moose {moose}

moose: mean squared out-of-sample error projection

Description

This function projects the mean squared out-of-sample error for a linear regression

Usage

moose(reg, dataset)

Arguments

reg

an lm object containing the regression to project out-of-sample

dataset

a data.frame containing new cases for out-of-sample projection

Value

mse

Projected mean squared out-of-sample error

R2o

Projected out-of-sample R-squared

hat

Leverage for each out-of-sample observation. For each i, this is the sum of the squared elements of xi [X'X]^-1 X', where X is the predictor matrix from the training sample.

Examples

# set the seed for reproducibility of the example
set.seed(04251978)
# randomly generate 100 observations of data
mydata <- data.frame(x1=rnorm(100),x2=rnorm(100),x3=rnorm(100))
# true outcome variable is y = x1 + x2 + x3 + e
y <- mydata$x1 + mydata$x2 + mydata$x3 + rnorm(100)
# regression with the first 25 observations from the dataset
reg <- lm(y ~ x1 + x2 + x3,data=cbind(y,mydata)[1:25,])
# using the predictor values from the first 25 observations,
# project the out-of-sample error we can expect in the case of
# "non-stochastic" predictors whose values are the same in the
# test sample as in the training sample.
# note that mydata does not include the outcome variable.
same.predictor.values.error <- moose(reg,mydata[1:25,])
# by comparison, the in-sample R-squared value observed
# in training is:
summary(reg)$r.squared
# using the predictor values from the next 75 obsevervations,
# project the out-of-sample error we can expect in the case
# of stochastic predictors whose values potentially differ
# from those used in training.
new.predictor.values.error <- moose(reg,mydata[26:100,])
# by comparison, the actual mse and out-of-sample R-squared value
# obtained from observations 26-100 of this random sample are:
mse <- mean((y[26:100]-predict(reg,mydata[26:100,]))^2)
mse
m.total.sqs <- mean((y[26:100]-mean(y[26:100]))^2)
r2o <- 1-mse/m.total.sqs
r2o