R/metrics.R

In flexCountReg: Estimation of a Variety of Count Regression Models

#' Calculate Akaike Information Criterion (AIC)
#'
#' This function calculates the Akaike Information Criterion (AIC) for a given
#' model.
#'
#' @param LL Numeric value representing the log-likelihood of the model.
#' @param nparam Numeric value representing the number of parameters in the
#'   model.
#' @returns Numeric value representing the AIC.
#' @details The AIC is calculated using the formula:
#' \deqn{AIC = -2 \cdot LL + 2 \cdot nparam}
#' Where \eqn{LL} is the log-likelihood of the model and \eqn{nparam} is the
#' number of parameters.
#' @examples
#' LL <- -120.5
#' nparam <- 5
#' myAIC(LL, nparam)
#' 
#' @export
myAIC <- function(LL, nparam){
  return(-2 * LL + 2 * nparam)
}

#' Calculate Bayesian Information Criterion (BIC)
#'
#' This function calculates the Bayesian Information Criterion (BIC) for a given
#' model.
#'
#' @param LL Numeric value representing the log-likelihood of the model.
#' @param nparam Numeric value representing the number of parameters in the
#'   model.
#' @param n Numeric value representing the number of observations.
#' @return Numeric value representing the BIC.
#' @details The BIC is calculated using the formula:
#' \deqn{BIC = -2 \cdot LL + nparam \cdot \log(n)}
#' Where \eqn{LL} is the log-likelihood of the model, \eqn{nparam} is the number
#' of parameters, and \eqn{n} is the number of observations.
#' @examples
#' LL <- -120.5
#' nparam <- 5
#' n <- 100
#' myBIC(LL, nparam, n)
#' 
#' @export
myBIC <- function(LL, nparam, n){
  return(-2 * LL + nparam * log(n))
}

#' Calculate Root Mean Squared Error (RMSE)
#'
#' This function calculates the Root Mean Squared Error (RMSE) between observed
#' and predicted values.
#'
#' @param y Numeric vector representing the observed values.
#' @param mu Numeric vector representing the predicted values.
#' @return Numeric value representing the RMSE.
#' @details The RMSE is calculated using the formula:
#' \deqn{RMSE = \sqrt{\frac{1}{n} \sum_{i=1}^{n} (y_i - \mu_i)^2}}
#' Where \eqn{y} is the vector of observed values and \eqn{\mu} is the vector of
#' predicted values.
#' 
#' @examples
#' y <- c(1, 2, 3)
#' mu <- c(1.1, 1.9, 3.2)
#' rmse(y, mu)
#' 
#' @export
rmse <- function(y, mu){
  return(sqrt(mean((y - mu)^2)))
}

#' Calculate Mean Absolute Error (MAE)
#'
#' This function calculates the Mean Absolute Error (MAE) between observed and
#' predicted values.
#'
#' @param y Numeric vector representing the observed values.
#' @param mu Numeric vector representing the predicted values.
#' @return Numeric value representing the MAE.
#' @details The MAE is calculated using the formula:
#' \deqn{MAE = \frac{1}{n} \sum_{i=1}^{n} |y_i - \mu_i|}
#' Where \eqn{y} is the vector of observed values and \eqn{\mu} is the vector of
#' predicted values.
#' @examples
#' y <- c(1, 2, 3)
#' mu <- c(1.1, 1.9, 3.2)
#' mae(y, mu)
#' 
#' @export
mae <- function(y, mu){
  return(mean(abs(y - mu)))
}