| Title: | Mean Squared Out-of-Sample Error Projection |
| Version: | 0.0.1 |
| Description: | Projects mean squared out-of-sample error for a linear regression based upon the methodology developed in Rohlfs (2022) <doi:10.48550/arXiv.2209.01493>. It consumes as inputs the lm object from an estimated OLS regression (based on the "training sample") and a data.frame of out-of-sample cases (the "test sample") that have non-missing values for the same predictors. The test sample may or may not include data on the outcome variable; if it does, that variable is not used. The aim of the exercise is to project what what mean squared out-of-sample error can be expected given the predictor values supplied in the test sample. Output consists of a list of three elements: the projected mean squared out-of-sample error, the projected out-of-sample R-squared, and a vector of out-of-sample "hat" or "leverage" values, as defined in the paper. |
| License: | MIT + file LICENSE |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.2.1 |
| NeedsCompilation: | no |
| Packaged: | 2022-09-09 00:07:54 UTC; chris |
| Author: | Chris Rohlfs 
[aut, cre] |
| Maintainer: | Chris Rohlfs <car2228@columbia.edu> |
| Repository: | CRAN |
| Date/Publication: | 2022-09-09 08:20:02 UTC |
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