R/ldBetaStretched.R

In jasp-stats/jaspDistributions: Distributions Module for JASP

#
# Copyright (C) 2013-2020 University of Amsterdam
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 2 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <http://www.gnu.org/licenses/>.
#

LDbetaStretchedInternal <- function(jaspResults, dataset, options, state=NULL){
  options <- .ldRecodeOptionsBetaStretched(options)

  #### Show beta section ----
  .ldShowDistribution(jaspResults = jaspResults, options = options, name = gettext("beta distribution"),
                      parSupportMoments = .ldBetaStretchedParsSupportMoments,
                      formulaPDF        = .ldFormulaBetaStretchedPDF,
                      formulaCDF        = .ldFormulaBetaStretchedCDF,
                      formulaQF         = .ldFormulaBetaStretchedQF)

  #### Generate and Display data section ----
  # simulate and read data
  .simulateData(jaspResults, options)

  ready <- options[['variable']] != ""
  errors <- FALSE
  if(ready){
    variable <- dataset[[options[['variable']]]]
    variable <- variable[!is.na(variable)]
    errors <- .hasErrors(dataset, type = c("observations", "variance", "infinity", "limits"),
                         observations.amount = "<2",
                         limits.min = options$support$min, limits.max = options$support$max,
                         exitAnalysisIfErrors = FALSE)
  }

  # overview of the data
  .ldDescriptives(jaspResults, variable, options, ready, errors, "continuous")

  #### Fit data and assess fit ----
  .ldMLE(jaspResults, variable, options, ready, errors, .ldFillBetaStretchedEstimatesTable)

  return()
}

### options ----
.ldRecodeOptionsBetaStretched <- function(options){
  options[['parValNames']] <- c("alpha", "beta", "lowerBoundPar", "upperBoundPar")

  options[['pars']]   <- list(shape1 = options[['alpha']], shape2 = options[['beta']],
                              lowerbound = options[['lowerBoundPar']], upperbound = options[['upperBoundPar']])
  options[['fix.pars']] <- list(lowerbound = options[['lowerBoundPar']], upperbound = options[['upperBoundPar']])

  options[['pdfFun']] <- dsbeta
  options[['cdfFun']] <- psbeta
  options[['qFun']]   <- qsbeta
  options[['rFun']]   <- rsbeta
  options[['distNameInR']] <- "sbeta"

  options <- .ldOptionsDeterminePlotLimits(options)

  options$support <- list(min = options[['lowerBoundPar']], max = options[['upperBoundPar']])
  options$lowerBound <- c(0, 0)
  options$upperBound <- c(Inf, Inf)

  options$transformations <- c(alpha = "shape1", beta = "shape2")

  options
}

### text fill functions -----

.ldBetaStretchedParsSupportMoments <- function(jaspResults, options){
  if(options$parsSupportMoments && is.null(jaspResults[['parsSupportMoments']])){
    pars <- list()
    pars[[1]] <- gettextf("shape: %s", "&alpha; \u2208 \u211D<sup>+</sup>")
    pars[[2]] <- gettextf("shape: %s", "&beta; \u2208 \u211D<sup>+</sup>")
    pars[[3]] <- gettextf("lower bound: %s", "a \u2208 \u211D<sup>+</sup>")
    pars[[4]] <- gettextf("upper bound: %s", "b \u2208 \u211D<sup>+</sup>")

    support <- "x \u2208 [a, b]"

    moments <- list()
    moments$expectation <- "b + &alpha; (&alpha; + &beta;)<sup>-1</sup> &times; (a-b)"
    moments$variance    <- "&alpha;&beta; (&alpha; + &beta;)<sup>-2</sup> (&alpha; + &beta; + 1)<sup>-1</sup> &times; (a-b)<sup>2</sup>"

    jaspResults[['parsSupportMoments']] <- .ldParsSupportMoments(pars, support, moments)
  }
}

.ldFormulaBetaStretchedPDF <- function(options){
  text <- "<MATH>
  f(x; <span style='color:red'>&alpha;</span>, <span style='color:blue'>&beta;</span>) =
  </MATH>"

  return(gsub(pattern = "\n", replacement = " ", x = text))
}

.ldFormulaBetaStretchedCDF <- function(options){
  text <- "<MATH>
  F(x; <span style='color:red'>&alpha;</span>, <span style='color:blue'>&beta;</span>) =
  </MATH>"

  return(gsub(pattern = "\n", replacement = " ", x = text))
}

.ldFormulaBetaStretchedQF <- function(options){
  text <- "<MATH>
  Q(p; <span style='color:red'>&alpha;</span>, <span style='color:blue'>&beta;</span>) =
  </MATH>"

  return(gsub(pattern = "\n", replacement = " ", x = text))
}

#### Table functions ----

.ldFillBetaStretchedEstimatesTable <- function(table, results, options, ready){
  if(!ready) return()
  if(is.null(results)) return()
  if(is.null(table)) return()

  pars <- c(alpha = "\u03B1", beta = "\u03B2")

  res <- results$structured
  res <- res[res$par %in% names(pars),]
  res$parName <- c(pars)

  if(results$fitdist$convergence != 0){
    table$addFootnote(gettext("The optimization did not converge, try adjusting the parameter values."), symbol = gettext("<i>Warning.</i>"))
  }
  if(!is.null(results$fitdist$optim.message)){
    table$addFootnote(results$fitdist$message, symbol = gettext("<i>Warning.</i>"))
  }

  table$setData(res)

  return()
}


dsbeta <- function(x, shape1, shape2, lowerbound, upperbound, log = FALSE) {
  xx <- (x-lowerbound) / (upperbound - lowerbound)

  out <- stats::dbeta(xx, shape1, shape2, log = TRUE)
  out <- out - log(upperbound-lowerbound)
  if(!log) out <- exp(out)

  return(out)
}

psbeta <- function(q, shape1, shape2, lowerbound, upperbound, lower.tail = TRUE, log.p = FALSE) {
  qq <- (q-lowerbound) / (upperbound - lowerbound)
  out <- stats::pbeta(qq, shape1, shape2, lower.tail = lower.tail, log.p = log.p)
  return(out)
}

qsbeta <- function(p, shape1, shape2, lowerbound, upperbound, lower.tail = TRUE, log.p = FALSE) {
  out <- stats::qbeta(p, shape1, shape2, lower.tail = lower.tail, log.p = log.p)
  out <- lowerbound + out * (upperbound-lowerbound)

  return(out)
}

rsbeta <- function(n, shape1, shape2, lowerbound, upperbound) {
  x <- stats::rbeta(n, shape1, shape2)
  x <- lowerbound + x * (upperbound-lowerbound)

  return(x)
}