allowed in the response. If the response is of class zoo,
## xts, or ts then time series information it contains will be used in
## many of the plot methods called by plot.bsts.
## state.specification: a list with elements created by AddLocalLinearTrend,
## AddSeasonal, and similar functions for adding components of state.
## family: The model family of the observation equation. Standard state
## space models require the observation family to be Gaussian. However
## this requirement can be relaxed to mixtures of Gaussians, which opens
## the door to several other error distributions such as binomial (logit),
## Poisson, and T.
## data: an optional data frame, list or environment (or object coercible by
## ‘as.data.frame’ to a data frame) containing the variables in the model.
## If not found in ‘data’, the variables are taken from
## ‘environment(formula)’, typically the environment from which ‘bsts’ is
## called.
## prior: If a regression component is present then this a prior
## distribution for the regression component of the model, as created by
## SpikeSlabPrior. The prior for the time series component of the model
## will be specified during the creation of state.specification. If no
## regression components are specified then this is a prior for the
## residual standard deviation, created by SdPrior. In either case the
## prior is optional. A weak default prior will be used if no prior is
## specified explicitly.
## contrasts: an optional list containing the names of contrast functions to
## use when converting factors numeric variables in a regression formula.
## This argument works exactly as it does in 'lm'. The names of the list
## elements correspond to factor variables in your model formula. The
## list elements themselves are the names of contrast functions (see
## help(contrast) and the 'contrasts.arg' argument to
## 'model.matrix.default'). This argument is only used if a model formula
## is specified. It can usually be ignored even then.
## na.action: What to do about missing values. The default is to allow
## missing responses, but no missing predictors. Set this to na.omit or
## na.exclude if you want to omit missing responses altogether, but do so
## with care, as that will remove observations from the time series.
## niter: a positive integer giving the desired number of MCMC draws
## ping: A scalar. If ping > 0 then the program will print a status message
## to the screen every 'ping' MCMC iterations.
## model.options: An object (list) returned by BstsOptions(). See that
## function for details.
## timestamps: The timestamp associated with each value of the response.
## This argument is primarily useful in cases where the response has
## missing gaps or duplicate values. If the response is a regular time
## series with a single observation per time point, then you can leave the
## 'timestamps' argument as NULL and the timestamps will be taken from the
## 'response' or 'data' objects (if they are 'zoo' objects).
## seed: An integer to use as the C++ random seed. If NULL then
## the C++ seed will be set using the clock.
## ...: Extra arguments to be passed to SpikeSlabPrior.
## Returns:
## An object of class 'bsts', which is a list containing the MCMC draws of
## model parameters, state contributions, etc.
##
## The returned object will also contain named elements holding the MCMC
## draws of model parameters belonging to the state models. The names of
## each component are supplied by the entries in state.specification. If a
## model parameter is a scalar, then the list element is a vector with
## 'niter' elements. If the parameter is a vector then the list element is
## a matrix with 'niter' rows, and if the parameter is a matrix then the
## list element is a 3-way array with first dimension 'niter'.
##
## Finally, if a model formula was supplied, then the returned object will
## contain the information necessary for the predict method to build the
## predictor matrix when a new prediction is made.
##
## Details:
## If the model family is logit, then there are two ways one can format the
## response variable. If the response is 0/1, TRUE/FALSE, or 1/-1, then the
## response variable can be passed as a vector. If the response is a set of
## counts out of a specified number of trials then it can be passed as a
## two-column matrix, where the first column contains the counts of
## successes and the second contains the count of failures.
##
## Likewise, if the model family is Poisson, the response can be passed as a
## single vector of counts, under the assumption that each observation has
## unit exposure. If the exposures differ across observations, then the
## resopnse can be a two column matrix, with the first column containing the
## event counts and the second containing exposure times.
## Do some error checking before we get started.
check.nonnegative.scalar(niter)
check.scalar.integer(ping)
stopifnot(is.null(seed) || length(seed) == 1)
if (!is.null(seed)) {
seed <- as.integer(seed)
}
family <- match.arg(family)
has.regression <- !is.numeric(formula)
if (has.regression) {
##----------------------------------------------------------------------
## Here begins some black magic to extract the responses and the matrix of
## predictors from the model formula and either the 'data' argument or from
## objects present in the parent frame at the time of calling. Most of this
## was copied from 'lm'.
function.call <- match.call()
my.model.frame <- match.call(expand.dots = FALSE)
frame.match <- match(c("formula", "data", "na.action"),
names(my.model.frame), 0L)
my.model.frame <- my.model.frame[c(1L, frame.match)]
my.model.frame$drop.unused.levels <- TRUE
# In an ordinary regression model the default action for NA's is to delete
# them. This makes sense in ordinary regression models, but is dangerous in
# time series, because it artificially shortens the time between two data
# points. If the user has not specified an na.action function argument then
# we should use na.pass as a default, so that NA's are passed through to the
# underlying C++ code.
if (! "na.action" %in% names(my.model.frame)) {
my.model.frame$na.action <- na.pass
}
my.model.frame[[1L]] <- as.name("model.frame")
my.model.frame <- eval(my.model.frame, parent.frame())
model.terms <- attr(my.model.frame, "terms")
predictors <- model.matrix(model.terms, my.model.frame, contrasts)
if (any(is.na(predictors))) {
stop("bsts does not allow NA's in the predictors, only the responses.")
}
response <- model.response(my.model.frame, "any")
## Check that response and predictors are the right size. The response
## might be a matrix if the model family is logit or Poisson.
sample.size <- if (is.matrix(response)) nrow(response) else length(response)
stopifnot(nrow(predictors) == sample.size)
## End of black magic to get predictors and response.
} else {
## No static regression formula.
response <- formula
stopifnot(is.numeric(response))
predictors <- NULL
}
## Grab the timestamps for the response before passing it to
## .FormatBstsDataAndOptions so we can use them later.
if (missing(data)) {
## This should be handled in the argument list by setting a default argument
## data = NULL, but doing that messes up the "regression black magic"
## section above.
data <- NULL
}
timestamp.info <- TimestampInfo(response, data, timestamps)
formatted.data.and.options <- .FormatBstsDataAndOptions(
family, response, predictors, model.options, timestamp.info)
data.list <- formatted.data.and.options$data.list
model.options <- formatted.data.and.options$model.options
##----------------------------------------------------------------------
## If no prior was supplied for the observation model then assign a
## default prior.
if (is.null(prior)) {
prior <- .SetDefaultPrior(
data.list,
family = family,
bma.method = model.options$bma.method,
...)
}
## Check that the prior is appropriate for the data, options and
## observation model family.
if (has.regression) {
stopifnot(inherits(prior, "SpikeSlabPriorBase"))
## Identify any predictor columns that are all zero, and assign
## them zero prior probability of being included in the model.
## This must be done after the prior has been validated.
all.zero <- apply(predictors, 2, function(z) all(z == 0))
prior$prior.inclusion.probabilities[all.zero] <- 0
if (model.options$bma.method == "ODA") {
stopifnot(inherits(prior, "IndependentSpikeSlabPrior"))
stopifnot(is.list(model.options$oda.options))
check.scalar.probability(model.options$oda.options$fallback.probability)
check.positive.scalar(model.options$oda.options$eigenvalue.fudge.factor)
}
if (is.null(prior$max.flips)) {
prior$max.flips <- -1
}
}
## Check state compatibility. There are some combinations of options and
## state models that just don't work together.
.CheckCompatibility(data.list, state.specification, model.options,
family)
##----------------------------------------------------------------------
ans <- .Call("analysis_common_r_fit_bsts_model_",
data.list,
state.specification,
prior,
model.options,
family,
niter,
ping,
model.options$timeout.seconds,
seed,
PACKAGE = "bsts")
ans$has.regression <- has.regression
ans$state.specification <- state.specification
ans$prior <- prior
ans$timestamp.info <- timestamp.info
model.options$timestamp.info <- NULL
ans$model.options <- model.options
ans$family <- family
ans$niter <- niter
if (!is.null(ans$ngood)) {
ans <- .Truncate(ans)
}
ans$original.series <- .ComputeOriginalSeries(timestamp.info,
data.list$response)
##----------------------------------------------------------------------
## Add names to state.contributions.
if (model.options$save.state.contributions) {
## Store the names of each state model in the appropriate dimname
## for state.contributions.
number.of.state.components <- length(state.specification)
state.names <- character(number.of.state.components)
for (i in seq_len(number.of.state.components)) {
state.names[i] <- state.specification[[i]]$name
}
if (ans$has.regression) {
state.names <- c(state.names, "regression")
}
dimnames(ans$state.contributions) <- list(
mcmc.iteration = NULL,
component = state.names,
time = NULL)
}
##----------------------------------------------------------------------
## Put all the regression junk back in, so things like predict() will work.
if (ans$has.regression) {
## Save meta-data about the regression model
ans$contrasts <- attr(predictors, "contrasts")
ans$xlevels <- .getXlevels(model.terms, my.model.frame)
ans$terms <- model.terms
## Save the predictors, and assign names to the regression coefficients.
ans$predictors <- predictors
variable.names <- colnames(predictors)
if (!is.null(variable.names)) {
colnames(ans$coefficients) <- variable.names
}
ans <- .RemoveInterceptAmbiguity(ans)
}
##----------------------------------------------------------------------
## Add in family specific data.
if (family == "logit") {
ans$trials <- data.list$trials
} else if (family == "poisson") {
ans$exposure <- data.list$exposure
}
class(ans) <- "bsts"
return(ans)
}
###======================================================================
BstsOptions <- function(save.state.contributions = TRUE,
save.prediction.errors = TRUE,
bma.method = c("SSVS", "ODA"),
oda.options = list(
fallback.probability = 0.0,
eigenvalue.fudge.factor = 0.01),
timeout.seconds = Inf,
save.full.state = FALSE) {
## A collection of somewhat more obscure options that can be used to control a
## bsts model.
##
## Args:
## save.state.contributions: Logical. If TRUE then a 3-way array
## named 'state.contributions' will be stored in the returned
## object. The indices correspond to MCMC iteration, state
## model number, and time. Setting 'save.state.contributions'
## to 'FALSE' yields a smaller object, but plot() will not be
## able to plot the the "state", "components", or "residuals"
## for the fitted model.
## save.prediction.errors: Logical. If TRUE then a matrix named
## 'one.step.prediction.errors' will be saved as part of the
## model object. The rows of the matrix represent MCMC
## iterations, and the columns represent time. The matrix
## entries are the one-step-ahead prediction errors from the
## Kalman filter.
## bma.method: If the model contains a regression component, this
## argument specifies the method to use for Bayesian model
## averaging. "SSVS" is stochastic search variable selection,
## which is the classic approach from George and McCulloch
## (1997). "ODA" is orthoganal data augmentation, from Ghosh
## and Clyde (2011). It adds a set of latent observations that
## make the X^TX matrix diagonal, simplifying complete data MCMC
## for model selection.
## oda.options: A list (which is ignored unless bma.method ==
## "ODA") with the following elements:
## * fallback.probability: Each MCMC iteration will use SSVS
## instead of ODA with this probability. In cases where the
## latent data have high leverage, ODA mixing can suffer.
## Mixing in a few SSVS steps can help keep an errant
## algorithm on track.
## * eigenvalue.fudge.factor: The latent X's will be chosen so
## that the complete data X'X matrix (after scaling) is a
## constant diagonal matrix equal to the largest eigenvalue
## of the observed (scaled) X'X times (1 +
## eigenvalue.fudge.factor). This should be a small
## positive number.
## timeout.seconds: The number of seconds that sampler will be
## allowed to run. If the timeout is exceeded the returned
## object will be truncated to the final draw that took place
## before the timeout occurred, as if that had been the
## requested value of 'niter'. A timeout is reported through a
## warning.
## save.full.state: Logical: If TRUE then the full distribution of state
## will be saved. This gets expensive if complex high-dimensional state
## models are used, so the default is to not save the full state. If
## saved, the state is stored as a 3-way array with indices
## [mcmc.iteration, state.dimension, time.dimension]
bma.method <- match.arg(bma.method)
stopifnot(is.logical(save.state.contributions),
length(save.state.contributions) == 1)
stopifnot(is.logical(save.prediction.errors),
length(save.prediction.errors) == 1)
stopifnot(is.list(oda.options))
stopifnot(is.numeric(oda.options$fallback.probability),
length(oda.options$fallback.probability) == 1)
stopifnot(is.numeric(oda.options$eigenvalue.fudge.factor),
length(oda.options$eigenvalue.fudge.factor) == 1)
stopifnot(is.numeric(timeout.seconds),
length(timeout.seconds) == 1,
timeout.seconds >= 0)
stopifnot(is.logical(save.full.state),
length(save.full.state) == 1)
ans <- list(save.state.contributions = save.state.contributions,
save.prediction.errors = save.prediction.errors,
bma.method = bma.method,
oda.options = oda.options,
timeout.seconds = timeout.seconds,
save.full.state = save.full.state)
class(ans) <- "BstsOptions"
return(ans)
}
###======================================================================
.SetDefaultPrior <- function(
data.list,
family = c("gaussian", "logit", "poisson", "student"),
bma.method = c("SSVS", "ODA"),
...) {
## Creates a default prior for the bsts observation equation.
## Args:
## data.list: The formatted list of data produced by
## .FormatBstsDataAndOptions.
## family: The model family for which a prior is needed.
## bma.method: The method to use for Bayesian model averaging.
## ...: Additional arguments passed to SpikeSlabPrior,
## IndependentSpikeSlabPrior, LogitZellnerPrior, or
## PoissonZellnerPrior, depending on the model family and
## bma.method.
## Returns:
## A default prior distribution.
family <- match.arg(family)
has.regression <- !is.null(data.list$predictors)
if (family == "gaussian") {
## By default, don't accept any draws of the residual standard
## deviation that are greater than 20% larger than the empirical
## SD.
sdy <- sqrt(var(data.list$response, na.rm = TRUE))
dots <- list(...)
if ("sigma.upper.limit" %in% names(dots)) {
sigma.upper.limit <- dots $sigma.upper.limit
} else {
sigma.upper.limit <- sdy * 1.2
}
if (!has.regression) {
prior <- SdPrior(sigma.guess = sdy,
sample.size = .01,
upper.limit = sigma.upper.limit)
} else {
bma.method <- match.arg(bma.method)
zero <- rep(0, ncol(data.list$predictors))
if (bma.method == "SSVS") {
## If using SSVS then the default prior is Zellner's g-prior.
### TODO(steve):
## replace the raw function call with do.call. You need to name each
## of the function parameters as they're named in SpikeSlabPrior, and
## pass the list of arguments. When you do this pass
## sigma.upper.limit as part of 'dots' and not as a separate argument.
# The call looks like prior <- do.call(SpikeSlabPrior, dots) you'll need
# to put dots$x = data.list$predictors, dots$y = data.list$response,
# dots$optional.coefficient.estimate = zero, etc.
prior <- SpikeSlabPrior(data.list$predictors,
data.list$response,
optional.coefficient.estimate = zero,
sigma.upper.limit = sigma.upper.limit,
...)
} else if (bma.method == "ODA") {
## If using ODA then you need an independent prior for
## sigma^2, and independent conditional priors for each
## element of beta.
prior <- IndependentSpikeSlabPrior(
data.list$predictors,
data.list$response,
optional.coefficient.estimate = zero,
sigma.upper.limit = sigma.upper.limit,
...)
}
}
} else if (family == "logit") {
if (!has.regression) {
## No prior is necessary, but we need to signal the C++ code to
## create a sampler.
prior <- NULL
} else {
prior <- LogitZellnerPrior(predictors = data.list$predictors,
successes = data.list$response,
trials = data.list$trials,
...)
}
} else if (family == "poisson") {
if (!has.regression) {
## No prior is necessary, but we need to signal the C++ code to
## create a sampler.
prior <- NULL
} else {
prior <- PoissonZellnerPrior(predictors = data.list$predictors,
counts = data.list$response,
exposure = data.list$exposure,
...)
}
} else if (family == "student") {
sdy <- sqrt(var(data.list$response, na.rm = TRUE))
dots = list(...)
if ("sigma.upper.limit" %in% names(dots)) {
sigma.upper.limit = dots$sigma.upper.limit
} else {
sigma.upper.limit <- sdy * 1.2
}
if (!has.regression) {
y <- data.list$response
prior <- StudentSpikeSlabPrior(
matrix(1.0, nrow = length(y), ncol = 1),
y,
prior.inclusion.probabilities = 0,
sigma.upper.limit = sigma.upper.limit,
...)
} else {
zero <- rep(0, ncol(data.list$predictors))
prior <- StudentSpikeSlabPrior(
data.list$predictors,
data.list$response,
optional.coefficient.estimate = zero,
sigma.upper.limit = sigma.upper.limit,
...)
}
} else {
stop("Argument 'family' had an illegal value in the call to",
".SetDefaultPrior")
}
return(prior)
}
.RemoveInterceptAmbiguity <- function(bsts.object) {
## If the model contains a regression with an intercept term then
## there is an indeterminacy between the intercept and the trend.
## We need to subtract the intercept term from the regression
## component and add it to the trend component.
if (!bsts.object$has.regression) return(bsts.object)
## Compute a logical vector indicating which columns contain all 1's.
all.ones <- apply(bsts.object$predictors,
2,
function(column)(all(column == 1)))
state.sizes <- StateSizes(bsts.object$state.specification)
has.trend <- "trend" %in% names(state.sizes)
if (has.trend && any(all.ones)) {
if (sum(all.ones) > 1) {
warning("The predictor matrix contains multiple columns of 1's. ",
"Treating the first one as the intercept.")
}
intercept.position = match(TRUE, all.ones)
intercept <- bsts.object$coefficients[, intercept.position]
state.names <- dimnames(bsts.object$state.contributions)[[2]]
trend.position <- match("trend", state.names)
if (is.na(trend.position)) trend.position <- 1
bsts.object$state.contributions[, trend.position, ] <-
bsts.object$state.contributions[, trend.position, ] + intercept
bsts.object$state.contributions[, "regression", ] <-
bsts.object$state.contributions[, "regression", ] - intercept
bsts.object$coefficients[, intercept.position] <- 0
## We also need to add the intercept term into the right component
## of "final state". We need to find the right location again,
## because final.state (a full state vector) is indexed
## differently than state.contributions (which just gives the
## overall contribution of each state component).
trend.components.index <- match("trend", names(state.sizes))
trend.components.index <-
trend.components.index[!is.na(trend.components.index)]
stopifnot(length(trend.components.index) == 1)
trend.starting.position <- 1
if (trend.components.index > 1) {
trend.starting.position <-
1 + cumsum(state.sizes[1:(trend.components.index - 1)])
}
bsts.object$final.state[, trend.starting.position] <-
bsts.object$final.state[, trend.starting.position] + intercept
}
return(bsts.object)
}
.ComputeOriginalSeries <- function(timestamp.info, response) {
## Computes the original series passed to the bsts function. This is harder
## than it sounds, because the response has been massaged with as.numeric and
## potentially been converted from a two-column matrix to a vector.
##
## Ensuring that response retains the zoo-ness of the input series is a pain
## in the butt.
##
## Args:
## timestamp.info: The
## response: The response used to fit the bsts model, which may be a numeric
## vector or a two-column matrix.
## Need to wrap timestamp.info in a "bsts.object" to match the signiture
## expeceed by HasDuplicateTimestamps.
fake.bsts.object <- list(timestamp.info = timestamp.info)
if (!HasDuplicateTimestamps(fake.bsts.object)) {
response <- zoo(response, timestamp.info$timestamps)
}
return(response)
}
.Truncate <- function(object) {
## Looks through all the elements in object. Replace any vectors of
## length object$niter, or arrays with leading dimension
## object$niter, with their first object$ngood observations. This
## function is designed to remove space that was allocated but not
## used because the algorithm experienced an exception or a timeout.
##
## Args:
## object: An object that has been fit by bsts.
##
## Returns:
## object, with its trailing niter - ngood observations removed,
## with ngood removed, and with niter set to ngood.
if (is.null(object$ngood)) {
return(object)
}
ngood <- object$ngood
niter <- object$niter
if (ngood >= niter) {
return(object)
}
for (i in seq_along(object)) {
if (is.array(object[[i]]) && dim(object[[i]])[1] == niter) {
array.dim <- dim(object[[i]])
if (length(array.dim) == 2) {
object[[i]] <- object[[i]][1:ngood, , drop = FALSE]
} else if (length(array.dim) == 3) {
object[[i]] <- object[[i]][1:ngood, , , drop = FALSE]
} else if (length(array.dim) == 4) {
object[[i]] <- object[[i]][1:ngood, , , , drop = FALSE]
} else {
stop("Array dimension is too large.")
}
} else if (is.numeric(object[[i]]) && length(object[[i]] == niter)) {
object[[i]] <- object[[i]][1:ngood]
}
}
object$niter <- ngood
object$ngood <- NULL
return(object)
}
.CheckCompatibility <- function(data.list, state.specification,
model.options, family) {
## Ensure that any incompatible combinations of state models, model options,
## data formats, etc. raise an error in R before they get to crash C++.
##
## Args:
## data.list: A list containing the packaged data to be sent to C++.
## state.specification: A list of state component objects.
## model.options: A list of model options.
## family: string denoting the model family.
dynamic.regression <- any(sapply(state.specification,
inherits, "DynamicRegression"))
if (!data.list$timestamp.info$timestamps.are.trivial && dynamic.regression) {
stop("Dynamic regression models are only supported with trivial time stamps.")
}
is.state.model <- sapply(state.specification, inherits, "StateModel")
if (!all(is.state.model)) {
error.message <- paste0(
"The state.specification should be a list of StateModel objects. ")
if (sum(!is.state.model) == 1) {
error.message <- paste0(
error.message,
"The list element in position: ", which(is.state.model),
" is not a StateModel object.")
} else {
error.message <- paste0(
"The list elements in positions: ", which(is.state.model),
" are not StateModel objects.")
}
stop(error.message)
}
}