Predict from a sequence of regression models

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Description

Make predictions from a sequence of regression models, such as submodels along a robust or groupwise least angle regression sequence, or sparse least trimmed squares regression models for a grid of values for the penalty parameter. For autoregressive time series models with exogenous inputs, h-step ahead forecasts are performed.

Usage

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## S3 method for class 'seqModel'
predict(object, newdata, s = NA, ...)

## S3 method for class 'tslarsP'
predict(object, newdata, ...)

## S3 method for class 'tslars'
predict(object, newdata, p, ...)

## S3 method for class 'sparseLTS'
predict(object, newdata, s = NA, fit = c("reweighted",
  "raw", "both"), ...)

Arguments

object

the model fit from which to make predictions.

newdata

new data for the predictors. If the model fit was computed with the formula method, this should be a data frame from which to extract the predictor variables. Otherwise this should be a matrix containing the same variables as the predictor matrix used to fit the model (including a column of ones to account for the intercept).

s

for the "seqModel" method, an integer vector giving the steps of the submodels for which to make predictions (the default is to use the optimal submodel). For the "sparseLTS" method, an integer vector giving the indices of the models for which to make predictions. If fit is "both", this can be a list with two components, with the first component giving the indices of the reweighted fits and the second the indices of the raw fits. The default is to use the optimal model for each of the requested estimators. Note that the optimal models may not correspond to the same value of the penalty parameter for the reweighted and the raw estimator.

p

an integer giving the lag length for which to make predictions (the default is to use the optimal lag length).

fit

a character string specifying for which fit to make predictions. Possible values are "reweighted" (the default) for predicting values from the reweighted fit, "raw" for predicting values from the raw fit, or "both" for predicting values from both fits.

...

for the "tslars" method, additional arguments to be passed down to the "tslarsP" method. For the other methods, additional arguments to be passed down to the respective method of coef.

Details

The newdata argument defaults to the matrix of predictors used to fit the model such that the fitted values are computed.

For autoregressive time series models with exogenous inputs with forecast horizon h, the h most recent observations of the predictors are omitted from fitting the model since there are no corresponding values for the response. Hence the newdata argument for predict.tslarsP and predict.tslars defaults to those h observations of the predictors.

Value

A numeric vector or matrix containing the requested predicted values.

Author(s)

Andreas Alfons

See Also

predict, rlars, grplars, rgrplars, tslarsP, rtslarsP, tslars, rtslars, sparseLTS

Examples

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## generate data
# example is not high-dimensional to keep computation time low
library("mvtnorm")
set.seed(1234)  # for reproducibility
n <- 100  # number of observations
p <- 25   # number of variables
beta <- rep.int(c(1, 0), c(5, p-5))  # coefficients
sigma <- 0.5      # controls signal-to-noise ratio
epsilon <- 0.1    # contamination level
Sigma <- 0.5^t(sapply(1:p, function(i, j) abs(i-j), 1:p))
x <- rmvnorm(n, sigma=Sigma)    # predictor matrix
e <- rnorm(n)                   # error terms
i <- 1:ceiling(epsilon*n)       # observations to be contaminated
e[i] <- e[i] + 5                # vertical outliers
y <- c(x %*% beta + sigma * e)  # response
x[i,] <- x[i,] + 5              # bad leverage points


## robust LARS
# fit model
fitRlars <- rlars(x, y, sMax = 10)
# compute fitted values via predict method
predict(fitRlars)
head(predict(fitRlars, s = 1:5))


## sparse LTS over a grid of values for lambda
# fit model
frac <- seq(0.2, 0.05, by = -0.05)
fitSparseLTS <- sparseLTS(x, y, lambda = frac, mode = "fraction")
# compute fitted values via predict method
predict(fitSparseLTS)
head(predict(fitSparseLTS, fit = "both"))
head(predict(fitSparseLTS, s = NULL))
head(predict(fitSparseLTS, fit = "both", s = NULL))

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