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R/predict.R
In BAS: Bayesian Variable Selection and Model Averaging using Bayesian Adaptive Sampling
Defines functions
variable.names.pred.bas
.se.bma
.se.fit
fitted.bas
predict.bas
predict.basglm
Documented in
fitted.bas
predict.bas
predict.basglm
variable.names.pred.bas
#' Prediction Method for an Object of Class basglm
#' @description Predictions under model averaging from a BMA (BAS) object for GLMs
#' under different loss functions.
#' @aliases predict.basglm
#' @param object An object of class "basglm", created by \code{bas.glm}
#' @param newdata dataframe, new matrix or vector of data for predictions. May
#' include a column for the intercept or just the predictor variables. If a
#' dataframe, the variables are extracted using model.matrix using the call
#' that created 'object'. May be missing in which case the data used for
#' fitting will be used for prediction.
#' @param se.fit indicator for whether to compute se of fitted and predicted
#' values
#' @param type Type of predictions required. The default is "response" is on the scale of the
#' response variable, with the alternative being on the linear predictor
#' scale, `type ='link'`. Thus for a default binomial model
#' `type = 'response'` gives
#' the predicted probabilities, while with `'link'`, the estimates
#' are of log-odds (probabilities on logit scale).
#' @param top A scalar integer M. If supplied, calculate results using the subset of the top M models
#' based on posterior probabilities.
#' @param estimator estimator used for predictions. Currently supported
#' options include: \cr 'HPM' the highest probability model \cr 'BMA' Bayesian
#' model averaging, using optionally only the 'top' models \cr 'MPM' the median
#' probability model of Barbieri and Berger. \cr 'BPM' the model that is
#' closest to BMA predictions under squared error loss. BMA may be computed
#' using only the 'top' models if supplied
#' @param na.action function determining what should be done with missing values in newdata.
#' The default is to predict NA.
#' @param ... optional extra arguments
#' @return a list of
#' \item{fit}{predictions using BMA or other estimators}
#' \item{Ypred}{matrix of predictions under model(s)}
#' \item{postprobs}{renormalized probabilities of
#' the top models}
#' \item{best}{index of top models included}
#' @details This function first calls the predict method for class bas
#' (linear models) to form predictions on the linear predictor
#' scale for `BMA`, `HPM`, `MPM` etc. If the estimator is `BMA`
#' and `type='response'` then the
#' inverse link is applied to fitted values for type equal `'link'`
#' and model averaging takes place in the `response` scale. Thus applying
#' the inverse link to BMA estimate with `type = 'link'` is
#' not equal to the fitted values for `type = 'response'` under
#' BMA due to the nonlinear transformation under the inverse link.
#'
#' @author Merlise Clyde
#' @seealso \code{\link{bas.glm}}, \code{\link{predict.bas}},
#' \code{\link{fitted.bas}}
#' @keywords regression
#' @examples
#'
#'
#' data(Pima.tr, package="MASS")
#' data(Pima.te, package="MASS")
#' Pima.bas = bas.glm(type ~ ., data=Pima.tr, n.models= 2^7, method="BAS",
#' betaprior=CCH(a=1, b=nrow(Pima.tr)/2, s=0), family=binomial(),
#' modelprior=uniform())
#' pred = predict(Pima.bas, newdata=Pima.te, top=1) # Highest Probability model
#' cv.summary.bas(pred$fit, Pima.te$type, score="miss-class")
#'
#' @rdname predict.basglm
#' @family predict methods
#' @family bas methods
#' @export
predict.basglm <- function(object,
newdata,
se.fit = FALSE,
type = c("response", "link"),
top = NULL,
estimator = "BMA",
na.action = na.pass,
...) {
# browser()
if (estimator == "HPM") {
top <- 1
}
# get predictions on linear predictor scale
pred <- predict.bas(
object,
newdata = newdata,
se.fit = se.fit,
top = top,
estimator = estimator,
na.action = na.action,
...
)
if (length(type) > 1) {
type <- type[1]
}
#
# if type is 'link' do not need to do anything; just return
# pred at end
#
if (type == "response") {
model.specs <- attributes(pred$fit)
if (estimator == "BMA") {
Ypred <- apply(
pred$Ypred,
1,
FUN = function(x) {
eval(object$family)$linkinv(x)
}
)
if (length(pred$postprobs) > 1) {
fit <- as.vector(Ypred %*% pred$postprobs)
} else {
fit <- as.vector(Ypred)
}
}
else {
fit <- eval(object$family)$linkinv(pred$fit)
}
attributes(fit) <- model.specs
# replace predictions
#
pred$fit <- fit
if (se.fit) {
se.fit <- pred$se.fit * abs(eval(object$family)$mu.eta(pred$fit))
se.pred <- pred$se.pred * abs(eval(object$family)$mu.eta(pred$fit))
pred$se.fit <- se.fit
pred$se.pred <- se.pred
}
}
return(pred)
}
#' Prediction Method for an object of class BAS
#'
#' Predictions under model averaging or other estimators from a BMA object of
#' class inheriting from 'bas'.
#'
#' Use BMA and/or model selection to form predictions using the top highest
#' probability models.
#'
#' @aliases predict.bas predict
#' @param object An object of class BAS, created by \code{bas}
#' @param newdata dataframe for predictions. If missing, then use the dataframe
#' used for fitting for obtaining fitted and predicted values.
#' @param se.fit indicator for whether to compute se of fitted and predicted
#' values
#' @param type Type of predictions required. "link" which is on the scale of
#' the linear predictor is the only option currently for linear models, which for the normal model
#' is equivalent to type='response'.
#' @param top a scalar integer M. If supplied, subset the top M models, based
#' on posterior probabilities for model predictions and BMA.
#' @param estimator estimator used for predictions. Currently supported
#' options include: \cr 'HPM' the highest probability model \cr 'BMA' Bayesian
#' model averaging, using optionally only the 'top' models \cr 'MPM' the median
#' probability model of Barbieri and Berger. \cr 'BPM' the model that is
#' closest to BMA predictions under squared error loss. BMA may be computed
#' using only the 'top' models if supplied
#' @param na.action function determining what should be done with missing values in newdata.
#' The default is to predict NA.
#' @param ... optional extra arguments
#' @return a list of
#' \item{fit}{fitted values based on the selected estimator}
#' \item{Ybma}{predictions using BMA, the same as fit for non-BMA methods for
#' compatibility; will be deprecated}
#' \item{Ypred}{matrix of predictions under
#' each model for BMA}
#' \item{se.fit}{se of fitted values; in the case of BMA
#' this will be a matrix}
#' \item{se.pred}{se for predicted values; in the case
#' of BMA this will be a matrix}
#' \item{se.bma.fit}{vector of posterior sd under
#' BMA for posterior mean of the regression function.
#' This will be NULL if estimator is not 'BMA'}
#' \item{se.bma.pred}{vector of posterior sd under BMA
#' for posterior predictive values. this will be NULL if estimator is not
#' 'BMA'}
#' \item{best}{index of top models included}
#' \item{bestmodels}{subset of
#' bestmodels used for fitting or prediction}
#' \item{best.vars}{names of variables in the top model; NULL if estimator='BMA'}
#' \item{df}{scalar or vector of
#' degrees of freedom for models}
#' \item{estimator}{estimator upon which 'fit'
#' is based.}
#' @author Merlise Clyde
#' @seealso \code{\link{bas}}, \code{\link{fitted.bas}},
#' \code{\link{confint.pred.bas}}, \code{\link{variable.names.pred.bas}}
#' @keywords regression
#' @examples
#'
#' data("Hald")
#' hald.gprior = bas.lm(Y ~ ., data=Hald, alpha=13, prior="g-prior")
#'
#' predict(hald.gprior, newdata=Hald, estimator="BPM", se.fit=TRUE)
#' # same as fitted
#' fitted(hald.gprior,estimator="BPM")
#' # default is BMA and estimation of mean vector
#' hald.bma = predict(hald.gprior, top=5, se.fit=TRUE)
#' confint(hald.bma)
#'
#' hald.bpm = predict(hald.gprior, newdata=Hald[1,],
#' se.fit=TRUE,
#' estimator="BPM")
#' confint(hald.bpm)
#' # extract variables
#' variable.names(hald.bpm)
#'
#' hald.hpm = predict(hald.gprior, newdata=Hald[1,],
#' se.fit=TRUE,
#' estimator="HPM")
#' confint(hald.hpm)
#' variable.names(hald.hpm)
#'
#' hald.mpm = predict(hald.gprior, newdata=Hald[1,],
#' se.fit=TRUE,
#' estimator="MPM")
#' confint(hald.mpm)
#' variable.names(hald.mpm)
#'
#' @rdname predict.bas
#' @family predict methods
#' @family bas methods
#' @export
predict.bas <- function(object,
newdata,
se.fit = FALSE,
type = "link",
top = NULL,
estimator = "BMA",
na.action = na.pass,
...) {
if (!(estimator %in% c("BMA", "HPM", "MPM", "BPM"))) {
stop("Estimator must be one of 'BMA', 'BPM', 'HPM', or 'MPM'.")
}
tt <- terms(object)
if (missing(newdata) || is.null(newdata)) {
newdata <- object$X
insample <- TRUE
}
else {
if (is.data.frame(newdata)) {
# newdata = model.matrix(eval(object$call$formula), newdata)
Terms <- delete.response(tt)
m <- model.frame(Terms,
newdata,
na.action = na.action,
xlev = object$xlevels
)
newdata <- model.matrix(Terms, m,
contrasts.arg = object$contrasts
)
insample <- FALSE
}
else {
stop("use of newdata as a vector is depricated,
please supply newdata as a dataframe")
# if (is.vector(newdata)) newdata=matrix(newdata, nrow=1)
}
}
# browser()
n <- nrow(newdata)
if (ncol(newdata) == object$n.vars) {
newdata <- newdata[, -1, drop = FALSE]
} # drop intercept
if (ncol(newdata) != (object$n.vars - 1)) {
stop("Dimension of newdata does not match orginal model")
}
if (!is.null(object$mean.x)) {
newdata <- sweep(newdata, 2, object$mean.x)
}
df <- object$df
if (estimator == "MPM") {
nvar <- object$n.vars - 1
bestmodel <- (0:nvar)[object$probne0 > .5]
newX <- cbind(1, newdata)
best <- 1
models <- rep(0, nvar + 1)
models[bestmodel + 1] <- 1
if (sum(models) > 1) {
if (is.null(eval(object$call$weights))) {
object <- bas.lm(
eval(object$call$formula),
data = eval(object$call$data, parent.frame()),
n.models = 1,
alpha = object$g,
initprobs = object$probne0,
prior = object$prior,
modelprior = object$modelprior,
update = NULL,
bestmodel = models,
prob.local = .0
)
}
else {
object <- bas.lm(
eval(object$call$formula),
data = eval(object$call$data, parent.frame()),
weights = eval(object$call$weights),
n.models = 1,
alpha = object$g,
initprobs = object$probne0,
prior = object$prior,
modelprior = object$modelprior,
update = NULL,
bestmodel = models,
prob.local = .0
)
}
best <- which.max(object$postprobs)
fit <-
as.vector(newX[, object$which[[best]] + 1, drop = FALSE] %*% object$mle[[best]]) * object$shrinkage[[best]]
fit <- fit + (1 - object$shrinkage[[best]]) * (object$mle[[best]])[1]
df <- df[best]
}
else {
fit <- rep(nrow(newX), 1) * as.numeric(object$mle[object$size == 1])
}
models <- bestmodel
attributes(fit) <- list(
model = models,
best = best,
estimator = estimator
)
Ybma <- fit
Ypred <- NULL
postprobs <- NULL
best <- NULL
df <- object$n - 1
}
else {
if (estimator == "HPM") {
top <- 1
}
postprobs <- object$postprobs
best <- order(-postprobs)
if (!is.null(top)) {
best <- best[1:top]
}
models <- object$which[best]
beta <- object$mle[best]
gg <- object$shrinkage[best]
intercept <- object$intercept[best]
postprobs <- postprobs[best]
postprobs <- postprobs / sum(postprobs)
M <- length(postprobs)
Ypred <- matrix(0, M, n)
# lm case
if (is.null(intercept)) {
for (i in 1:M) {
beta.m <- beta[[i]]
model.m <- models[[i]]
Ypred[i, ] <-
(newdata[, model.m[-1], drop = FALSE] %*% beta.m[-1]) * gg[i] + beta.m[1]
}
}
else {
for (i in 1:M) {
beta.m <- beta[[i]]
model.m <- models[[i]]
Ypred[i, ] <-
(newdata[, model.m[-1], drop = FALSE] %*% beta.m[-1]) * gg[i] + intercept[i]
}
}
df <- df[best]
Ybma <- t(Ypred) %*% postprobs
fit <- as.vector(Ybma)
if (estimator == "HPM") {
models <- unlist(object$which[best])
attributes(fit) <- list(
model = models,
best = best,
estimator = estimator
)
}
if (estimator == "BPM") {
# browser()
dis <- apply(
sweep(Ypred, 2, Ybma),
1,
FUN = function(x) {
x[is.na(x)] <- 0 # ignore NA's in finding closest model
sum(x^2)
}
)
bestBPM <- which.min(dis)
fit <- as.vector(Ypred[bestBPM, ])
models <- unlist(object$which[best[bestBPM]])
best <- best[bestBPM]
df <- df[best]
attributes(fit) <- list(
model = models,
best = best,
estimator = estimator
)
}
}
# browser()
se <- list(
se.fit = NULL,
se.pred = NULL,
se.bma.fit = NULL,
se.bma.pred = NULL
)
if (se.fit) {
if (estimator != "BMA") {
se <- .se.fit(fit, newdata, object, insample)
}
else {
se <- .se.bma(
Ybma, newdata, Ypred, best, object,
insample
)
}
}
best.vars <- object$namesx # BMA case
if (!is.list(models)) {
best.vars <- object$namesx[models + 1]
}
out <- list(
fit = fit,
Ybma = Ybma,
Ypred = Ypred,
postprobs = postprobs,
se.fit = se$se.fit,
se.pred = se$se.pred,
se.bma.fit = se$se.bma.fit,
se.bma.pred = se$se.bma.pred,
df = df,
best = best,
bestmodel = models,
best.vars = best.vars,
estimator = estimator
)
class(out) <- "pred.bas"
return(out)
}
#' Fitted values for a BAS BMA objects
#'
#' Calculate fitted values for a BAS BMA object
#'
#' Calculates fitted values at observed design matrix using either the highest
#' probability model, 'HPM', the posterior mean (under BMA) 'BMA', the median
#' probability model 'MPM' or the best predictive model 'BPM". The median
#' probability model is defined by including variable where the marginal
#' inclusion probability is greater than or equal to 1/2. For type="BMA", the
#' weighted average may be based on using a subset of the highest probability
#' models if an optional argument is given for top. By default BMA uses all
#' sampled models, which may take a while to compute if the number of variables
#' or number of models is large. The "BPM" is found be computing the squared
#' distance of the vector of fitted values for a model and the fitted values
#' under BMA and returns the model with the smallest distance. In the presence
#' of multicollinearity this may be quite different from the MPM, with extreme
#' collinearity may drop relevant predictors.
#'
#' @aliases fitted.bas fitted
#' @param object An object of class 'bas' as created by \code{\link{bas}}
#' @param type type equals "response" or "link" in the case of GLMs (default is 'link')
#' @param estimator estimator type of fitted value to return. Default is to use
#' BMA with all models. Options include \cr 'HPM' the highest probability model
#' \cr 'BMA' Bayesian model averaging, using optionally only the 'top' models
#' \cr 'MPM' the median probability model of Barbieri and Berger. 'BPM' the
#' model that is closest to BMA predictions under squared error loss
#' @param top optional argument specifying that the 'top' models will be used
#' in constructing the BMA prediction, if NULL all models will be used. If
#' top=1, then this is equivalent to 'HPM'
#' @param na.action function determining what should be done with missing values in newdata. The default is to predict NA.
#' @param ... optional arguments, not used currently
#' @return A vector of length n of fitted values.
#' @author Merlise Clyde \email{clyde@duke.edu}
#' @seealso \code{\link{predict.bas}} \code{\link{predict.basglm}}
#' @references Barbieri, M. and Berger, J.O. (2004) Optimal predictive model
#' selection. Annals of Statistics. 32, 870-897. \cr
#' \url{https://projecteuclid.org/euclid.aos/1085408489&url=/UI/1.0/Summarize/euclid.aos/1085408489}
#'
#' Clyde, M. Ghosh, J. and Littman, M. (2010) Bayesian Adaptive Sampling for
#' Variable Selection and Model Averaging. Journal of Computational Graphics
#' and Statistics. 20:80-101 \cr
#' \doi{10.1198/jcgs.2010.09049}
#' @keywords regression
#' @examples
#'
#' data(Hald)
#' hald.gprior = bas.lm(Y~ ., data=Hald, prior="ZS-null", initprobs="Uniform")
#' plot(Hald$Y, fitted(hald.gprior, estimator="HPM"))
#' plot(Hald$Y, fitted(hald.gprior, estimator="BMA", top=3))
#' plot(Hald$Y, fitted(hald.gprior, estimator="MPM"))
#' plot(Hald$Y, fitted(hald.gprior, estimator="BPM"))
#'
#' @rdname fitted
#' @family bas methods
#' @family predict methods
#' @export
fitted.bas <- function(object,
type = "link",
estimator = "BMA",
top = NULL,
na.action = na.pass,
...) {
nmodels <- length(object$which)
X <- object$X
if (is.null(top)) {
top <- nmodels
}
if (estimator == "HPM") {
yhat <- predict(
object,
newdata = NULL,
top = 1,
estimator = "HPM", type = type,
na.action = na.action
)$fit
}
if (estimator == "BMA") {
yhat <- predict(
object,
newdata = NULL,
top = top,
estimator = "BMA", type = type,
na.action = na.action
)$fit
}
if (estimator == "MPM") {
yhat <- predict(
object,
newdata = NULL,
top = top,
estimator = "MPM", type = type,
na.action = na.action
)$fit
}
if (estimator == "BPM") {
yhat <- predict(
object,
newdata = NULL,
top = top,
estimator = "BPM", type = type,
na.action = na.action
)$fit
}
return(as.vector(yhat))
}
.se.fit <- function(yhat, X, object, insample) {
n <- object$n
model <- attr(yhat, "model")
best <- attr(yhat, "best")
df <- object$df[best]
shrinkage <- object$shrinkage[best]
if (insample) {
xiXTXxiT <- hat(object$X[, model + 1]) - 1 / n
} else {
X <- cbind(1, X[, model[-1], drop = FALSE])
oldX <- (sweep(object$X[, -1], 2, object$mean.x))[, model[-1]]
# browser()
XRinv <- X %*% solve(qr.R(qr(cbind(1, oldX))))
xiXTXxiT <- apply(XRinv^2, 1, sum) - 1 / n
}
scale_fit <- 1 / n + object$shrinkage[best] * xiXTXxiT
if (is.null(object$family)) {
family <- gaussian()
}
if (eval(family)$family == "gaussian") {
ssy <- var(object$Y) * (n - 1)
bayes_mse <- ssy * (1 - shrinkage * object$R2[best]) / df
}
else {
bayes_mse <- 1
} # ToDo add overdispersion
se.fit <- sqrt(bayes_mse * scale_fit)
se.pred <- sqrt(bayes_mse * (1 + scale_fit))
return(list(
se.fit = se.fit,
se.pred = se.pred,
residual.scale = sqrt(bayes_mse)
))
}
.se.bma <- function(fit, Xnew, Ypred, best, object, insample) {
n <- object$n
df <- object$df[best]
shrinkage <- object$shrinkage[best]
if (insample) {
xiXTXxiT <- sapply(
object$which[best],
FUN = function(model, X) {
n <- nrow(X)
hat(X[, model[-1] + 1]) - 1 / n
},
object$X
)
}
else {
Xnew <- cbind(1, Xnew)
Xold <- cbind(1, sweep(object$X[, -1], 2, object$mean.x))
xiXTXxiT <- sapply(
object$which[best],
FUN = function(model, Xnew, Xold) {
Xnew <- Xnew[, model + 1]
oldX <- Xold[, model + 1]
n <- nrow(Xold)
XRinv <- Xnew %*% solve(qr.R(qr(oldX)))
xiXTXxiT <- apply(XRinv^2, 1, sum) - 1 / n
},
Xnew,
Xold
)
}
ssy <- var(object$Y) * (n - 1)
bayes_mse <- ssy * (1 - shrinkage * object$R2[best]) / df
if (is.vector(xiXTXxiT)) {
xiXTXxiT <- matrix(xiXTXxiT, nrow = 1)
}
scale_fit <- 1 / n + sweep(xiXTXxiT, 2, shrinkage, FUN = "*")
var.fit <- sweep(scale_fit, 2, bayes_mse, FUN = "*")
var.pred <- sweep((1 + scale_fit), 2, bayes_mse, FUN = "*")
postprobs <- object$postprobs[best]
# expected variance
evar.fit <- as.vector(var.fit %*% postprobs)
evar.pred <- as.vector(var.pred %*% postprobs)
# variance of expectations
var.efit <- as.vector(postprobs %*% (sweep(Ypred, 2, fit))^2)
se.fit <- sqrt(evar.fit + var.efit)
se.pred <- sqrt(evar.pred + var.efit)
return(
list(
se.bma.fit = se.fit,
se.bma.pred = se.pred,
se.fit = t(sqrt(var.fit)),
se.pred = t(sqrt(var.pred)),
residual.scale = sqrt(bayes_mse)
)
)
}
#' Extract the variable names for a model from a BAS prediction object
#'
#' @description S3 method for class 'pred.bas'. Simple utility
#' function to extract the variable names. Used to print names
#' for the selected models using estimators for 'HPM', 'MPM' or 'BPM".
#' for the selected model created by \code{predict} for BAS
#' objects.
#' @param object a BAS object created by \code{predict} from a BAS
#' `bas.lm` or `bas.glm` object
#' @param ... other arguments to pass on
#' @return a character vector with the names of the variables
#' included in the selected model; in the case of 'BMA' this will
#' be all variables
#' @seealso \code{\link{predict.bas}}
#' @method variable.names pred.bas
#' @rdname variable.names.pred.bas
#' @aliases variable.names.pred.bas variable.names
#' @family predict methods
#' @family bas methods
#' @examples
#' data(Hald)
#' hald.gprior = bas.lm(Y~ ., data=Hald, prior="ZS-null", modelprior=uniform())
#' hald.bpm = predict(hald.gprior, newdata=Hald[1,],
#' se.fit=TRUE,
#' estimator="BPM")
#' variable.names(hald.bpm)
#' @export
#'
variable.names.pred.bas <- function(object, ...) {
if (inherits(object, "pred.bas")) {
object$best.vars
}
}
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Defines functions variable.names.pred.bas .se.bma .se.fit fitted.bas predict.bas predict.basglm
Documented in fitted.bas predict.bas predict.basglm variable.names.pred.bas
#' Prediction Method for an Object of Class basglm
#' @description Predictions under model averaging from a BMA (BAS) object for GLMs
#' under different loss functions.
#' @aliases predict.basglm
#' @param object An object of class "basglm", created by \code{bas.glm}
#' @param newdata dataframe, new matrix or vector of data for predictions. May
#' include a column for the intercept or just the predictor variables. If a
#' dataframe, the variables are extracted using model.matrix using the call
#' that created 'object'. May be missing in which case the data used for
#' fitting will be used for prediction.
#' @param se.fit indicator for whether to compute se of fitted and predicted
#' values
#' @param type Type of predictions required. The default is "response" is on the scale of the
#' response variable, with the alternative being on the linear predictor
#' scale, `type ='link'`. Thus for a default binomial model
#' `type = 'response'` gives
#' the predicted probabilities, while with `'link'`, the estimates
#' are of log-odds (probabilities on logit scale).
#' @param top A scalar integer M. If supplied, calculate results using the subset of the top M models
#' based on posterior probabilities.
#' @param estimator estimator used for predictions. Currently supported
#' options include: \cr 'HPM' the highest probability model \cr 'BMA' Bayesian
#' model averaging, using optionally only the 'top' models \cr 'MPM' the median
#' probability model of Barbieri and Berger. \cr 'BPM' the model that is
#' closest to BMA predictions under squared error loss. BMA may be computed
#' using only the 'top' models if supplied
#' @param na.action function determining what should be done with missing values in newdata.
#' The default is to predict NA.
#' @param ... optional extra arguments
#' @return a list of
#' \item{fit}{predictions using BMA or other estimators}
#' \item{Ypred}{matrix of predictions under model(s)}
#' \item{postprobs}{renormalized probabilities of
#' the top models}
#' \item{best}{index of top models included}
#' @details This function first calls the predict method for class bas
#' (linear models) to form predictions on the linear predictor
#' scale for `BMA`, `HPM`, `MPM` etc. If the estimator is `BMA`
#' and `type='response'` then the
#' inverse link is applied to fitted values for type equal `'link'`
#' and model averaging takes place in the `response` scale. Thus applying
#' the inverse link to BMA estimate with `type = 'link'` is
#' not equal to the fitted values for `type = 'response'` under
#' BMA due to the nonlinear transformation under the inverse link.
#'
#' @author Merlise Clyde
#' @seealso \code{\link{bas.glm}}, \code{\link{predict.bas}},
#' \code{\link{fitted.bas}}
#' @keywords regression
#' @examples
#'
#'
#' data(Pima.tr, package="MASS")
#' data(Pima.te, package="MASS")
#' Pima.bas = bas.glm(type ~ ., data=Pima.tr, n.models= 2^7, method="BAS",
#' betaprior=CCH(a=1, b=nrow(Pima.tr)/2, s=0), family=binomial(),
#' modelprior=uniform())
#' pred = predict(Pima.bas, newdata=Pima.te, top=1) # Highest Probability model
#' cv.summary.bas(pred$fit, Pima.te$type, score="miss-class")
#'
#' @rdname predict.basglm
#' @family predict methods
#' @family bas methods
#' @export
predict.basglm <- function(object,
newdata,
se.fit = FALSE,
type = c("response", "link"),
top = NULL,
estimator = "BMA",
na.action = na.pass,
...) {
# browser()
if (estimator == "HPM") {
top <- 1
}
# get predictions on linear predictor scale
pred <- predict.bas(
object,
newdata = newdata,
se.fit = se.fit,
top = top,
estimator = estimator,
na.action = na.action,
...
)
if (length(type) > 1) {
type <- type[1]
}
#
# if type is 'link' do not need to do anything; just return
# pred at end
#
if (type == "response") {
model.specs <- attributes(pred$fit)
if (estimator == "BMA") {
Ypred <- apply(
pred$Ypred,
1,
FUN = function(x) {
eval(object$family)$linkinv(x)
}
)
if (length(pred$postprobs) > 1) {
fit <- as.vector(Ypred %*% pred$postprobs)
} else {
fit <- as.vector(Ypred)
}
}
else {
fit <- eval(object$family)$linkinv(pred$fit)
}
attributes(fit) <- model.specs
# replace predictions
#
pred$fit <- fit
if (se.fit) {
se.fit <- pred$se.fit * abs(eval(object$family)$mu.eta(pred$fit))
se.pred <- pred$se.pred * abs(eval(object$family)$mu.eta(pred$fit))
pred$se.fit <- se.fit
pred$se.pred <- se.pred
}
}
return(pred)
}
#' Prediction Method for an object of class BAS
#'
#' Predictions under model averaging or other estimators from a BMA object of
#' class inheriting from 'bas'.
#'
#' Use BMA and/or model selection to form predictions using the top highest
#' probability models.
#'
#' @aliases predict.bas predict
#' @param object An object of class BAS, created by \code{bas}
#' @param newdata dataframe for predictions. If missing, then use the dataframe
#' used for fitting for obtaining fitted and predicted values.
#' @param se.fit indicator for whether to compute se of fitted and predicted
#' values
#' @param type Type of predictions required. "link" which is on the scale of
#' the linear predictor is the only option currently for linear models, which for the normal model
#' is equivalent to type='response'.
#' @param top a scalar integer M. If supplied, subset the top M models, based
#' on posterior probabilities for model predictions and BMA.
#' @param estimator estimator used for predictions. Currently supported
#' options include: \cr 'HPM' the highest probability model \cr 'BMA' Bayesian
#' model averaging, using optionally only the 'top' models \cr 'MPM' the median
#' probability model of Barbieri and Berger. \cr 'BPM' the model that is
#' closest to BMA predictions under squared error loss. BMA may be computed
#' using only the 'top' models if supplied
#' @param na.action function determining what should be done with missing values in newdata.
#' The default is to predict NA.
#' @param ... optional extra arguments
#' @return a list of
#' \item{fit}{fitted values based on the selected estimator}
#' \item{Ybma}{predictions using BMA, the same as fit for non-BMA methods for
#' compatibility; will be deprecated}
#' \item{Ypred}{matrix of predictions under
#' each model for BMA}
#' \item{se.fit}{se of fitted values; in the case of BMA
#' this will be a matrix}
#' \item{se.pred}{se for predicted values; in the case
#' of BMA this will be a matrix}
#' \item{se.bma.fit}{vector of posterior sd under
#' BMA for posterior mean of the regression function.
#' This will be NULL if estimator is not 'BMA'}
#' \item{se.bma.pred}{vector of posterior sd under BMA
#' for posterior predictive values. this will be NULL if estimator is not
#' 'BMA'}
#' \item{best}{index of top models included}
#' \item{bestmodels}{subset of
#' bestmodels used for fitting or prediction}
#' \item{best.vars}{names of variables in the top model; NULL if estimator='BMA'}
#' \item{df}{scalar or vector of
#' degrees of freedom for models}
#' \item{estimator}{estimator upon which 'fit'
#' is based.}
#' @author Merlise Clyde
#' @seealso \code{\link{bas}}, \code{\link{fitted.bas}},
#' \code{\link{confint.pred.bas}}, \code{\link{variable.names.pred.bas}}
#' @keywords regression
#' @examples
#'
#' data("Hald")
#' hald.gprior = bas.lm(Y ~ ., data=Hald, alpha=13, prior="g-prior")
#'
#' predict(hald.gprior, newdata=Hald, estimator="BPM", se.fit=TRUE)
#' # same as fitted
#' fitted(hald.gprior,estimator="BPM")
#' # default is BMA and estimation of mean vector
#' hald.bma = predict(hald.gprior, top=5, se.fit=TRUE)
#' confint(hald.bma)
#'
#' hald.bpm = predict(hald.gprior, newdata=Hald[1,],
#' se.fit=TRUE,
#' estimator="BPM")
#' confint(hald.bpm)
#' # extract variables
#' variable.names(hald.bpm)
#'
#' hald.hpm = predict(hald.gprior, newdata=Hald[1,],
#' se.fit=TRUE,
#' estimator="HPM")
#' confint(hald.hpm)
#' variable.names(hald.hpm)
#'
#' hald.mpm = predict(hald.gprior, newdata=Hald[1,],
#' se.fit=TRUE,
#' estimator="MPM")
#' confint(hald.mpm)
#' variable.names(hald.mpm)
#'
#' @rdname predict.bas
#' @family predict methods
#' @family bas methods
#' @export
predict.bas <- function(object,
newdata,
se.fit = FALSE,
type = "link",
top = NULL,
estimator = "BMA",
na.action = na.pass,
...) {
if (!(estimator %in% c("BMA", "HPM", "MPM", "BPM"))) {
stop("Estimator must be one of 'BMA', 'BPM', 'HPM', or 'MPM'.")
}
tt <- terms(object)
if (missing(newdata) || is.null(newdata)) {
newdata <- object$X
insample <- TRUE
}
else {
if (is.data.frame(newdata)) {
# newdata = model.matrix(eval(object$call$formula), newdata)
Terms <- delete.response(tt)
m <- model.frame(Terms,
newdata,
na.action = na.action,
xlev = object$xlevels
)
newdata <- model.matrix(Terms, m,
contrasts.arg = object$contrasts
)
insample <- FALSE
}
else {
stop("use of newdata as a vector is depricated,
please supply newdata as a dataframe")
# if (is.vector(newdata)) newdata=matrix(newdata, nrow=1)
}
}
# browser()
n <- nrow(newdata)
if (ncol(newdata) == object$n.vars) {
newdata <- newdata[, -1, drop = FALSE]
} # drop intercept
if (ncol(newdata) != (object$n.vars - 1)) {
stop("Dimension of newdata does not match orginal model")
}
if (!is.null(object$mean.x)) {
newdata <- sweep(newdata, 2, object$mean.x)
}
df <- object$df
if (estimator == "MPM") {
nvar <- object$n.vars - 1
bestmodel <- (0:nvar)[object$probne0 > .5]
newX <- cbind(1, newdata)
best <- 1
models <- rep(0, nvar + 1)
models[bestmodel + 1] <- 1
if (sum(models) > 1) {
if (is.null(eval(object$call$weights))) {
object <- bas.lm(
eval(object$call$formula),
data = eval(object$call$data, parent.frame()),
n.models = 1,
alpha = object$g,
initprobs = object$probne0,
prior = object$prior,
modelprior = object$modelprior,
update = NULL,
bestmodel = models,
prob.local = .0
)
}
else {
object <- bas.lm(
eval(object$call$formula),
data = eval(object$call$data, parent.frame()),
weights = eval(object$call$weights),
n.models = 1,
alpha = object$g,
initprobs = object$probne0,
prior = object$prior,
modelprior = object$modelprior,
update = NULL,
bestmodel = models,
prob.local = .0
)
}
best <- which.max(object$postprobs)
fit <-
as.vector(newX[, object$which[[best]] + 1, drop = FALSE] %*% object$mle[[best]]) * object$shrinkage[[best]]
fit <- fit + (1 - object$shrinkage[[best]]) * (object$mle[[best]])[1]
df <- df[best]
}
else {
fit <- rep(nrow(newX), 1) * as.numeric(object$mle[object$size == 1])
}
models <- bestmodel
attributes(fit) <- list(
model = models,
best = best,
estimator = estimator
)
Ybma <- fit
Ypred <- NULL
postprobs <- NULL
best <- NULL
df <- object$n - 1
}
else {
if (estimator == "HPM") {
top <- 1
}
postprobs <- object$postprobs
best <- order(-postprobs)
if (!is.null(top)) {
best <- best[1:top]
}
models <- object$which[best]
beta <- object$mle[best]
gg <- object$shrinkage[best]
intercept <- object$intercept[best]
postprobs <- postprobs[best]
postprobs <- postprobs / sum(postprobs)
M <- length(postprobs)
Ypred <- matrix(0, M, n)
# lm case
if (is.null(intercept)) {
for (i in 1:M) {
beta.m <- beta[[i]]
model.m <- models[[i]]
Ypred[i, ] <-
(newdata[, model.m[-1], drop = FALSE] %*% beta.m[-1]) * gg[i] + beta.m[1]
}
}
else {
for (i in 1:M) {
beta.m <- beta[[i]]
model.m <- models[[i]]
Ypred[i, ] <-
(newdata[, model.m[-1], drop = FALSE] %*% beta.m[-1]) * gg[i] + intercept[i]
}
}
df <- df[best]
Ybma <- t(Ypred) %*% postprobs
fit <- as.vector(Ybma)
if (estimator == "HPM") {
models <- unlist(object$which[best])
attributes(fit) <- list(
model = models,
best = best,
estimator = estimator
)
}
if (estimator == "BPM") {
# browser()
dis <- apply(
sweep(Ypred, 2, Ybma),
1,
FUN = function(x) {
x[is.na(x)] <- 0 # ignore NA's in finding closest model
sum(x^2)
}
)
bestBPM <- which.min(dis)
fit <- as.vector(Ypred[bestBPM, ])
models <- unlist(object$which[best[bestBPM]])
best <- best[bestBPM]
df <- df[best]
attributes(fit) <- list(
model = models,
best = best,
estimator = estimator
)
}
}
# browser()
se <- list(
se.fit = NULL,
se.pred = NULL,
se.bma.fit = NULL,
se.bma.pred = NULL
)
if (se.fit) {
if (estimator != "BMA") {
se <- .se.fit(fit, newdata, object, insample)
}
else {
se <- .se.bma(
Ybma, newdata, Ypred, best, object,
insample
)
}
}
best.vars <- object$namesx # BMA case
if (!is.list(models)) {
best.vars <- object$namesx[models + 1]
}
out <- list(
fit = fit,
Ybma = Ybma,
Ypred = Ypred,
postprobs = postprobs,
se.fit = se$se.fit,
se.pred = se$se.pred,
se.bma.fit = se$se.bma.fit,
se.bma.pred = se$se.bma.pred,
df = df,
best = best,
bestmodel = models,
best.vars = best.vars,
estimator = estimator
)
class(out) <- "pred.bas"
return(out)
}
#' Fitted values for a BAS BMA objects
#'
#' Calculate fitted values for a BAS BMA object
#'
#' Calculates fitted values at observed design matrix using either the highest
#' probability model, 'HPM', the posterior mean (under BMA) 'BMA', the median
#' probability model 'MPM' or the best predictive model 'BPM". The median
#' probability model is defined by including variable where the marginal
#' inclusion probability is greater than or equal to 1/2. For type="BMA", the
#' weighted average may be based on using a subset of the highest probability
#' models if an optional argument is given for top. By default BMA uses all
#' sampled models, which may take a while to compute if the number of variables
#' or number of models is large. The "BPM" is found be computing the squared
#' distance of the vector of fitted values for a model and the fitted values
#' under BMA and returns the model with the smallest distance. In the presence
#' of multicollinearity this may be quite different from the MPM, with extreme
#' collinearity may drop relevant predictors.
#'
#' @aliases fitted.bas fitted
#' @param object An object of class 'bas' as created by \code{\link{bas}}
#' @param type type equals "response" or "link" in the case of GLMs (default is 'link')
#' @param estimator estimator type of fitted value to return. Default is to use
#' BMA with all models. Options include \cr 'HPM' the highest probability model
#' \cr 'BMA' Bayesian model averaging, using optionally only the 'top' models
#' \cr 'MPM' the median probability model of Barbieri and Berger. 'BPM' the
#' model that is closest to BMA predictions under squared error loss
#' @param top optional argument specifying that the 'top' models will be used
#' in constructing the BMA prediction, if NULL all models will be used. If
#' top=1, then this is equivalent to 'HPM'
#' @param na.action function determining what should be done with missing values in newdata. The default is to predict NA.
#' @param ... optional arguments, not used currently
#' @return A vector of length n of fitted values.
#' @author Merlise Clyde \email{clyde@duke.edu}
#' @seealso \code{\link{predict.bas}} \code{\link{predict.basglm}}
#' @references Barbieri, M. and Berger, J.O. (2004) Optimal predictive model
#' selection. Annals of Statistics. 32, 870-897. \cr
#' \url{https://projecteuclid.org/euclid.aos/1085408489&url=/UI/1.0/Summarize/euclid.aos/1085408489}
#'
#' Clyde, M. Ghosh, J. and Littman, M. (2010) Bayesian Adaptive Sampling for
#' Variable Selection and Model Averaging. Journal of Computational Graphics
#' and Statistics. 20:80-101 \cr
#' \doi{10.1198/jcgs.2010.09049}
#' @keywords regression
#' @examples
#'
#' data(Hald)
#' hald.gprior = bas.lm(Y~ ., data=Hald, prior="ZS-null", initprobs="Uniform")
#' plot(Hald$Y, fitted(hald.gprior, estimator="HPM"))
#' plot(Hald$Y, fitted(hald.gprior, estimator="BMA", top=3))
#' plot(Hald$Y, fitted(hald.gprior, estimator="MPM"))
#' plot(Hald$Y, fitted(hald.gprior, estimator="BPM"))
#'
#' @rdname fitted
#' @family bas methods
#' @family predict methods
#' @export
fitted.bas <- function(object,
type = "link",
estimator = "BMA",
top = NULL,
na.action = na.pass,
...) {
nmodels <- length(object$which)
X <- object$X
if (is.null(top)) {
top <- nmodels
}
if (estimator == "HPM") {
yhat <- predict(
object,
newdata = NULL,
top = 1,
estimator = "HPM", type = type,
na.action = na.action
)$fit
}
if (estimator == "BMA") {
yhat <- predict(
object,
newdata = NULL,
top = top,
estimator = "BMA", type = type,
na.action = na.action
)$fit
}
if (estimator == "MPM") {
yhat <- predict(
object,
newdata = NULL,
top = top,
estimator = "MPM", type = type,
na.action = na.action
)$fit
}
if (estimator == "BPM") {
yhat <- predict(
object,
newdata = NULL,
top = top,
estimator = "BPM", type = type,
na.action = na.action
)$fit
}
return(as.vector(yhat))
}
.se.fit <- function(yhat, X, object, insample) {
n <- object$n
model <- attr(yhat, "model")
best <- attr(yhat, "best")
df <- object$df[best]
shrinkage <- object$shrinkage[best]
if (insample) {
xiXTXxiT <- hat(object$X[, model + 1]) - 1 / n
} else {
X <- cbind(1, X[, model[-1], drop = FALSE])
oldX <- (sweep(object$X[, -1], 2, object$mean.x))[, model[-1]]
# browser()
XRinv <- X %*% solve(qr.R(qr(cbind(1, oldX))))
xiXTXxiT <- apply(XRinv^2, 1, sum) - 1 / n
}
scale_fit <- 1 / n + object$shrinkage[best] * xiXTXxiT
if (is.null(object$family)) {
family <- gaussian()
}
if (eval(family)$family == "gaussian") {
ssy <- var(object$Y) * (n - 1)
bayes_mse <- ssy * (1 - shrinkage * object$R2[best]) / df
}
else {
bayes_mse <- 1
} # ToDo add overdispersion
se.fit <- sqrt(bayes_mse * scale_fit)
se.pred <- sqrt(bayes_mse * (1 + scale_fit))
return(list(
se.fit = se.fit,
se.pred = se.pred,
residual.scale = sqrt(bayes_mse)
))
}
.se.bma <- function(fit, Xnew, Ypred, best, object, insample) {
n <- object$n
df <- object$df[best]
shrinkage <- object$shrinkage[best]
if (insample) {
xiXTXxiT <- sapply(
object$which[best],
FUN = function(model, X) {
n <- nrow(X)
hat(X[, model[-1] + 1]) - 1 / n
},
object$X
)
}
else {
Xnew <- cbind(1, Xnew)
Xold <- cbind(1, sweep(object$X[, -1], 2, object$mean.x))
xiXTXxiT <- sapply(
object$which[best],
FUN = function(model, Xnew, Xold) {
Xnew <- Xnew[, model + 1]
oldX <- Xold[, model + 1]
n <- nrow(Xold)
XRinv <- Xnew %*% solve(qr.R(qr(oldX)))
xiXTXxiT <- apply(XRinv^2, 1, sum) - 1 / n
},
Xnew,
Xold
)
}
ssy <- var(object$Y) * (n - 1)
bayes_mse <- ssy * (1 - shrinkage * object$R2[best]) / df
if (is.vector(xiXTXxiT)) {
xiXTXxiT <- matrix(xiXTXxiT, nrow = 1)
}
scale_fit <- 1 / n + sweep(xiXTXxiT, 2, shrinkage, FUN = "*")
var.fit <- sweep(scale_fit, 2, bayes_mse, FUN = "*")
var.pred <- sweep((1 + scale_fit), 2, bayes_mse, FUN = "*")
postprobs <- object$postprobs[best]
# expected variance
evar.fit <- as.vector(var.fit %*% postprobs)
evar.pred <- as.vector(var.pred %*% postprobs)
# variance of expectations
var.efit <- as.vector(postprobs %*% (sweep(Ypred, 2, fit))^2)
se.fit <- sqrt(evar.fit + var.efit)
se.pred <- sqrt(evar.pred + var.efit)
return(
list(
se.bma.fit = se.fit,
se.bma.pred = se.pred,
se.fit = t(sqrt(var.fit)),
se.pred = t(sqrt(var.pred)),
residual.scale = sqrt(bayes_mse)
)
)
}
#' Extract the variable names for a model from a BAS prediction object
#'
#' @description S3 method for class 'pred.bas'. Simple utility
#' function to extract the variable names. Used to print names
#' for the selected models using estimators for 'HPM', 'MPM' or 'BPM".
#' for the selected model created by \code{predict} for BAS
#' objects.
#' @param object a BAS object created by \code{predict} from a BAS
#' `bas.lm` or `bas.glm` object
#' @param ... other arguments to pass on
#' @return a character vector with the names of the variables
#' included in the selected model; in the case of 'BMA' this will
#' be all variables
#' @seealso \code{\link{predict.bas}}
#' @method variable.names pred.bas
#' @rdname variable.names.pred.bas
#' @aliases variable.names.pred.bas variable.names
#' @family predict methods
#' @family bas methods
#' @examples
#' data(Hald)
#' hald.gprior = bas.lm(Y~ ., data=Hald, prior="ZS-null", modelprior=uniform())
#' hald.bpm = predict(hald.gprior, newdata=Hald[1,],
#' se.fit=TRUE,
#' estimator="BPM")
#' variable.names(hald.bpm)
#' @export
#'
variable.names.pred.bas <- function(object, ...) {
if (inherits(object, "pred.bas")) {
object$best.vars
}
}
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