CircularRegression

CircularRegression is an R package for fitting regression models when the response is circular, such as a movement direction or an angle measured in radians. It implements homogeneous angular regression, consensus angular regression, a two-step workflow, selected model-specific interfaces, and a random-intercept extension for clustered circular responses.

CRAN version: 0.5.1, published on June 10, 2026.

CRAN GitHub CRAN vignette Methodological reference

Visual preview

The illustration below is produced from the bison data included in the package. The left panel compares observed directions with model-fitted directions, and the right panel summarizes angular residuals.

Usage example

The code below fits a circular regression model to the bison data included in the package. Formula syntax can use directional variables directly, or directions weighted by a non-negative modifier with the x:z form.

# Load library
library(CircularRegression)

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

# Fit a circular regression model
fit <- circular_regression(
  y.dir ~ y.prec + x.meadow:z.meadow,
  data = d
)

# Inspect the fitted model
summary(fit)
coef(fit)
head(predict(fit))

What is CircularRegression for?

• modeling angular or directional responses;
• fitting homogeneous angular regression or consensus angular regression models;
• using a two-step workflow that connects consensus and homogeneous models;
• analyzing clustered circular responses with a random-intercept extension;
• producing diagnostics, predictions, residuals, information criteria, and summaries adapted to circular models.