Spherical regression using the SESPC distribution {Directional}

Spherical regression using the SESPC distribution

Description

Spherical regression using the SESPC distribution.

Usage

sespc.reg(y, x, con = TRUE, xnew = NULL, lati = 10, longi = 10, tol = 1e-06)

Arguments

y

A matrix with 3 columns containing the (unit vector) spherical data.

x

The predictor variable(s), they can be continnuous, spherical, categorical or a mix of them.

con

Do you want the constant term in the regression?

xnew

If you have new data use it, otherwise leave it NULL.

lati

A positive number determing the range of degrees to move left and right from the latitude center. This number and the next determine the grid of points to search for the Q matrix described in Tsagris and Alzeley (2023).

longi

A positive number determing the range of degrees to move up and down from the longitude center. This number and the previous determine the grid of points to search for the Q matrix described in Tsagris and Alzeley (2023).

tol

A tolerance value to decide when to stop the successive optimizations.

Details

Regression based on the SESPC distribution (Tsagris and Alzeley, 2023) is applied.

Value

A list including:

loglik

The log-likelihood of the regression model.

param

A vector with three numbers. A measure of fit of the estimated values, defined as \sum_{i=1}^ny_i^T\hat{y}_i. This appears if the argument "xnew" is NULL. The \rho \in (0,1] (smallest eigenvalue of the covariance matrix)), and the angle of rotation psi.

theta

The two \theta parameters.

beta

The beta coefficients.

seb

The standard error of the beta coefficients.

est

The fitted values of xnew if "xnew" is NULL. If it is not NULL, the fitted values for the "xnew" you supplied will be returned.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris [e-mail].

References

Tsagris M. and Alzeley O. (2023). Circular and spherical projected Cauchy distributions: A Novel Framework for Circular and Directional Data Modeling. https://arxiv.org/pdf/2302.02468.pdf

See Also

esag.mle, iag.reg, spml.reg

Examples

y <- rsespc( 150, rnorm(3), c(1, 1) )
## this is a small example to pass CRAN's check because the default argument values
## of lati and longi require many seconds
a <- sespc.reg(y, iris[, 4], lati = 2, longi = 2)