Package {CircularRegression}

CircularRegression: Regression models for circular data

Description

This package implements various regression models for circular data.

Author(s)

Maintainer: Aurelien Nicosia aurelien.nicosia@mat.ulaval.ca

See Also

Useful links:

• https://github.com/AurelienNicosiaULaval/CircularRegression

• Report bugs at https://github.com/AurelienNicosiaULaval/CircularRegression/issues

Sandhopper Escape Orientation Data

Description

This dataset contains repeated measurements on the escape orientation of 59 sandhoppers (Talitrus saltator) in a circular arena experiment with a diameter of 120 cm. Each individual was released five times, and its escape angle with respect to the north was recorded. Several explanatory variables were also measured during the experiment.

Usage

data(Sandhopper)

Format

A data frame with 72 rows and 22 variables:

Anim

Individual identifier (integer).

Day

Day of the experiment.

Daytime

Part of the day (character, e.g., "mor", "aft").

Azimuth

Sun azimuth at release (degrees).

LN1

Escape orientation, trial 1 (degrees).

LN2

Escape orientation, trial 2 (degrees).

LN3

Escape orientation, trial 3 (degrees).

LN4

Escape orientation, trial 4 (degrees).

LN5

Escape orientation, trial 5 (degrees).

Umidity

Relative humidity (%).

Temp

Air temperature (degrees Celsius).

Tsab

Sand temperature (degrees Celsius).

DirW

Wind direction (degrees).

SpeedW

Wind speed (arbitrary units).

Sex

Sex of the sandhopper ("f" or "m").

Weight

Weight of the sandhopper (grams).

Odmx

Morphometric measurement.

Odmn

Morphometric measurement.

Osmx

Morphometric measurement.

Osmn

Morphometric measurement.

Artdx

Morphometric measurement.

Artsx

Morphometric measurement.

Details

The dataset was originally presented and analyzed by D'Elia (2001) and later used in Rivest & Kato (2019) to illustrate angular regression models with repeated measures.

Angular variables such as Azimuth, LN1-LN5 and DirW are stored in degrees. The repository does not include a full raw-data reconstruction script for this processed dataset. The package maintainer has confirmed that this processed package dataset may be redistributed with the package.

Source

Package data file corresponding to the sandhopper example discussed by D'Elia (2001) and Rivest and Kato (2019). The repository does not include a raw-data reconstruction script.

References

D'Elia, G. (2001). Orientation in sandhoppers. *Behavioural Ecology*. Rivest, L.-P., & Kato, S. (2019). A random-effects model for clustered circular data. *Canadian Journal of Statistics*, 47(4), 712-728.

Angular Regression Model with Homogeneous von Mises Errors

Description

Fits the homogeneous angular regression model of Rivest et al. (2016), where the mean direction is the orientation of a weighted resultant vector and one reference angle has coefficient fixed to 1.

Usage

angular(
  formula,
  data,
  reference = c("auto", "first", "name"),
  initbeta = NULL,
  control = list(),
  na.action = stats::na.omit
)

Arguments

Value

An object of class "angular".

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.

Likelihood-ratio test (T2) between two homogeneous angular models

Description

Computes the statistic from Rivest et al. (2016), Section 3.6:

T_2 = 2 n \hat\kappa_1 (\bar C_1 - \bar C_0),

where model 1 is the full model and model 0 the nested reduced model.

Usage

angular_lrtest(full, reduced, check = TRUE)

Arguments

Value

An object of class "htest".

Angular mixed-effects regression with von Mises random intercepts

Description

Fits the homogeneous angular regression of Rivest et al. (2016) augmented with a cluster-specific random intercept a_i \sim \mathrm{VM}(0, \kappa_a) and unit-errors e_{ij} \sim \mathrm{VM}(0, \kappa_e), following Rivest & Kato (2019). The fixed-effects component shares the simplified syntax of angular(), where the first term provides the reference direction and subsequent terms are written x:z.

Usage

angular_re(
  formula,
  data,
  cluster,
  init = list(),
  control = list(),
  na.action = stats::na.omit
)

Arguments

Value

An object of class "angular_re" containing fixed-effect estimates, model-based and cluster-robust covariance matrices, concentration estimates, fitted marginal mean directions, fixed and conditional residuals, and estimated random intercepts.

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.

Examples

data(Sandhopper)
sh <- Sandhopper[seq_len(24), ]
sh$y <- sh$LN1 * pi / 180
sh$ref <- sh$Azimuth * pi / 180
sh$wind <- sh$DirW * pi / 180
sh$wind_speed <- sh$SpeedW / max(sh$SpeedW, na.rm = TRUE)

fit <- angular_re(
  y ~ ref + wind:wind_speed,
  data = sh,
  cluster = sh$Anim,
  control = list(maxit = 25, reltol = 1e-6)
)
coef(fit)
head(predict(fit))

Two-step angular regression workflow (consensus then homogeneous)

Description

Implements the strategy recommended by Rivest et al. (2016): fit the consensus model first, choose the reference angle, then fit the homogeneous model with the reference fixed and initialized from consensus ratios.

Usage

angular_two_step(
  formula,
  data,
  weights = NULL,
  reference = c("auto", "first", "name"),
  control_consensus = list(),
  control_angular = list(),
  na.action = stats::na.omit
)

Arguments

Value

An object of class "angular_two_step".

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.

Create autoregressive dataset

Description

This function augments a data frame with lagged versions of an angular response variable so that autoregressive circular regression models can be fitted.

Usage

autoregressivedata(data, response, p, ID = NULL)

Arguments

Value

The input data with p additional columns named response_tmk for k=1,\ldots,p containing the lagged values of response.

Bison movement data

Description

A subset of the bison movement dataset used for illustrating angular regression models of the form y = x_1 + x_2:z_2 + \cdots, where 'x.*' denote angular covariates (target directions) and 'z.*' the corresponding positive covariates (weights) in the product x:z. The data originate from GPS-tracked bison trajectories and environmental variables describing landscape features such as meadows and canopy gaps.

Usage

bison

Format

A data frame with 5,696 rows and 7 columns:

y.dir

Direction of movement at time t.

y.prec

Direction of movement at time t-1.

y.prec2

Direction of movement at time t-2.

x.meadow

Angle toward the nearest meadow.

z.meadow

Distance toward the nearest meadow associated with x.meadow.

x.gap

Angle toward the nearest canopy gap.

z.gap

Distance toward the nearest canopy gap associated with x.gap.

Details

All angular variables in this processed dataset are stored in radians.

This reduced dataset is designed to work directly with the functions of the CircularRegression package implementing the general angular regression model of Rivest et al. (2016). Each x:z pair represents a weighted target direction contributing to the mean resultant vector \sum_j \beta_j z_j (\cos x_j, \sin x_j), where z.* modulates the attraction toward the angular covariate x.*. Variables y.prec and y.prec2 can be included to model directional persistence between successive movement steps.

Ecologically, these variables describe the orientation of bison movement relative to attractive features in the landscape: open meadows and canopy gaps. The dataset serves as a clean example for model testing, illustration, and teaching applications involving directional movement analysis.

The repository does not include the raw GPS files or a full reconstruction script for this processed dataset. The package maintainer has confirmed that this processed package dataset may be redistributed with the package.

Source

Reduced package dataset derived from the bison movement application described by Rivest et al. (2016). The repository does not include raw GPS files or a reconstruction script for this reduced teaching dataset.

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.

See Also

angular, consensus, pick_reference_angle

Examples

# View structure
str(bison)

Fit Circular Regression Models with a Common Interface

Description

circular_regression() is the recommended high-level interface for fixed-effect circular regression models in this package. It keeps the existing model-specific functions available while providing a common, glm()-like entry point for the homogeneous angular model, the consensus model, and the two-step workflow.

Usage

circular_regression(
  formula,
  data,
  method = c("two_step", "homogeneous", "consensus"),
  weights = NULL,
  reference = c("auto", "first", "name"),
  control = list(),
  control_consensus = list(),
  control_angular = list(),
  na.action = stats::na.omit,
  ...
)

Arguments

Value

An object of class "circular_regression" containing the fitted model, the method used, the original call, and the formula.

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.

Examples

data(bison)
d <- bison[seq_len(100), ]
fit <- circular_regression(
  y.dir ~ y.prec + x.meadow:z.meadow,
  data = d
)
coef(fit)
head(predict(fit))

Consensus Angular Regression Model

Description

Fits the consensus model of Rivest et al. (2016), where each formula term of the form x or x:z receives a \kappa_j coefficient in the log-likelihood parameterization.

Usage

consensus(
  formula,
  data,
  weights = NULL,
  initkappa = NULL,
  initbeta = NULL,
  control = list(),
  na.action = stats::na.omit
)

Arguments

Value

An object of class "consensus".

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.

Decentered Predictor Model Wrapper (two-step workflow)

Description

Fits the decentered-predictor special case by augmenting the data with synthetic orthogonal directions and applying angular_two_step(). Natural parameters are returned with model-based and robust delta-method standard errors.

Usage

decentredPredictorModel(data, response, w, ...)

Arguments

Value

A list with consensus_fit, homogeneous_fit, reference, data_aug, formula, and natural-parameter outputs natural_parameters, natural_vcov_model, natural_vcov_robust, natural_jacobian.

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.

Examples

data(bison)
d <- na.omit(bison[seq_len(80), c("y.dir", "y.prec")])
fit <- decentredPredictorModel(d, response = "y.dir", w = "y.prec")
fit$natural_parameters

Jammalamadaka-Sengupta Model Wrapper (two-step workflow)

Description

Fits the Jammalamadaka-Sengupta special case by creating the required sine/cosine-equivalent angular terms and returning the corresponding natural parameters through a delta-method transformation.

Usage

jammalamadakaModel(data, response, w, ...)

Arguments

Value

A list with consensus_fit, homogeneous_fit, reference, data_aug, formula, and natural-parameter outputs natural_parameters, natural_vcov_model, natural_vcov_robust, natural_jacobian.

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.

Examples

data(bison)
d <- na.omit(bison[seq_len(80), c("y.dir", "y.prec")])
fit <- jammalamadakaModel(d, response = "y.dir", w = "y.prec")
fit$natural_parameters

Mean Direction Model Wrapper (two-step workflow)

Description

Fits the mean-direction special case through the same two-step workflow used by angular_two_step(). The wrapper creates synthetic reference directions internally and returns natural-parameter summaries obtained by a delta-method transformation of the homogeneous fit.

Usage

meanDirectionModel(data, response, mu0 = NULL, ...)

Arguments

Value

A list with consensus_fit, homogeneous_fit, reference, data_aug, formula, and natural-parameter outputs natural_parameters, natural_vcov_model, natural_vcov_robust, natural_jacobian.

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.

Examples

data(bison)
d <- na.omit(bison[seq_len(80), "y.dir", drop = FALSE])
fit <- meanDirectionModel(d, response = "y.dir")
fit$natural_parameters

Two plains bison tracked by GPS (Prince Albert National Park, 2013)

Description

Hourly GPS-derived movement metrics for two plains bison (IDs '1044-a' and '1045-a') monitored in Prince Albert National Park (Saskatchewan, Canada) during July-October 2013. From the hourly locations, the dataset includes per-animal direction of movement, step length (distance between consecutive fixes), latitude/longitude, the inter-animal distance at each hour, and turning-angles (difference between consecutive movement directions).

Usage

multiplebison

Format

A data frame with n = 1475 rows (hours kept after filtering) and the following columns (direction and turning-angle variables are in degrees):

datetime_round_next

POSIXct. Timestamp of the retained hourly record.

heure

integer. Hour of day (0-23).

bearing_ang

numeric. Bearing from bison 1044-a to 1045-a.

diff

numeric. Source variable retained from the merged GPS-derived data.

direction_1044-a

numeric. Movement direction of bison 1044-a, in degrees.

direction_1045-a

numeric. Movement direction of bison 1045-a, in degrees.

distance_1044-a

numeric. Step length (m) of bison 1044-a between consecutive fixes.

distance_1045-a

numeric. Step length (m) of bison 1045-a between consecutive fixes.

distance

numeric. Inter-animal distance (m) at the timestamp.

lat_1044-a

numeric. Latitude of bison 1044-a (decimal degrees).

lat_1045-a

numeric. Latitude of bison 1045-a (decimal degrees).

long_1044-a

numeric. Longitude of bison 1044-a (decimal degrees).

long_1045-a

numeric. Longitude of bison 1045-a (decimal degrees).

turn_ang_1044

numeric. Turning angle of bison 1044-a between consecutive directions, in degrees.

turn_ang_1045

numeric. Turning angle of bison 1045-a between consecutive directions, in degrees.

Details

The file results from merging individual hourly GPS tracks (one per animal), retaining rows where the time gap between successive fixes is exactly one hour, and reshaping to a "wide" format with one row per timestamp holding both animals' variables. Turning-angles are computed from consecutive directions.

- Angles are measured around the circle and stored in degrees in this package dataset. Convert to radians before modeling, for example with x * pi / 180. - Step lengths and distances were computed from consecutive GPS fixes; rows are kept only when the time difference equals one hour. - The turning-angle columns are circular differences between consecutive movement directions, stored in degrees on a 0-360 scale. - Scientific provenance is partially documented in the repository. The maintainer identifies these GPS tracks as associated with doctoral work and/or an article on bison movement. A closely related scientific article is Nicosia et al. (2017), which analyzes GPS-collared bison movement in Prince Albert National Park using an individual winter trajectory from November 2013 to April 2014. The repository does not verify whether the current two-bison July-October 2013 data file is a direct subset or preprocessing product of that analysis. - The repository does not include raw GPS files or a full reconstruction script for this processed dataset. The package maintainer has confirmed that this processed package dataset may be redistributed with the package.

Source

Derived package dataset prepared from GPS tracks of two plains bison monitored in Prince Albert National Park in 2013. The repository does not include raw GPS files or a reconstruction script. The package maintainer has confirmed that this processed package dataset may be redistributed with the package. Nicosia et al. (2017) is a related bison movement article from the same study context, but the exact mapping from that article to this processed data file is not verified in the repository.

References

Nicosia, A., Duchesne, T., Rivest, L.-P., and Fortin, D. (2017). A multi-state conditional logistic regression model for the analysis of animal movement. The Annals of Applied Statistics, 11(3), 1537-1560. DOI: doi:10.1214/17-AOAS1045.

Examples

head(multiplebison)


mean(multiplebison$distance < 500, na.rm = TRUE)

Noshiro earthquake direction data

Description

This data frame contains two circular variables for 678 locations associated with the Noshiro earthquake. The variables are DIRDSC, the direction of steepest descent, and DIRMV, the direction of movement.

Usage

data(noshiro)

Format

A data frame with 678 rows and 2 columns:

DIRDSC

Direction of steepest descent.

DIRMV

Direction of movement.

Details

The data were used by Rivest (1997) for circular-circular regression. The processed version included in this package was provided by Louis-Paul Rivest to the package maintainer after duplicate observations had been removed, yielding n = 678. In the original analysis, DIRMV is the response variable to be predicted from DIRDSC.

The angular units are not documented in the repository or in the provenance notes provided to the maintainer. Raw data and a reconstruction script are not present in the repository. The package maintainer has confirmed that this processed package dataset may be redistributed with the package.

Source

Processed Noshiro earthquake data used in Rivest (1997), provided by Louis-Paul Rivest to the package maintainer. Duplicate observations were removed before inclusion in this package, yielding n = 678. The package maintainer has confirmed that this processed package dataset may be redistributed with the package.

References

Rivest, L.-P. (1997). A decentered predictor for circular-circular regression. Biometrika, 84, 717–726.

Backward-compatible wrapper for reference-angle selection

Description

Backward-compatible wrapper for reference-angle selection

Usage

pick_reference_angle(formula, data, tie_method = c("first", "random"), ...)

Arguments

Value

A select_reference_angle object, with legacy class pick_reference_angle prepended.

Plot method for angular_re objects

Description

Draws rose/circular plots of residuals: fixed (y - mu) and conditional (y - mu - a_hat[cluster]) as in Rivest & Kato (2019), Fig. 1-2. If the 'circular' package is available, uses it; otherwise falls back to a simple polar scatter with density ticks.

Usage

## S3 method for class 'angular_re'
plot(
  x,
  which = c("both", "fixed", "conditional"),
  breaks = 24,
  points = TRUE,
  main = "Residuals",
  ...
)

Arguments

Value

Draws residual diagnostic plots and invisibly returns the input angular_re object.

Plot random-intercept directions for an angular_re fit

Description

Draws one arrow per cluster pointing in the direction of the estimated random intercept \hat a_i. Arrow length is either A1(kappa_a) or 1. If the 'circular' package is available, uses it for nicer axes; otherwise falls back to base polar plotting.

Usage

plot_ranef.angular_re(
  x,
  scale = c("A1_kappa_a", "unit"),
  labels = FALSE,
  cex.labels = 0.7,
  main = "Random intercepts (a_hat[i])",
  ...
)

Arguments

Value

Draws a random-intercept direction plot and invisibly returns the input angular_re object.

Predict method for angular_re objects

Description

Predict method for angular_re objects

Usage

## S3 method for class 'angular_re'
predict(
  object,
  newdata = NULL,
  cluster = NULL,
  type = c("auto", "marginal", "conditional"),
  a_hat = NULL,
  se.fit = FALSE,
  ...
)

Arguments

Value

numeric vector (angles in radians).

Presnell Model Wrapper (two-step workflow)

Description

Fits the Presnell special case by building the linear and orthogonal synthetic terms required by the homogeneous angular formulation. The returned natural parameters are ratios computed from the homogeneous coefficients.

Usage

presnellModel(data, response, w, ...)

Arguments

Value

A list with consensus_fit, homogeneous_fit, reference, data_aug, formula, and natural-parameter outputs natural_parameters, natural_vcov_model, natural_vcov_robust, natural_jacobian.

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.

Examples

data(bison)
d <- na.omit(bison[500:579, c("y.dir", "z.gap")])
fit <- presnellModel(d, response = "y.dir", w = "z.gap")
fit$natural_parameters

Methods for Angular Regression Objects

Description

Methods for Angular Regression Objects

Usage

## S3 method for class 'angular'
print(x, ...)

## S3 method for class 'angular'
coef(object, ...)

## S3 method for class 'angular'
vcov(object, robust = FALSE, ...)

## S3 method for class 'angular'
fitted(object, ...)

## S3 method for class 'angular'
residuals(object, ...)

## S3 method for class 'angular'
predict(object, newdata = NULL, type = c("response", "components"), ...)

## S3 method for class 'angular'
summary(object, ...)

## S3 method for class 'summary.angular'
print(x, ...)

## S3 method for class 'angular'
plot(x, ...)

Arguments

Value

print() prints a compact model summary and invisibly returns the input object. coef() returns a numeric vector of non-reference coefficient estimates. vcov() returns the requested covariance matrix. fitted() returns fitted mean directions in radians. residuals() returns wrapped circular residuals in radians. predict() returns fitted or predicted angles in radians, or a matrix with cosine and sine components when type = "components". summary() returns a "summary.angular" object with residual summaries and coefficient estimates. plot() draws diagnostic plots and invisibly returns the input object.

Methods for Angular Random-Effects Fits

Description

Methods for Angular Random-Effects Fits

Usage

## S3 method for class 'angular_re'
print(x, ...)

## S3 method for class 'angular_re'
summary(object, ...)

## S3 method for class 'summary.angular_re'
print(x, ...)

## S3 method for class 'angular_re'
coef(object, ...)

## S3 method for class 'angular_re'
vcov(object, robust = FALSE, ...)

## S3 method for class 'angular_re'
residuals(object, type = c("fixed", "conditional"), ...)

## S3 method for class 'angular_re'
fitted(object, ...)

Arguments

Value

coef() returns the parameter estimates. vcov() returns the requested covariance matrix. fitted() returns marginal fitted mean directions. residuals() returns wrapped circular residuals. summary() returns a list with convergence information, likelihood, sample sizes, concentration estimates, residual summaries and coefficient table. print() invisibly returns the input object.

Methods for two-step angular regression objects

Description

Methods for two-step angular regression objects

Usage

## S3 method for class 'angular_two_step'
print(x, ...)

## S3 method for class 'angular_two_step'
summary(object, ...)

## S3 method for class 'summary.angular_two_step'
print(x, ...)

## S3 method for class 'angular_two_step'
coef(object, step = c("homogeneous", "consensus"), ...)

## S3 method for class 'angular_two_step'
fitted(object, ...)

## S3 method for class 'angular_two_step'
residuals(object, ...)

## S3 method for class 'angular_two_step'
predict(object, newdata = NULL, type = c("response", "components"), ...)

## S3 method for class 'angular_two_step'
plot(x, ...)

## S3 method for class 'angular_two_step'
logLik(object, ...)

## S3 method for class 'angular_two_step'
AIC(object, ..., k = 2)

## S3 method for class 'angular_two_step'
BIC(object, ...)

Arguments

Value

print() prints a compact workflow summary and invisibly returns the input object. summary() returns a "summary.angular_two_step" object containing summaries for the consensus and homogeneous fits, and print() on that summary returns it invisibly. coef() returns coefficient estimates from the selected step. fitted(), residuals(), and predict() return the corresponding results from the homogeneous fit. plot() draws the homogeneous-fit diagnostic plots and invisibly returns the input object. logLik() returns the homogeneous-fit log-likelihood object, and AIC() and BIC() return numeric information criteria.

Methods for Circular Regression Objects

Description

Methods for Circular Regression Objects

Usage

## S3 method for class 'circular_regression'
print(x, ...)

## S3 method for class 'circular_regression'
summary(object, ...)

## S3 method for class 'summary.circular_regression'
print(x, ...)

## S3 method for class 'circular_regression'
coef(object, ...)

## S3 method for class 'circular_regression'
fitted(object, ...)

## S3 method for class 'circular_regression'
residuals(object, ...)

## S3 method for class 'circular_regression'
predict(object, newdata = NULL, type = c("response", "components"), ...)

## S3 method for class 'circular_regression'
plot(x, ...)

## S3 method for class 'circular_regression'
logLik(object, ...)

## S3 method for class 'circular_regression'
AIC(object, ..., k = 2)

## S3 method for class 'circular_regression'
BIC(object, ...)

Arguments

Value

print() prints a compact model summary and invisibly returns the input object. summary() returns a "summary.circular_regression" object, and print() on that summary returns it invisibly. coef(), fitted(), residuals(), predict(), plot(), logLik(), AIC(), and BIC() delegate to the primary fitted model and return the corresponding coefficients, fitted angles, residuals, predictions, diagnostic plots, log-likelihood, and information criteria.

Methods for Consensus Objects

Description

Methods for Consensus Objects

Usage

## S3 method for class 'consensus'
print(x, ...)

## S3 method for class 'consensus'
coef(
  object,
  type = c("kappa", "beta"),
  reference = c("auto", "first", "name"),
  ...
)

## S3 method for class 'consensus'
vcov(object, robust = FALSE, ...)

## S3 method for class 'consensus'
fitted(object, ...)

## S3 method for class 'consensus'
residuals(object, ...)

## S3 method for class 'consensus'
predict(object, newdata = NULL, type = c("response", "components"), ...)

## S3 method for class 'consensus'
summary(object, ...)

## S3 method for class 'summary.consensus'
print(x, ...)

## S3 method for class 'consensus'
plot(x, ...)

## S3 method for class 'consensus'
AIC(object, ..., k = 2)

## S3 method for class 'consensus'
BIC(object, ...)

## S3 method for class 'consensus'
logLik(object, ...)

Arguments

Value

print() prints a compact model summary and invisibly returns the input object. coef() returns a numeric vector of kappa coefficients or beta ratios, depending on type. vcov() returns the covariance matrix for kappa coefficients. fitted() returns fitted mean directions in radians. residuals() returns wrapped circular residuals in radians. predict() returns fitted or predicted angles in radians, or a matrix with cosine and sine components when type = "components". summary() returns a "summary.consensus" object. plot() draws diagnostic plots and invisibly returns the input object. AIC() and BIC() return numeric information criteria with degrees-of-freedom and observation-count attributes. logLik() returns a "logLik" object.

Print method for pick_reference_angle

Description

Print method for pick_reference_angle

Usage

## S3 method for class 'pick_reference_angle'
print(x, ...)

Arguments

Value

Invisibly returns the printed pick_reference_angle object.

Extract estimated random intercepts from an angular mixed model

Description

Returns the cluster-specific random intercepts \hat a_i estimated by angular_re().

Usage

ranef.angular_re(object, ...)

Arguments

Value

A named numeric vector of random intercept estimates, one per cluster.

Select Reference Angle for Homogeneous Angular Model

Description

Selects the reference direction using the criterion of Rivest et al. (2016): the angle variable maximizing the empirical mean cosine \overline{\cos(y-x_j)} among plain angle terms x present in the formula.

Usage

select_reference_angle(
  formula,
  data,
  tie_method = c("first", "random"),
  na.action = stats::na.omit
)

Arguments

Value

An object of class "select_reference_angle".