output	github_document

Introduction

This is nprotreg, an R package that exploits nonparametric rotations in the analysis of Sphere-Sphere regression models.

The package implements methods proposed by Di Marzio, Panzera & Taylor (2018).

Thanks to package nprotreg, regressing data represented as points on a hypersphere you can

• simulate a very flexible regression model where, for each location of the manifold, a specific rotation matrix is applied to obtain a spherical response;
• fit Sphere-Sphere regression models by allowing for approximations of rotation matrices based on a series expansion;
• reduce estimation bias applying iterative estimation procedures within a Newton-Raphson learning scheme;
• use cross-validation to select smoothing parameters.

Getting Started

The following script shows how to fit a Sphere-Sphere regression model using simulated data via package nprotreg.

library(nprotreg)
# Define a matrix of explanatory points.number_of_explanatory_points<-50explanatory_points<- get_equally_spaced_points(
number_of_explanatory_points)
# Define a matrix of response points by simulation.# - define the response local rotation model (eg Model 2 in Table 1 of [Di Marzio, Panzera & Taylor (2018)])local_rotation_composer<-function(point) {
independent_components<- (1/2) *
c(exp(2.0*point[3]), - exp(2.0*point[2]), exp(2.0*point[1]))
}
# - define a rotation (error) perturbation model using random skew symmetric matrix:local_error_sampler<-function(point) {
rnorm(3,mean=0,sd=.25)
}
response_points<- simulate_regression(explanatory_points,
local_rotation_composer,
local_error_sampler)
# Define a matrix of evaluation points for prediction.evaluation_points<- rbind(
cbind(.5, 0, .8660254),
cbind(-.5, 0, .8660254),
cbind(1, 0, 0),
cbind(0, 1, 0),
cbind(-1, 0, 0),
cbind(0, -1, 0),
cbind(.5, 0, -.8660254),
cbind(-.5, 0, -.8660254)
)
# Use a default weights generator.weights_generator<-weight_explanatory_points# Set the concentration parameter (kappa).concentration<-5# Fit regression.fit_info<- fit_regression(
evaluation_points,
explanatory_points,
response_points,
concentration,
weights_generator,
number_of_expansion_terms=1,
number_of_iterations=2
)

See the documentation for addressing additional scenarios.

Installation

To download and install the package from the CRAN repository, execute the following command:

install.packages("nprotreg")