linear_projection: Linear Projection

In VSdecomp: Variance and Skewness Decomposition

Description

estimates the linear model y = β*X + ε and returns its linear components, grouped according to X.list.

Usage

linear_projection(
  y,
  X.list,
  data,
  wgt = rep(1, nrow(data)),
  year = rep(1, nrow(data)),
  comp.names = NULL
)

Arguments

y	a character specifying the name of the outcome variable (e.g. "wage"). Note that this variable is standardized before it's projected onto X.
X.list	a list containing the names of all the variables needed for the linear projection, grouped according to the components will later be used in the skewness decomposition. For example: for X.list = list("x1", c("x2", "x3")) the following components are returned: β1X1, (β2X2+ β3X3), ε. Currently interactions aren't supported, so the user should insert them manually.
data	a data frame with all the variables specified in X.list and y.
wgt	an optional vector of weights.
year	an optional vector of years. if provided, the projection is done for each year separately.
comp.names	an optional vector specifying name for each component.

Value

a matrix with the (centered) components specified by X.list + residuals. Note that each row is summed (up to a constant) to the standardized version of y, and each column to 0 (both by year).

Examples

#gen data
n <- 1000
X <- matrix(rnorm(n*3), ncol = 3)
colnames(X) <- c("x1", "x2", "x3")
beta <- c(1,2,3)
wage <- X %*% beta + rnorm(n)
dat <- as.data.frame(cbind(wage, X))
colnames(dat)[1] <- "wage"
res <- linear_projection("wage", X.list = list("x1", c("x2", "x3")), data = dat)
#each row is summed (up to a constant) to the standardized wage:
stand_wage <- (wage - mean(wage)) / sd(wage)
diff <- apply(res, 1, sum) - stand_wage
summary(diff)

VSdecomp documentation built on May 18, 2021, 9:06 a.m.