R/FIC.R

In ICglm: Information Criteria for Generalized Linear Regression

#' @title  Fisher Information Criterion
#'
#' @description Calculates Fisher Information Criterion (FIC) for "lm" and "glm" objects.
#'
#' @param model a "lm" or "glm" object
#'
#' @details
#' FIC (Wei, 1992) is calculated as
#'
#' \deqn{-2LL(theta) + log(|X^T X|)}
#'
#' @return FIC measurement of the model
#'
#' @importFrom stats logLik model.matrix
#' @examples
#' x1 <- rnorm(100, 3, 2)
#' x2 <- rnorm(100, 5, 3)
#' x3 <- rnorm(100, 67, 5)
#' err <- rnorm(100, 0, 4)
#'
#' ## round so we can use it for Poisson regression
#' y <- round(3 + 2*x1 - 5*x2 + 8*x3 + err)
#'
#' m1 <- lm(y~x1 + x2 + x3)
#' m2 <- glm(y~x1 + x2 + x3, family = "gaussian")
#' m3 <- glm(y~x1 + x2 + x3, family = "poisson")
#'
#'FIC(m1)
#'FIC(m2)
#'FIC(m3)
#'
#' @references
#' Wei, C. Z. (1992). On predictive least squares principles. The Annals of Statistics, 20(1), 1-42.
#'
#' @export

FIC <- function(model) {
  LL <- logLik(object = model)
  X <- model.matrix(model)
  c(-2*LL + log(det(crossprod(X))))
}