Find X Matrix and Y Vector for Residual Surrealism

This function implements the Residual (Sur)Realism algorithm as described by Leonard A. Stefanski (2007). It finds a matrix X and vector y such that the fitted values and residuals of lm(y ~ X) are similar to the inputs y_hat and R_0.

Usage

surreal(
  data,
  y_hat = data[, 1],
  R_0 = data[, 2],
  R_squared = 0.3,
  p = 5,
  n_add_points = 40,
  max_iter = 100,
  tolerance = 0.01,
  verbose = FALSE
)

Arguments

data

A data frame or matrix with two columns representing the y_hat and R_0 values.

y_hat

Numeric vector of desired fitted values (only used if data is not provided).

R_0

Numeric vector of desired residuals (only used if data is not provided).

R_squared

Numeric. Desired R-squared value. Default is 0.3.

p

Integer. Desired number of columns for matrix X. Default is 5.

n_add_points

Integer. Number of points to add in border transformation. Default is 40.

max_iter

Integer. Maximum number of iterations for convergence. Default is 100.

tolerance

Numeric. Criteria for detecting convergence and stopping optimization early. Default is 0.01.

verbose

Logical. If TRUE, prints progress information. Default is FALSE.

Value

A data frame containing the generated X matrix and y vector.

Details

To disable the border augmentation, set n_add_points = 0.

References

Stefanski, L. A. (2007). Residual (Sur)Realism. The American Statistician, 61(2), 163-177.

Examples

# Generate a 2D data set
data <- cbind(y_hat = rnorm(100), R_0 = rnorm(100))

# Display original data
plot(data, pch = 16, main = "Original data")


# Apply the surreal method
result <- surreal(data)

# View the expanded data after transformation
pairs(y ~ ., data = result, main = "Data after transformation")


# Fit a linear model to the transformed data
model <- lm(y ~ ., data = result)

# Plot the residuals
plot(model$fitted, model$resid, type = "n", main = "Residual plot from transformed data")
points(model$fitted, model$resid, pch = 16)