CBPE (version 0.1.0)

CBPLogisticE: Correlation-based Estimator for Logistic Regression Models

Description

This function computes the correlation-based estimator for logistic regression models.

Usage

CBPLogisticE(X, y, lambda, max_iter = 100, tol = 1e-06)

Value

A numeric vector of the estimated coefficients for the specified model.

Arguments

X

A numeric matrix of predictors where rows represent observations and columns represent variables.

y

A numeric vector of binary outcomes (0 or 1).

lambda

A regularization parameter.

max_iter

An integer specifying the maximum number of iterations for the logistic regression algorithm. Default is 100.

tol

A numeric value specifying the convergence tolerance for the logistic regression algorithm. Default is 1e-10.

Details

The correlation-based penalized logistic estimator is calculated as: $$ \hat{\beta} = \text{argmin}\left\{ \sum_{i=1}^n \left( y_i \ln(\pi_i) + (1 - y_i) \ln(1 - \pi_i) \right) + \lambda \sum_{i=1}^{p-1} \sum_{j>i} \left( \frac{(\beta_i - \beta_j)^2}{1 - \rho_{ij}} + \frac{(\beta_i + \beta_j)^2}{1 + \rho_{ij}} \right) \right\} $$ where \(\pi_i = \text{Pr}(y_i = 1|\mathbf{x}_i)\) and \(\rho_{ij}\) denotes the (empirical) correlation between the \(i\)th and the \(j\)th predictor.

References

Algamal, Z. Y., & Lee, M. H. (2015). Penalized logistic regression with the adaptive LASSO for gene selection in high-dimensional cancer classification. Expert Systems with Applications, 42(23), 9326-9332.

Examples

set.seed(42)
n <- 100
p <- 4
X <- matrix(rnorm(n * p), n, p)
beta_true <- c(0.5, -1, 2, 5)
y <- rbinom(n, 1, 1 / (1 + exp(-X %*% beta_true)))
lambda <- 0.1

result <- CBPLogisticE(X, y, lambda)
print(result)