R/add1_AIC.R

In pengyuwei94/evreg: Extreme value regression modelling

#' Add one possible covariate on GEV parameter based on AIC
#'
#' Add a single term to either mu, sigma, and xi based on AIC.
#'
#' @param fit An object of class \code{c("gev", "evreg")} returned from
#'   \code{\link{gevreg}} summarising the current model fit.
#' @return An object (a list) of class \code{c("gev", "evreg")} summarising
#'   the new model fit (which may be the same as \code{fit}) and containing the
#'   following additional components
#'     \item{Input_fit}{The input object of the class \code{c("gev", "evreg")}.}
#'     \item{Note}{A message that tells if a covariate has been added or not.}
#'     \item{Output_fit}{A list that contains formulae for the parameter,
#'     and the output object of the class \code{c("gev", "evreg")} if the output fit
#'     is different from the input fit.}
#'     \item{added_covariate}{A character vector shows added covariate}
#'     \item{AIC}{AIC values for both input model and output model if two models
#'     are different.}
#' @examples
#'
#' ### Fremantle sea levels
#' # Parameter mu
#' f0 <- gevreg(SeaLevel, data = evreg::fremantle[,-1])
#' add1_AIC_mu(f0)
#'
#' # Parameter sigma
#' f3 <- gevreg(y = SeaLevel, data = evreg::fremantle[,-1], mu = ~Year01 + SOI)
#' add1_AIC_sigma(f3)
#'
#' # Parameter xi
#' f4 <- gevreg(y = SeaLevel, data = evreg::fremantle[,-1], mu = ~Year01 + SOI, sigma = ~SOI)
#' add1_AIC_xi(f4)
#'
#'
#' ### Annual Maximum and Minimum Temperature
#'
#' P0 <- gevreg(y = TMX1, data = PORTw[, -1])
#' add1_AIC_mu(P0)
#' add1_AIC_sigma(P0)
#' add1_AIC_xi(P0)
#'
#' @name add1_AIC
NULL
## NULL

# ----------------------------- mu ---------------------------------

#' @rdname add1_AIC
#' @export
add1_AIC_mu <- function(fit){
  ##1. Check if input arguments are missing
  if(missing(fit))  stop("fit must be specified")

  ##2. Check if input fit is an 'evreg' objects
  m <- deparse(substitute(fit))
  if(!inherits(get(m, envir = parent.frame()), "evreg")){
    stop("Use only with 'evreg' objects")
  }

  data    <- eval(fit$call$data)         #save data
  y       <- fit$call$y                  #response variable
  y_index <- which(colnames(data) == y)  #index of column y
  X       <- data[-y_index]              #data only with covariates
  n       <- ncol(X) + 1          #number of covatiates +1 in the data

  ##3. Check if input fit already has all covariates on mu
  n_mu <- ncol(fit$data$D$mu)
  if(n_mu == n){
    stop("All covariates has been added on mu for input fit")
  }

  ##identify family from the fit

  ###################################################################
  ####----------------------------GEV----------------------------####
  ###################################################################
  if(inherits(get(m, envir = parent.frame()), "gev")){

    ###Extract covariates on mu if there are in input fit
    if(n_mu != 1){
      x_name <- all.vars(fit$formulae$mu)
      index  <- which(colnames(X) %in% x_name)
      X <- X[-index]   #a data frame with covariates that are not in the mu formula
    }
    name <- names(X)   #get names from rest of covariates

    #General steps
    # 1. Fit all of the possible models obtained by adding 1 covariate to the original model
    # 2. Calculate the value of AIC for all these models.
    aic <- c()
    m_list <- list()
    for(i in 1:length(name)){
      # adding more variables on mu, one at a time
      mu  <- update(fit$formulae$mu, paste("", name[i], sep = "~.+"))  #update mu formula
      # update a model call by adding one additional covariate on mu
      # when we fit a new model in which an extra covariate is added,
      # we use starting values based on the fit of the smaller model.
      # The start value for the new added variable will be set to be zero.
      fcoefs <- fit$coefficients
      n_sigma <- ncol(fit$data$D$sigma)
      mustart <- c(unname(fcoefs[1:n_mu]), 0)
      sigmastart <- unname(fcoefs[(n_mu + 1):(n_mu + n_sigma)])
      xistart <- unname(fcoefs[(n_mu + n_sigma + 1):length(fcoefs)])
      new_fit     <- update(fit, mu = mu,
                            mustart = mustart,
                            sigmastart = sigmastart,
                            xistart =xistart)     #update fit
      m_list[[i]] <- new_fit
      aic[i]      <- AIC(m_list[[i]])         #get AIC for update fit
    }

    x_i  <- which(aic == min(aic))

    # 3. Identify which of these models has the smallest AIC.
    # 4. If this AIC is smaller than that of the current model then
    #    return this model.  Otherwise, return the original model

    if(min(aic) < AIC(fit)){
      output <- m_list[[x_i]]
      output$added_covariate <- paste0("mu:", name[x_i])
      output$Note <- "covariate added"
      output$Input_fit <- fit$call

      list <- list()
      list$mu  <- m_list[[x_i]]$formulae$mu
      list$fit <- m_list[[x_i]]$call
      output$Output_fit <- list

      output$AIC        <- c(AIC(fit), min(aic))
      names(output$AIC) <- c("Input model", "Output model")
    }else{
      output <- fit
      output$added_covariate <- paste0("mu:", "NULL")
      output$Note      <- "Input fit and output fit are the same"
      output$Input_fit <- fit$call
    }
  }
  return(output)

}


# ----------------------------- sigma ---------------------------------

#' @rdname add1_LRT
#' @export
add1_AIC_sigma <- function(fit){
  ##1. Check if input arguments are missing
  if(missing(fit))  stop("fit must be specified")

  ##2. Check if input fit is an 'evreg' objects
  m <- deparse(substitute(fit))
  if(!inherits(get(m, envir = parent.frame()), "evreg")){
    stop("Use only with 'evreg' objects")
  }

  data    <- eval(fit$call$data)         #save data
  y       <- fit$call$y                  #response variable
  y_index <- which(colnames(data) == y)  #index of column y
  X       <- data[-y_index]              #data only with covariates
  n       <- ncol(X) + 1          #number of covatiates +1 in the data

  ##3. Check if input fit already has all covariates on sigma
  n_sigma <- ncol(fit$data$D$sigma)
  if(n_sigma == n){
    stop("All covariates has been added on sigma for input fit")
  }

  ##identify family from the fit

  ###################################################################
  ####----------------------------GEV----------------------------####
  ###################################################################
  if(inherits(get(m, envir = parent.frame()), "gev")){

    ###Extract covariates on sigma if there are in input fit
    if(n_sigma != 1){
      x_name <- all.vars(fit$formulae$sigma)
      index  <- which(colnames(X) %in% x_name)
      X <- X[-index]   #a data frame with covariates that are not in the sigma formula
    }
    name <- names(X)   #get names from rest of covariates

    #General steps
    # 1. Fit all of the possible models obtained by adding 1 covariate to the original model
    # 2. Calculate the value of AIC for all these models.
    aic <- c()
    m_list <- list()
    for(i in 1:length(name)){
      # adding more variables on sigma, one at a time
      sigma  <- update(fit$formulae$sigma, paste("", name[i], sep = "~.+"))  #update sigma formula
      # update a model call by adding one additional covariate on sigma
      # when we fit a new model in which an extra covariate is added,
      # we use starting values based on the fit of the smaller model.
      # The start value for the new added variable will be set to be zero.
      fcoefs <- fit$coefficients
      n_mu   <- ncol(fit$data$D$mu)
      mustart <- unname(fcoefs[1:n_mu])
      sigmastart <- c(unname(fcoefs[(n_mu + 1):(n_mu + n_sigma)]), 0)
      xistart <- unname(fcoefs[(n_mu + n_sigma + 1):length(fcoefs)])
      new_fit     <- update(fit, mu = fit$formulae$mu, sigma = sigma,
                            mustart = mustart,
                            sigmastart = sigmastart,
                            xistart =xistart)     #update fit
      m_list[[i]] <- new_fit
      aic[i]      <- AIC(m_list[[i]])         #get AIC for update fit
    }

    x_i  <- which(aic == min(aic))

    # 3. Identify which of these models has the smallest AIC.
    # 4. If this AIC is smaller than that of the current model then
    #    return this model.  Otherwise, return the original model

    if(min(aic) < AIC(fit)){
      output <- m_list[[x_i]]
      output$added_covariate <- paste0("sigma:", name[x_i])
      output$Note <- "covariate added"
      output$Input_fit <- fit$call

      list <- list()
      list$sigma <- m_list[[x_i]]$formulae$sigma
      list$fit   <- m_list[[x_i]]$call
      output$Output_fit <- list

      output$AIC        <- c(AIC(fit), min(aic))
      names(output$AIC) <- c("Input model", "Output model")
    }else{
      output <- fit
      output$added_covariate <- paste0("sigma:", "NULL")
      output$Note      <- "Input fit and output fit are the same"
      output$Input_fit <- fit$call
    }
  }
  return(output)

}


# ----------------------------- xi ---------------------------------

#' @rdname add1_LRT
#' @export
add1_AIC_xi <- function(fit){
  ##1. Check if input arguments are missing
  if(missing(fit))  stop("fit must be specified")

  ##2. Check if input fit is an 'evreg' objects
  m <- deparse(substitute(fit))
  if(!inherits(get(m, envir = parent.frame()), "evreg")){
    stop("Use only with 'evreg' objects")
  }

  data    <- eval(fit$call$data)         #save data
  y       <- fit$call$y                  #response variable
  y_index <- which(colnames(data) == y)  #index of column y
  X       <- data[-y_index]              #data only with covariates
  n       <- ncol(X) + 1          #number of covatiates +1 in the data

  ##3. Check if input fit already has all covariates on xi
  n_xi <- ncol(fit$data$D$xi)
  if(n_xi == n){
    stop("All covariates has been added on xi for input fit")
  }

  ##identify family from the fit

  ###################################################################
  ####----------------------------GEV----------------------------####
  ###################################################################
  if(inherits(get(m, envir = parent.frame()), "gev")){

    ###Extract covariates on xi if there are in input fit
    if(n_xi != 1){
      x_name <- all.vars(fit$formulae$xi)
      index  <- which(colnames(X) %in% x_name)
      X <- X[-index]   #a data frame with covariates that are not in the xi formula
    }
    name <- names(X)   #get names from rest of covariates

    #General steps
    # 1. Fit all of the possible models obtained by adding 1 covariate to the original model
    # 2. Calculate the value of AIC for all these models.
    aic <- c()
    m_list <- list()
    for(i in 1:length(name)){
      # adding more variables on xi, one at a time
      xi  <- update(fit$formulae$xi, paste("", name[i], sep = "~.+"))  #update xi formula
      # update a model call by adding one additional covariate on xi
      # when we fit a new model in which an extra covariate is added,
      # we use starting values based on the fit of the smaller model.
      # The start value for the new added variable will be set to be zero.
      fcoefs  <- fit$coefficients
      n_mu    <- ncol(fit$data$D$mu)
      n_sigma <- ncol(fit$data$D$sigma)
      mustart <- unname(fcoefs[1:n_mu])
      sigmastart <- unname(fcoefs[(n_mu + 1):(n_mu + n_sigma)])
      xistart <- c(unname(fcoefs[(n_mu + n_sigma + 1):length(fcoefs)]), 0)
      new_fit <- try(update(fit, mu = fit$formulae$mu, sigma = fit$formulae$sigma,
                            xi = xi,
                            mustart = mustart,
                            sigmastart = sigmastart,
                            xistart =xistart))     #update fit
      m_list[[i]] <- new_fit
      aic[i]      <- AIC(m_list[[i]])         #get AIC for update fit
    }

    x_i  <- which(aic == min(aic))

    # 3. Identify which of these models has the smallest AIC.
    # 4. If this AIC is smaller than that of the current model then
    #    return this model.  Otherwise, return the original model

    if(min(aic) < AIC(fit)){
      output <- m_list[[x_i]]
      output$added_covariate <- paste0("xi:", name[x_i])
      output$Note <- "covariate added"
      output$Input_fit <- fit$call

      list <- list()
      list$xi  <- m_list[[x_i]]$formulae$xi
      list$fit <- m_list[[x_i]]$call
      output$Output_fit <- list

      output$AIC        <- c(AIC(fit), min(aic))
      names(output$AIC) <- c("Input model", "Output model")
    }else{
      output <- fit
      output$added_covariate <- paste0("xi:", "NULL")
      output$Note      <- "Input fit and output fit are the same"
      output$Input_fit <- fit$call
    }
  }
  return(output)

}