R/betapr_prob.R

In Shakeel95/bioFlex: Estimation and model selection for strictly positive heavy tailed data, using flexible parametric distributions

#' Conditional probability for Beta Prime distribution
#'
#' betapr_flexprob returns the conditional probability P(Y<k | X) of a model fitted via the function betapr_flexfit; where α has been specified to be a function of covariates the required value should be specified using the ‘features’ parameter. The function includes a procedure for visualizing the conditional probability. betapr_flexprob also allows for the correlation of estimated parameters via the Cholesky decomposition of the variance-covariance matrix.
#'@param K Value for which P(Y<k | X) is computed.
#'@param model An object of class "mle2" produced using the function betapr_flexfit.
#'@param features A numeric vector specifying the value of covriates at which the conditional probability should be evaluated; the covariates in the vector should appear in the same order as they do in the model. Where a model does not depend on covariates the argument may be left blank.
#'@param visualise Logical. If TRUE (the default) the conditional distribution is plotted at P(Y<k | x) is shaded. 
#'@param xlim Numeric vectors of length 2, giving the coordinate range of the dependent variable.
#'@param draws The number of random draws from multivariate random normal representing correlated parameters. If parameter correlation is not required draws should be set to zero.
#'@details This function uses the two parameter parametrization of the Beta Prime distribution is used in Johnson and Kotz (1995). The tow parameter distribution ins a special case of the three parameter distribution, with σ = 1. The probability probability density function is used is:
#'@details f(y) = [y^α-1 (1+y)^-(α+β)]/Β(α,β)
#'@details The function returns:
#'@details P(Y<k | X) = I(α,β)
#'@details α may be a function of covariates; in which case, the cannonical log link function is used.
#'@references Johnson, N.L., Kotz, S., Balakrishnan, N. (1995). Continuous Univariate Distributions, Volume 2 (2nd Edition), Wiley.
#'@export 

betapr_flexprob <- function(K, model, features, visualise = TRUE, draws = 5, xlim) {
  
  mod <- as.data.frame(tidy(model))
  
  #================================================================#
  # linear predictor has intercept and is a function of covariates # 
  #================================================================#
  
  if (isTRUE("Intercept" %in% mod[,1])) {
    beta <- -1 
    while(isTRUE(beta<0)) {
      params <- auto_cholesky(model = model, draws = draws)
      beta <- params[1]
      Intercept <- params[2]
      betas <- params[3:length(params)]
    }
    alpha <- exp(Intercept + sum(features*betas))
    
    if(isTRUE(visualise)) {
      preview <<- function(x) {
        dbetapr(x, shape1 = alpha, shape2 = beta)
      }
      plot(preview, xlim = xlim, ylab = "Density", xlab = "", lwd = 3)
      Shade(preview, breaks = c(0,K), xlim = xlim)
      abline(a = 0, b = 0)
      return(as.numeric(pbetapr(K, shape1 = alpha, shape2 = beta)))
    } else {
      return(as.numeric(pbetapr(K, shape1 = alpha, shape2 = beta)))
    }
    
    #=====================================#
    # mu is not a function of covariates  #
    #=====================================# 
    
  } else if (!isTRUE("beta1" %in% mod[,1])) {
    
    beta <- -1 
    alpha <- -1 
    while(isTRUE((beta<0) | (alpha<0))) {
      params <- auto_cholesky(model = model, draws = draws)
      alpha <- params[1]
      beta <- params[2]
    }
    
    if(isTRUE(visualise)) {
      preview <<- function(x) {
        dbetapr(x, shape1 = alpha, shape2 = beta)
      }
      plot(preview, xlim = xlim, ylab = "Density", xlab = "", lwd = 3)
      Shade(preview, breaks = c(0,K), xlim = xlim)
      abline(a = 0, b = 0)
      return(as.numeric(pbetapr(K, shape1 = alpha, shape2 = beta)))
    } else {
      return(as.numeric(pbetapr(K, shape1 = alpha, shape2 = beta)))
    }
    
    #====================================================================#
    # linear predictor has no intercept but is a function of covariates  # 
    #====================================================================#
    
  } else {
    
    beta <- -1 
    while(isTRUE(beta<0)) {
      params <- auto_cholesky(model = model, draws = draws)
      beta <- params[1]
      betas <- params[2:length(params)]
    }
    alpha <- exp(sum(features*betas))
    
    if(isTRUE(visualise)) {
      preview <<- function(x) {
        dbetapr(x, shape1 = alpha, shape2 = beta)
      }
      plot(preview, xlim = xlim, ylab = "Density", xlab = "", lwd = 3)
      Shade(preview, breaks = c(0,K), xlim = xlim)
      abline(a = 0, b = 0)
      return(as.numeric(pbetapr(K, shape1 = alpha, shape2 = beta)))
    } else {
      return(as.numeric(pbetapr(K, shape1 = alpha, shape2 = beta)))
    }
  }
}