# iag.reg: Spherical regression using rotationally symmetric... In Directional: A Collection of Functions for Directional Data Analysis

 Spherical regression using rotationally symmetric distributions R Documentation

## Spherical regression using rotationally symmetric distributions

### Description

Spherical regression using rotationally symmetric distributions.

### Usage

iag.reg(y, x, con = TRUE, xnew = NULL, tol = 1e-06)
vmf.reg(y, x, con = TRUE, xnew = NULL, tol = 1e-06)
sipc.reg(y, x, con = TRUE, xnew = NULL, 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. tol A tolerance value to decide when to stop the successive optimaizations.

### Details

The second parametrization of the projected normal and of the von Mises-Fisher regression (Paine et al., 2020) is applied. The same is true for the SIPC distribution. For more information see the paper by Paine et al. (2020).

### Value

A list including:

 loglik The log-likelihood of the regression model. fit This is 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. beta The beta coefficients. seb The standard error of the beta coefficients. ki The norm of the fitted values. In the von Mises-Fisher regression this is the concentration parameter of each observation. In the projected normal this are the norms of the fitted values before being projected onto the sphere. This is returned if the argument "xnew" is NULL. 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 mtsagris@uoc.gr.

### References

P. J. Paine, S. P. Preston, M. Tsagris and Andrew T. A. Wood (2020). Spherical regression models with general covariates and anisotropic errors. Statistics and Computing, 30(1): 153–165. https://link.springer.com/content/pdf/10.1007

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

 esag.reg, esag.mle, vmf.mle, spml.reg 

### Examples

y <- rvmf(150, rnorm(3), 5)
a1 <- iag.reg(y, iris[, 4])
a2 <- iag.reg(y, iris[, 4:5])

b1 <- vmf.reg(y, iris[, 4])
b2 <- vmf.reg(y, iris[, 4:5])


Directional documentation built on Oct. 12, 2023, 1:07 a.m.