GCElm.fit: Generalized Cross Entropy Linear Regression Models

In gcemodels/GCEmodels: GCE linear model estimation

Generalized Cross Entropy Linear Regression Models

Description

Fitting generalized cross entropy (GCE) linear models

Usage

GCElm.fit(y, X, Z, v, nu, p0, w0, k.sigma = 3, control = GCElm.control())

Arguments

y	numeric, n (Nx1) vector representing the dependent variable where N is the number of observations.
X	numeric, n (NxK) matrix representing a set of independent variables where K is the number of regressors.
Z	numeric, an (KxM) matrix representing support spaces for the regression coefficients (including intercept) where M is the dimension of the support spaces.
v	numeric, an optional argument representing a support space for error terms: (a) if missing then v is a (5x1) vector of equally spaced points in [a,b] interval; (b) if a scalar (e.g. H) then v is a (Hx1) vector of equally spaced points in [a,b] interval; (c) can be a user-supplied vector; (d) can be a user-supplied matrix. Please note that in case (a) and (b) the [a,b] interval is centered around zero, and a and b are calculated using the empirical three-sigma rule Pukelsheim (1994).
nu	numeric, an optional weight parameter representing the trade-off between prediction and precision.
p0	numeric, optional prior probabilities associated with the regression coefficients.
w0	numeric, optional prior probabilities associated with the error terms.
k.sigma	numeric, coefficient k in the k-sigma rule (default k=3).
control	list, a list of parameters for controlling the fitting process; for GCElm.fit this is passed to GCElm.control.

Details

Mettere qui eventuali details.

Value

A list with the following elements:

• lambda, estimated lagrange multipliers;

• coefficients, regression coefficients;

• var_beta, variance-covariance matrix of the regression coefficients;

• p, estimated probabilities associated with the regressions coefficients;

• w, estimated probabilities associated with the error terms;

• e, estimated residuals;

• Sp, the (signal) information of the whole system;

• Sp_k, the (signal) information associated with the k-th regression coefficient;

• H_p_w, value of the joint entropies of p and w at the final iteration;

• dH, delta-H from the Entropy Concentration Theorem;

• ER, entropy-ratio statistic;

• Pseudo-R2, pseudo R-squared;

• converged, convergence (same as in the lbfgs function).

Author(s)

Marco Sandri, Enrico Ciavolino, Maurizio Carpita ([e-mail])

References

Golan (1996)

Examples

set.seed(1234)
N <- 1000
K <- 10
betas <- c(-1,1,-1,1,0,0,0,0,0,0)
X <- matrix(runif(N*K), nrow = N, ncol = K)
y <- X %*% betas + rnorm(N)
X <- cbind(rep(1, N), X)
Z <- matrix(rep(seq(-10,10,2.5), K+1), nrow = K+1, byrow = TRUE)
GCEfit <- GCElm.fit(y, X, Z)
coef(GCEfit)      

gcemodels/GCEmodels documentation built on Aug. 10, 2024, 1:58 a.m.