mc_sic: Score Information Criterion for Regression Components

In mcglm: Multivariate Covariance Generalized Linear Models

Score Information Criterion for Regression Components

Description

Computes the Score Information Criterion (SIC) for regression components of a fitted mcglm object. The SIC can be used for selecting covariates in the linear predictor and supports stepwise selection procedures.

Usage

mc_sic(object, scope, data, response, penalty = 2, weights)

Arguments

object	An object of class mcglm.
scope	A character vector with the names of covariates to be tested for inclusion in the linear predictor.
data	A data frame containing all variables involved in the model.
response	An integer indicating the response variable for which the SIC is computed.
penalty	A numeric penalty term applied to the SIC (default is 2).
weights	An optional numeric vector of weights used in model fitting. If not provided, unit weights are assumed.

Details

The SIC is computed using the quasi-score function associated with the regression parameters. For each candidate covariate in scope, the method evaluates its contribution via a score-based test statistic and applies a penalty for model complexity.

Value

A data frame with the following columns:

SIC

Score Information Criterion value.

Covariates

Name of the candidate covariate.

df

Degrees of freedom associated with the test.

df_total

Total number of regression parameters in the extended model.

Tu

Score-based test statistic.

Chisq

Reference chi-squared quantile with 95% confidence level.

References

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

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.

See Also

mc_sic_covariance

Examples

set.seed(123)
x1 <- runif(100, -1, 1)
x2 <- gl(2, 50)
beta <- c(5, 0, 3)
X <- model.matrix(~ x1 + x2)
y <- rnorm(100, mean = X %*% beta, sd = 1)
data <- data.frame(y, x1, x2)

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

mc_sic(fit0, scope = c("x1", "x2"), data = data, response = 1)

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