Circular Regression Models

Implements regression models for circular response data, including homogeneous angular regression, consensus angular regression, a two-step workflow, selected special-case model wrappers, and a random-intercept extension for clustered circular outcomes. The main methodology follows Rivest et al. (2016) "A General Angular Regression Model for the Analysis of Data on Animal Movement in Ecology" .

CircularRegression

CircularRegression fits regression models for circular response data, such as movement directions or angles measured in radians. The package implements the general angular regression framework of Rivest, Duchesne, Nicosia and Fortin (2016), including homogeneous angular regression, consensus regression, a two-step workflow, and selected special-case wrappers.

Installation

install.packages("remotes")
remotes::install_github("AurelienNicosiaULaval/CircularRegression")

Main interface

library(CircularRegression)

data(bison)
d <- bison[seq_len(100), ]

fit <- circular_regression(
  y.dir ~ y.prec + x.meadow:z.meadow,
  data = d
)

summary(fit)
coef(fit)
head(predict(fit))

The formula syntax uses angular variables as terms. A term of the form x adds a direction directly. A term of the form x:z adds a direction x weighted by a finite non-negative modifier z.

Model-specific interfaces

The original interfaces remain available:

• angular() fits the homogeneous angular regression model.
• consensus() fits the consensus angular regression model.
• angular_two_step() fits the consensus model, selects a reference direction, and then fits the homogeneous model.
• angular_re() fits the random-intercept extension for clustered circular outcomes.

The package provides S3 methods for printing, summarising, coefficients, fitted values, residuals, predictions, plots, information criteria, and log-likelihoods where appropriate.

References

Rivest, L.-P., Duchesne, T., Nicosia, A. and Fortin, D. (2016). A general angular regression model for the analysis of data on animal movement in ecology. Journal of the Royal Statistical Society: Series C (Applied Statistics), 65(3), 445-463.

Rivest, L.-P. and Kato, S. (2019). A random-effects model for clustered circular data. Canadian Journal of Statistics, 47(4), 712-728.