mc_sic_covariance: Score Information Criterion for Covariance Components

In mcglm: Multivariate Covariance Generalized Linear Models

Score Information Criterion for Covariance Components

Description

Computes the Score Information Criterion (SIC) for covariance components of a fitted mcglm object. The SIC-covariance is used to select components of the matrix linear predictor and can be employed in stepwise selection procedures.

Usage

mc_sic_covariance(object, scope, idx, data, penalty = 2, response, weights)

Arguments

object	An object of class mcglm.
scope	A list of matrices to be tested for inclusion in the matrix linear predictor.
idx	An integer vector indicating which matrices in scope belong to the same effect. This is useful when more than one matrix represents a single covariance component.
data	A data frame containing all variables involved in the model.
penalty	A numeric penalty term applied to the SIC (default is 2).
response	An integer indicating the response variable for which the SIC-covariance is computed.
weights	An optional numeric vector of weights used in model fitting. If not provided, unit weights are assumed.

Details

The SIC-covariance is computed using the Pearson estimating function. For each group of matrices defined by idx, a score-based test statistic is calculated to assess the contribution of the associated covariance components, penalized by model complexity.

Value

A data frame with the following columns:

SIC

Score Information Criterion value.

df

Degrees of freedom associated with the test.

df_total

Total number of covariance parameters in the extended model.

Tu

Score-based test statistic.

Chisq

Reference chi-squared quantile with 95% confidence level.

References

Bonat, W. H., et al. (2016). Modelling the covariance structure in marginal multivariate count models: Hunting in Bioko Island. Journal of Agricultural, Biological and Environmental Statistics, 22(4), 446–464.

Bonat, W. H. (2018). Multiple Response Variables Regression Models in R: The mcglm Package. Journal of Statistical Software, 84(4), 1–30.

See Also

mc_sic

Examples

set.seed(123)
SUBJECT <- gl(10, 10)
y <- rnorm(100)
data <- data.frame(y, SUBJECT)

Z0 <- mc_id(data)
Z1 <- mc_mixed(~ 0 + SUBJECT, data = data)

fit0 <- mcglm(
  linear_pred = c(y ~ 1),
  matrix_pred = list(Z0),
  data = data
)

mc_sic_covariance(
  fit0,
  scope = Z1,
  idx = 1,
  data = data,
  response = 1
)

mcglm documentation built on Jan. 9, 2026, 1:07 a.m.