K-Conditional-Means Estimator

Implementation of the K-Conditional-Means estimator.

Usage

kcmeans(y, X, which_is_cat = 1, K = 2)

Arguments

y

The outcome variable, a numerical vector.

X

A (sparse) feature matrix where one column is the categorical predictor.

which_is_cat

An integer indicating which column of X corresponds to the categorical predictor.

K

The number of support points, an integer greater than 2.

Value

kcmeans returns an object of S3 class kcmeans. An object of class kcmeans is a list containing the following components:

cluster_map

A matrix that characterizes the estimated predictor of the residualized outcome \(\tilde{Y} \equiv Y - X_{2:}^\top \hat{\pi}\). The first column x denotes the value of the categorical variable that corresponds to the unrestricted sample mean mean_x of \(\tilde{Y}\), the sample share p_x, the estimated cluster cluster_x, and the estimated restricted sample mean mean_xK of \(\tilde{Y}\) with just K support points.

mean_y

The unconditional sample mean of \(\tilde{Y}\).

pi

The best linear prediction coefficients of \(Y\) on \(X\) corresponding to the non-categorical predictors \(X_{2:}\).

which_is_cat,K

Passthrough of user-provided arguments. See above for details.

References

Wang H and Song M (2011). "Ckmeans.1d.dp: optimal k-means clustering in one dimension by dynamic programming." The R Journal 3(2), 29--33.

Wiemann T (2023). "Optimal Categorical Instruments." https://arxiv.org/abs/2311.17021

Examples

# Simulate simple dataset with n=800 observations
X <- rnorm(800) # continuous predictor
Z <- sample(1:20, 800, replace = TRUE) # categorical predictor
Z0 <- Z %% 4 # lower-dimensional latent categorical variable
y <- Z0 + X + rnorm(800) # outcome
# Compute kcmeans with four support points
kcmeans_fit <- kcmeans(y, cbind(Z, X), K = 4)
# Print the estimated support points of the categorical predictor
print(unique(kcmeans_fit$cluster_map[, "mean_xK"]))
#> [1]  0.8919541  1.9124459  3.1148056 -0.1195223