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Heaped Distribution Estimation: Shiny app at http://www.statistics.calpoly.edu/shiny
Heaped Distribution Estimation Shiny App
Base R code created by Jimmy Wong
Shiny app files created by Jimmy Wong
Cal Poly Statistics Dept Shiny Series
http://statistics.calpoly.edu/shiny
Title: Heaped Distribution Estimation
Author: Jimmy Wong
AuthorUrl: https://www.linkedin.com/in/jimmywong46
License: MIT
DisplayMode: Normal
Tags: Heaped Distribution Estimation
Type: Shiny
The MIT License (MIT)
Copyright (c) 2015 Jimmy Wong
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.
# -----------------------------------------------------------------
# App Title: Heaped Distribution Estimation
# Author: Jimmy Wong
# -----------------------------------------------------------------
##############################################
##############################################
## Libraries
##############################################
##############################################
if (!require("ggplot2")) install.packages("ggplot2")
if (!require("gridExtra")) install.packages("gridExtra")
if (!require("CompGLM")) install.packages("CompGLM")
if (!require("VGAM")) install.packages("VGAM")
if (!require("actuar")) install.packages("actuar")
if (!require("compoisson")) install.packages("compoisson")
if (!require("Delaporte")) install.packages("Delaporte")
library(ggplot2)
library(gridExtra)
library(CompGLM)
library(VGAM)
library(actuar)
library(compoisson)
library(Delaporte)
##############################################
##############################################
## Expit function
##############################################
##############################################
expit = function(x)
{
exp(x)/(1+exp(x))
}
##############################################
##############################################
## Logit function
##############################################
##############################################
logit = function(p)
{
log(p/(1-p))
}
##############################################
##############################################
## Loglikelihood functions
##############################################
##############################################
loglik.nb = function(params, degree)
{
alpha1 = expit(params[1])
alpha2 = expit(params[2])
r = exp(params[3])
mu = exp(params[4])
prob.vec = rep(NA, length(degree))
ind1 = which(degree==0)
ind2 = which(degree==1 | degree==2 | degree==3 | degree==4)
ind3 = which(degree==5)
ind4 = which(degree>5 & degree%%5!=0)
ind5 = which(degree>5 & degree%%5==0)
prob.vec[ind1] = dnbinom(0, size=r, mu=mu)
prob.vec[ind2] = (1-alpha1)*(dnbinom(degree[ind2], size=r, mu=mu))
prob.vec[ind3] = dnbinom(5, size=r, mu=mu) + alpha1*sum(dnbinom(1:4, size=r, mu=mu)) + alpha2*sum(dnbinom(6:7, size=r, mu=mu))
prob.vec[ind4] = (1-alpha2)*dnbinom(degree[ind4], size=r, mu=mu)
prob.vec[ind5] = alpha2*(dnbinom(degree[ind5]-2, size=r, mu=mu) + dnbinom(degree[ind5]-1, size=r, mu=mu) +
dnbinom(degree[ind5]+1, size=r, mu=mu) + dnbinom(degree[ind5]+2, size=r, mu=mu)) +
dnbinom(degree[ind5], size=r, mu=mu)
loglik.sum = sum(log(prob.vec)[which(log(prob.vec)!=-Inf & !is.na(prob.vec))])
return(loglik.sum)
}
loglik.bb = function(params, degree)
{
alpha1 = expit(params[1])
alpha2 = expit(params[2])
r = round(exp(params[3]))
p = expit(params[4])
cor = expit(params[5])
prob.vec = rep(NA, length(degree))
ind1 = which(degree==0)
ind2 = which(degree==1 | degree==2 | degree==3 | degree==4)
ind3 = which(degree==5)
ind4 = which(degree>5 & degree%%5!=0)
ind5 = which(degree>5 & degree%%5==0)
prob.vec[ind1] = dbetabinom(0, size=r, prob=p, rho=cor)
prob.vec[ind2] = (1-alpha1)*(dbetabinom(degree[ind2], size=r, prob=p, rho=cor))
prob.vec[ind3] = dbetabinom(5, size=r, prob=p, rho=cor) + alpha1*sum(dbetabinom(1:4, size=r, prob=p, rho=cor)) +
alpha2*sum(dbetabinom(6:7, size=r, prob=p, rho=cor))
prob.vec[ind4] = (1-alpha2)*dbetabinom(degree[ind4], size=r, prob=p, rho=cor)
prob.vec[ind5] = alpha2*(dbetabinom(degree[ind5]-2, size=r, prob=p, rho=cor) + dbetabinom(degree[ind5]-1, size=r, prob=p, rho=cor) +
dbetabinom(degree[ind5]+1, size=r, prob=p, rho=cor) + dbetabinom(degree[ind5]+2, size=r, prob=p, rho=cor)) +
dbetabinom(degree[ind5], size=r, prob=p, rho=cor)
loglik.sum = sum(log(prob.vec)[which(log(prob.vec)!=-Inf | !is.na(prob.vec))])
return(loglik.sum)
}
loglik.cmp = function(params, degree)
{
alpha1 = expit(params[1])
alpha2 = expit(params[2])
lambda = exp(params[3])
nu = exp(params[4])
prob.vec = rep(NA, length(degree))
ind1 = which(degree==0)
ind2 = which(degree==1 | degree==2 | degree==3 | degree==4)
ind3 = which(degree==5)
ind4 = which(degree>5 & degree%%5!=0)
ind5 = which(degree>5 & degree%%5==0)
prob.vec[ind1] = dcom(0, lambda=lambda, nu=nu)
prob.vec[ind2] = (1-alpha1)*(dcom(degree[ind2], lambda=lambda, nu=nu))
prob.vec[ind3] = dcom(5, lambda=lambda, nu=nu) + alpha1*sum(dcom(1:4, lambda=lambda, nu=nu)) +
alpha2*sum(dcom(6:7, lambda=lambda, nu=nu))
prob.vec[ind4] = (1-alpha2)*dcom(degree[ind4], lambda=lambda, nu=nu)
prob.vec[ind5] = alpha2*(dcom(degree[ind5]-2, lambda=lambda, nu=nu) + dcom(degree[ind5]-1, lambda=lambda, nu=nu) +
dcom(degree[ind5]+1, lambda=lambda, nu=nu) + dcom(degree[ind5]+2, lambda=lambda, nu=nu)) +
dcom(degree[ind5], lambda=lambda, nu=nu)
loglik.sum = sum(log(prob.vec)[which(log(prob.vec)!=-Inf & !is.na(prob.vec))])
return(loglik.sum)
}
loglik.del = function(params, degree)
{
alpha1 = expit(params[1])
alpha2 = expit(params[2])
a.d = exp(params[3])
b.d = exp(params[4])
c.d = exp(params[5])
prob.vec = rep(NA, length(degree))
ind1 = which(degree==0)
ind2 = which(degree==1 | degree==2 | degree==3 | degree==4)
ind3 = which(degree==5)
ind4 = which(degree>5 & degree%%5!=0)
ind5 = which(degree>5 & degree%%5==0)
prob.vec[ind1] = ddelap(0,alpha=a.d,beta=b.d,lambda=c.d)
prob.vec[ind2] = (1-alpha1)*(ddelap(degree[ind2], alpha=a.d, beta=b.d, lambda=c.d))
prob.vec[ind3] = ddelap(5, alpha=a.d, beta=b.d, lambda=c.d) + alpha1*sum(ddelap(1:4, alpha=a.d, beta=b.d, lambda=c.d)) +
alpha2*sum(ddelap(6:7, alpha=a.d, beta=b.d, lambda=c.d))
prob.vec[ind4] = (1-alpha2)*ddelap(degree[ind4], alpha=a.d, beta=b.d, lambda=c.d)
prob.vec[ind5] = alpha2*(ddelap(degree[ind5]-2, alpha=a.d, beta=b.d, lambda=c.d) + ddelap(degree[ind5]-1, alpha=a.d, beta=b.d, lambda=c.d) +
ddelap(degree[ind5]+1, alpha=a.d, beta=b.d, lambda=c.d) + ddelap(degree[ind5]+2, alpha=a.d, beta=b.d, lambda=c.d)) +
ddelap(degree[ind5], alpha=a.d, beta=b.d, lambda=c.d)
loglik.sum = sum(log(prob.vec)[which(log(prob.vec)!=-Inf & !is.na(prob.vec))])
return(loglik.sum)
}
loglik.ys= function(params, degree)
{
alpha1 = expit(params[1])
alpha2 = expit(params[2])
r.ys = exp(params[3])
prob.vec = rep(NA, length(degree))
ind1 = which(degree==0)
ind2 = which(degree==1 | degree==2 | degree==3 | degree==4)
ind3 = which(degree==5)
ind4 = which(degree>5 & degree%%5!=0)
ind5 = which(degree>5 & degree%%5==0)
prob.vec[ind1] = dyules(0, rho=r.ys)
prob.vec[ind2] = (1-alpha1)*(dyules(degree[ind2], rho=r.ys))
prob.vec[ind3] = dyules(5, rho=r.ys) + alpha1*sum(dyules(1:4, rho=r.ys)) +
alpha2*sum(dyules(6:7, rho=r.ys))
prob.vec[ind4] = (1-alpha2)*dyules(degree[ind4], rho=r.ys)
prob.vec[ind5] = alpha2*(dyules(degree[ind5]-2, rho=r.ys) + dyules(degree[ind5]-1, rho=r.ys) +
dyules(degree[ind5]+1, rho=r.ys) + dyules(degree[ind5]+2, rho=r.ys)) +
dyules(degree[ind5], rho=r.ys)
loglik.sum = sum(log(prob.vec)[which(log(prob.vec)!=-Inf & !is.na(prob.vec))])
return(loglik.sum)
}
##############################################
##############################################
## Maximizing loglik functions
##############################################
##############################################
max.loglik.nb = function(a,b,c,d,e,f,g,h,degree)
{
i=a
m=1
mle.nb=NULL
conv.nb=NULL
pars.nb=list()
while(i<b)
{
i=i+.1
j=c
while(j<d)
{
j=j+.1
k=e
while(k<f)
{
k=k+1
l=g
while(l<h)
{
l=l+1
mle.res = optim(par=c(logit(i),logit(j),log(k),log(l)),
loglik.nb, degree=degree, control=list(fnscale=-1))
mle.nb[m] = mle.res$value
conv.nb[m] = mle.res$convergence
pars.nb[[m]] = c(expit(mle.res$par[1:2]), exp(mle.res$par[3:4]))
m=m+1
}
}
}
}
return(list(mle.nb, conv.nb, pars.nb))
}
max.loglik.bb = function(a,b,c,d,e,f,g,h,aa,bb,degree)
{
i=a
x=1
mle.bb=NULL
conv.bb=NULL
pars.bb=list()
while(i<b)
{
i=i+.2
j=c
while(j<d)
{
j=j+.2
k=e
while(k<f)
{
k=k+2
l=g
while(l<h)
{
l=l+.2
m=aa
while(m<bb)
{
m=m+.2
mle.res = try(optim(par=c(logit(i),logit(j),log(k),logit(l),logit(m)),
loglik.bb, degree=degree, control=list(fnscale=-1, maxit=10000)),
silent=TRUE)
if(class(mle.res)!="try-error")
{
mle.bb[x] = mle.res$value
conv.bb[x] = mle.res$convergence
pars.bb[[x]] = c(expit(mle.res$par[1:2]), exp(mle.res$par[3]), expit(mle.res$par[4:5]))
x=x+1
}
}
}
}
}
}
return(list(mle.bb, conv.bb, pars.bb))
}
max.loglik.cmp = function(a,b,c,d,e,f,g,h,degree)
{
i=a
x=1
mle.cmp=NULL
conv.cmp=NULL
pars.cmp=list()
while(i<b)
{
i=i+.2
j=c
while(j<d)
{
j=j+.2
k=e
while(k<f)
{
k=k+1
l=g
while(l<h)
{
l=l+1
mle.res = try(optim(par=c(logit(i),logit(j),log(k),log(l)),
loglik.cmp, degree=degree, control=list(fnscale=-1,maxit=10000)),
silent=TRUE)
if(class(mle.res)!="try-error")
{
mle.cmp[x] = mle.res$value
conv.cmp[x] = mle.res$convergence
pars.cmp[[x]] = c(expit(mle.res$par[1:2]), exp(mle.res$par[3:4]))
x=x+1
}
}
}
}
}
return(list(mle.cmp, conv.cmp, pars.cmp))
}
max.loglik.del = function(a,b,c,d,e,f,g,h,aa,bb,degree)
{
i=a
x=1
mle.d=NULL
conv.d=NULL
pars.d=list()
while(i<b)
{
i=i+.2
j=c
while(j<d)
{
j=j+.2
k=e
while(k<f)
{
k=k+2
l=g
while(l<h)
{
l=l+2
m=aa
while(m<bb)
{
m=m+2
mle.res = try(optim(par=c(logit(i),logit(j),log(k),log(l),log(m)),
loglik.del, degree=degree, control=list(fnscale=-1,maxit=10000)),
silent=TRUE)
if(class(mle.res)!="try-error")
{
mle.d[x] = mle.res$value
conv.d[x] = mle.res$convergence
pars.d[[x]] = c(expit(mle.res$par[1:2]), exp(mle.res$par[3:5]))
x=x+1
}
}
}
}
}
}
return(list(mle.d, conv.d, pars.d))
}
max.loglik.gp = function(a,b,c,d,e,f,g,h,aa,bb,cc,dd)
{
i=a
x=1
mle.gp.trunc=NULL
conv.gp.trunc=NULL
pars.gp.trunc=list()
while(i<b)
{
i=i+.1
j=c
while(j<d)
{
j=j+.1
k=e
while(k<f)
{
k=k+1
l=g
while(l<h)
{
l=l+1
m=aa
while(m<bb)
{
m=m+1
n=cc
while(n<dd)
{
n=n+.1
mle.res = try(optim(par=c(logit(i),logit(j),log(k),log(l),log(m),logit(n)),
loglik.gp.trunc, degree=yes.am, control=list(fnscale=-1)),
silent=TRUE)
if(class(mle.res)!="try-error")
{
mle.gp.trunc[x] = mle.res$value
conv.gp.trunc[x] = mle.res$convergence
pars.gp.trunc[[x]] = c(expit(mle.res$par[1:2]), exp(mle.res$par[3:5]), expit(mle.res$par[6]))
x=x+1
}
}
}
}
}
}
}
}
max.loglik.ys = function(a,b,c,d,e,f,degree)
{
i=a
x=1
mle.ys=NULL
conv.ys=NULL
pars.ys=list()
while(i<b)
{
i=i+.2
j=c
while(j<d)
{
j=j+.2
k=e
while(k<f)
{
k=k+2
mle.res = try(optim(par=c(logit(i),logit(j),log(k)),
loglik.ys, degree=degree, control=list(fnscale=-1,maxit=10000)),
silent=TRUE)
if(class(mle.res)!="try-error")
{
mle.ys[x] = mle.res$value
conv.ys[x] = mle.res$convergence
pars.ys[[x]] = c(expit(mle.res$par[1:2]), exp(mle.res$par[3]))
x=x+1
}
}
}
}
return(list(mle.ys, conv.ys, pars.ys))
}
##############################################
##############################################
## Simulation functions
##############################################
##############################################
nb.sim = function(n,a1,a2,size,mu,sample.size)
{
mle.sim=matrix(nrow=n, ncol=4)
i=0
while(i<n)
{
i=i+1
sim.deg = rnbinom(sample.size, size=size, mu=mu)
ind1 = which(sim.deg==1 | sim.deg==2 | sim.deg==3 | sim.deg==4)
ind2 = which(sim.deg>5 & sim.deg%%5!=0)
bin1 = rbinom(n=length(ind1), size=1, p=a1)
bin2 = rbinom(n=length(ind2), size=1, p=a2)
sim.deg[ind1][which(bin1==1)] = 5
sim.deg[ind2][which(bin2==1)] = (sim.deg[ind2][which(bin2==1)] - sim.deg[ind2][which(bin2==1)]%%5)*(sim.deg[ind2][which(bin2==1)]%%5<=2) +
(sim.deg[ind2][which(bin2==1)] + (5-sim.deg[ind2][which(bin2==1)]%%5))*(sim.deg[ind2][which(bin2==1)]%%5>2)
sim.res = optim(par=c(logit(a1),logit(a2),log(size),log(mu)), loglik.nb, degree=sim.deg,
control=list(fnscale=-1,maxit=10000))
mle.sim[i,1:2] = expit(sim.res$par[1:2])
mle.sim[i,3:4] = exp(sim.res$par[3:4])
}
return(mle.sim)
}
bb.sim = function(n,a1,a2,size,prob,rho,sample.size)
{
mle.sim=matrix(nrow=n, ncol=5)
i=0
while(i<n)
{
i=i+1
sim.deg = rbetabinom(sample.size,size=size,prob=prob,rho=rho)
ind1 = which(sim.deg==1 | sim.deg==2 | sim.deg==3 | sim.deg==4)
ind2 = which(sim.deg>5 & sim.deg%%5!=0)
bin1 = rbinom(n=length(ind1), size=1, p=a1)
bin2 = rbinom(n=length(ind2), size=1, p=a2)
sim.deg[ind1][which(bin1==1)] = 5
sim.deg[ind2][which(bin2==1)] = (sim.deg[ind2][which(bin2==1)] - sim.deg[ind2][which(bin2==1)]%%5)*(sim.deg[ind2][which(bin2==1)]%%5<=2) +
(sim.deg[ind2][which(bin2==1)] + (5-sim.deg[ind2][which(bin2==1)]%%5))*(sim.deg[ind2][which(bin2==1)]%%5>2)
sim.res = optim(par=c(logit(a1),logit(a2),log(size),logit(prob),logit(rho)),
loglik.bb, degree=sim.deg, control=list(fnscale=-1,maxit=10000))
mle.sim[i,1:2] = expit(sim.res$par[1:2])
mle.sim[i,3] = exp(sim.res$par[3])
mle.sim[i,4:5] = expit(sim.res$par[4:5])
}
return(mle.sim)
}
cmp.sim = function(n,a1,a2,lam,nu,sample.size)
{
mle.sim=matrix(nrow=n, ncol=4)
i=0
x=0
while(i<n)
{
i=i+1
sim.deg = rcom(sample.size,lambda=lam,nu=nu)
ind1 = which(sim.deg==1 | sim.deg==2 | sim.deg==3 | sim.deg==4)
ind2 = which(sim.deg>5 & sim.deg%%5!=0)
bin1 = rbinom(n=length(ind1), size=1, p=a1)
bin2 = rbinom(n=length(ind2), size=1, p=a2)
sim.deg[ind1][which(bin1==1)] = 5
sim.deg[ind2][which(bin2==1)] = (sim.deg[ind2][which(bin2==1)] - sim.deg[ind2][which(bin2==1)]%%5)*(sim.deg[ind2][which(bin2==1)]%%5<=2) +
(sim.deg[ind2][which(bin2==1)] + (5-sim.deg[ind2][which(bin2==1)]%%5))*(sim.deg[ind2][which(bin2==1)]%%5>2)
sim.res = try(optim(par=c(logit(a1),logit(a2),log(lam),log(nu)),loglik.cmp, degree=sim.deg,
control=list(fnscale=-1,maxit=10000)),silent=TRUE)
if(class(sim.res)!="try-error")
{
x=x+1
mle.sim[x,1:2] = expit(sim.res$par[1:2])
mle.sim[x,3:4] = exp(sim.res$par[3:4])
}
}
return(mle.sim)
}
del.sim = function(n,a1,a2,alpha,beta,lambda,sample.size)
{
mle.sim=matrix(nrow=n, ncol=5)
i=0
x=0
while(i<n)
{
i=i+1
sim.deg = rdelap(sample.size,alpha=alpha,beta=beta,lambda=lambda)
ind1 = which(sim.deg==1 | sim.deg==2 | sim.deg==3 | sim.deg==4)
ind2 = which(sim.deg>5 & sim.deg%%5!=0)
bin1 = rbinom(n=length(ind1), size=1, p=a1)
bin2 = rbinom(n=length(ind2), size=1, p=a2)
sim.deg[ind1][which(bin1==1)] = 5
sim.deg[ind2][which(bin2==1)] = (sim.deg[ind2][which(bin2==1)] - sim.deg[ind2][which(bin2==1)]%%5)*(sim.deg[ind2][which(bin2==1)]%%5<=2) +
(sim.deg[ind2][which(bin2==1)] + (5-sim.deg[ind2][which(bin2==1)]%%5))*(sim.deg[ind2][which(bin2==1)]%%5>2)
sim.res = try(optim(par=c(logit(a1),logit(a2),log(alpha),log(beta),log(lambda)), loglik.del, degree=sim.deg,
control=list(fnscale=-1,maxit=10000)),silent=TRUE)
if(class(sim.res)!="try-error")
{
x=x+1
mle.sim[x,1:2] = expit(sim.res$par[1:2])
mle.sim[x,3:5] = exp(sim.res$par[3:5])
}
}
return(mle.sim)
}
ys.sim = function(n,a1,a2,rho,sample.size)
{
mle.sim=matrix(nrow=n, ncol=3)
i=0
x=0
while(i<n)
{
i=i+1
sim.deg = ryules(sample.size,rho=rho)
ind1 = which(sim.deg==1 | sim.deg==2 | sim.deg==3 | sim.deg==4)
ind2 = which(sim.deg>5 & sim.deg%%5!=0)
bin1 = rbinom(n=length(ind1), size=1, p=a1)
bin2 = rbinom(n=length(ind2), size=1, p=a2)
sim.deg[ind1][which(bin1==1)] = 5
sim.deg[ind2][which(bin2==1)] = (sim.deg[ind2][which(bin2==1)] - sim.deg[ind2][which(bin2==1)]%%5)*(sim.deg[ind2][which(bin2==1)]%%5<=2) +
(sim.deg[ind2][which(bin2==1)] + (5-sim.deg[ind2][which(bin2==1)]%%5))*(sim.deg[ind2][which(bin2==1)]%%5>2)
sim.res = try(optim(par=c(logit(a1),logit(a2),log(rho)),loglik.ys, degree=sim.deg,
control=list(fnscale=-1,maxit=10000)),silent=TRUE)
if(class(sim.res)!="try-error")
{
x=x+1
mle.sim[x,1:2] = expit(sim.res$par[1:2])
mle.sim[x,3] = exp(sim.res$par[3])
}
}
return(mle.sim)
}
##############################################################################################################
##############################################################################################################
## Shiny server
##############################################################################################################
##############################################################################################################
shinyServer(function(input, output, session) {
##############################################
##############################################
## Simulate Data Panel
##############################################
##############################################
simdat = reactive({
if(input$dataupload & !is.null(input$file))
{
file = read.csv(input$file$datapath, header=input$header, sep=input$sep, quote=input$quote)
return(file)
}else if(!input$dataupload)
{
input$beginstudy
isolate({
if(input$distdat=="Negative Binomial")
{
x = rnbinom(input$nsim.dat,size=input$size.dat,mu=input$mu.dat)
y = dnbinom(min(x):max(x),size=input$size.dat,mu=input$mu.dat)
} else if(input$distdat=="Beta Binomial")
{
x = rbetabinom(input$nsim.dat,size=input$rbb.dat,prob=input$pbb.dat,rho=input$corbb.dat)
y = dbetabinom(min(x):max(x),size=input$rbb.dat,prob=input$pbb.dat,rho=input$corbb.dat)
} else if(input$distdat=="Conway-Maxwell Poisson")
{
x = rcom(input$nsim.dat,lambda=input$lam.dat,nu=input$nu.dat)
y = dcom(min(x):max(x),lambda=input$lam.dat,nu=input$nu.dat)
} else if(input$distdat=="Delaporte")
{
x = rdelap(input$nsim.dat,alpha=input$adel.dat,beta=input$bdel.dat,lambda=input$cdel.dat)
y = ddelap(min(x):max(x),alpha=input$adel.dat,beta=input$bdel.dat,lambda=input$cdel.dat)
} else if(input$distdat=="Yule-Simon")
{
x = ryules(input$nsim.dat,rho=input$rho.dat)
y = dyules(min(x):max(x),rho=input$rho.dat)
}
return(list(samp=x,dens=y))
})
}
})
output$simdatplot = renderPlot({
if(input$dataupload & !is.null(simdat()))
{
dat = data.frame(x=simdat()[[1]])
ggplot() + geom_histogram(data=dat, aes(x=x,y=..density..),color="navy",fill="white",binwidth=1) +
xlab("Uploaded data") + ylab("Relative frequency") + ggtitle("Histogram of uploaded data") +
theme_bw() + scale_x_continuous(breaks=seq(min(dat$x),max(dat$x),by=5))
}else if(!input$dataupload)
{
input$beginstudy
isolate({
if(input$beginstudy>0)
{
dat = data.frame(x=simdat()[[1]])
dat1 = data.frame(x=min(simdat()[[1]]):max(simdat()[[1]]),
y=simdat()[[2]])
ggplot() + geom_histogram(data=dat, aes(x=x,y=..density..),color="navy",fill="white",binwidth=1) +
xlab("Actual values") + ylab("Relative frequency") + ggtitle("Histogram of actual values C with underlying distribution overlayed") +
theme_bw() + geom_point(data=dat1, aes(x=x,y=y), size=3, shape=1) +
scale_x_continuous(breaks=seq(min(dat$x),max(dat$x),by=5))
}
})
}
})
output$distselect = renderUI({
if(input$beginstudy>=0)
{
if(input$distdat=="Negative Binomial")
{
return(p("You have selected: C ~", code(paste0("NB(",input$size.dat,",",input$mu.dat,")"),
style = "color:navy")))
} else if(input$distdat=="Beta Binomial")
{
return(p("You have selected: C ~",
code(paste0("BB(",input$rbb.dat,",",input$pbb.dat,",",input$corbb.dat,")"),
style = "color:navy")))
} else if(input$distdat=="Conway-Maxwell Poisson")
{
return(p("You have selected: C ~",
code(paste0("COM-Poisson(",input$lam.dat,",",input$nu.dat,")"),
style = "color:navy")))
} else if(input$distdat=="Delaporte")
{
return(p("You have selected: C ~",
code(paste0("DEL(",input$adel.dat,",",input$bdel.dat,",",input$cdel.dat,")"),
style = "color:navy")))
} else if(input$distdat=="Yule-Simon")
{
return(p("You have selected: C ~", code(paste0("YS(",input$rho.dat,")"),
style = "color:navy")))
}
}
return(list(samp=x,dens=y))
})
##############################################
##############################################
## Heaping Process Panel
##############################################
##############################################
output$prob1 = renderUI({
withMathJax("\\(\\alpha_1 = P(Y=5\\,|\\,C\\in\\{1,2,3,4\\})\\)")
})
output$prob2 = renderUI({
withMathJax("\\(\\alpha_2 = P(Y= 5[C/5]\\,|\\,C>5\\,and\\,not\\,a\\,multiple\\,of\\,5)\\)")
})
heapeddat = reactive({
if(input$dataupload & !is.null(simdat()))
{
return(list(simdat()[[1]]))
}else if(!input$dataupload)
{
input$beginround
isolate({
dat = simdat()[[1]]
ind1 = which(dat==1 | dat==2 | dat==3 | dat==4)
ind2 = which(dat>5 & dat%%5!=0)
bin1 = rbinom(n=length(ind1), size=1, p=input$alpha1)
bin2 = rbinom(n=length(ind2), size=1, p=input$alpha2)
dat[ind1][which(bin1==1)] = 5
dat[ind2][which(bin2==1)] = (dat[ind2][which(bin2==1)] - dat[ind2][which(bin2==1)]%%5)*(dat[ind2][which(bin2==1)]%%5<=2) +
(dat[ind2][which(bin2==1)] + (5-dat[ind2][which(bin2==1)]%%5))*(dat[ind2][which(bin2==1)]%%5>2)
if(input$distdat=="Negative Binomial")
{
dens = dnbinom(min(dat):max(dat),size=input$size.dat,mu=input$mu.dat)
} else if(input$distdat=="Beta Binomial")
{
dens = dbetabinom(min(dat):max(dat),size=input$rbb.dat,prob=input$pbb.dat,rho=input$corbb.dat)
} else if(input$distdat=="Delaporte")
{
dens = ddelap(min(dat):max(dat),alpha=input$adel.dat,beta=input$bdel.dat,lambda=input$cdel.dat)
} else if(input$distdat=="Conway-Maxwell Poisson")
{
dens = dcom(min(dat):max(dat),lambda=input$lam.dat,nu=input$nu.dat)
} else if(input$distdat=="Yule-Simon")
{
dens = dyules(min(dat):max(dat),rho=input$rho.dat)
}
return(list(heaped=dat,dens=dens))
})
}
})
output$heapeddatplot = renderPlot({
if(input$dataupload & !is.null(simdat()))
{
dat3 = data.frame(x=simdat()[[1]])
g1 = ggplot() + geom_histogram(data=dat3, aes(x=x,y=..density..),color="darkred",fill="white",binwidth=1) +
xlab("Rounded values") + ylab("Relative frequency") + ggtitle("Histogram of rounded values Y") +
theme_bw() + scale_x_continuous(breaks=seq(min(dat3$x),max(dat3$x),by=5))
return(g1)
}else if(!input$dataupload)
{
input$beginround
isolate({
dat3 = data.frame(x=simdat()[[1]])
dat4 = data.frame(x=min(simdat()[[1]]):max(simdat()[[1]]),
y=simdat()[[2]])
g1 = ggplot() + geom_histogram(data=dat3, aes(x=x,y=..density..),color="navy",fill="white",binwidth=1) +
xlab("Actual values") + ylab("Relative frequency") + ggtitle("Histogram of actual values C with\nunderlying distribution overlayed") +
theme_bw() + geom_point(data=dat4, aes(x=x,y=y), size=3, shape=1) +
scale_x_continuous(breaks=seq(min(dat3$x),max(dat3$x),by=5))
if(input$beginround==0 & input$beginstudy>0)
{
graph = arrangeGrob(g1,nrow=1,ncol=2)
return(graph)
} else if(input$beginround>0 & input$beginstudy!=0)
{
dat1 = data.frame(x=heapeddat()[[1]])
dat2 = data.frame(x=min(heapeddat()[[1]]):max(heapeddat()[[1]]),
y=heapeddat()[[2]])
g2 = ggplot() + geom_histogram(data=dat1, aes(x=x,y=..density..),fill="white",color="darkred",binwidth=1) +
xlab("Rounded values") + ylab("Relative frequency") + ggtitle("Histogram of rounded values Y with\nunderlying distribution overlayed") +
theme_bw() + geom_point(data=dat2, aes(x=x,y=y), size=3, shape=1) +
scale_x_continuous(breaks=seq(min(dat1$x),max(dat1$x),by=5))
graph = arrangeGrob(g1,g2,nrow=1)
return(graph)
}
})
}
})
output$heapedpop = renderUI({
if(!input$dataupload & input$beginround>0)
return(bsPopover("heapeddatplot","Compare and contrast","Note the unusual peaks at multiples of 5 in the heaped distribution compared to the underlying distribution. In addition, when both rounding probabilities are 0, the heaped distribution is the same as the underlying distribution.",
trigger="hover",placement="left"))
})
##############################################
##############################################
## Maximum Likelihood Estimation Panel
##############################################
##############################################
createAlert(session, inputId = "optimtime",
message = "Choose each range of starting values to be close to the specified parameters; this will reduce the length of the optimization period.",
type = "warning", dismiss = TRUE, block = FALSE,append = TRUE
)
mleoptim = reactive({
input$startoptim
withProgress(session, {
setProgress(message = "Optimizing loglikelihood function...",value=1)
isolate({
if (input$startoptim>0)
{
if ((!input$dataupload & input$distdat=="Negative Binomial") | (input$dataupload & input$distdat1=="Negative Binomial"))
{
max.loglik.nb(input$alpha1.mle[1],input$alpha1.mle[2],input$alpha2.mle[1],input$alpha2.mle[2],
input$size.mle.nb[1],input$size.mle.nb[2],input$mu.mle.nb[1],input$mu.mle.nb[2],degree=heapeddat()[[1]])
} else if((!input$dataupload & input$distdat=="Beta Binomial") | (input$dataupload & input$distdat1=="Beta Binomial"))
{
max.loglik.bb(input$alpha1.mle[1],input$alpha1.mle[2],input$alpha2.mle[1],input$alpha2.mle[2],
input$size.mle.bb[1],input$size.mle.bb[2],input$prob.mle.bb[1],input$prob.mle.bb[2],
input$rho.mle.bb[1],input$rho.mle.bb[2],degree=heapeddat()[[1]])
} else if((!input$dataupload & input$distdat=="Conway-Maxwell Poisson") | (input$dataupload & input$distdat1=="Conway-Maxwell Poisson"))
{
max.loglik.cmp(input$alpha1.mle[1],input$alpha1.mle[2],input$alpha2.mle[1],input$alpha2.mle[2],
input$lam.mle.cmp[1],input$lam.mle.cmp[2],input$nu.mle.cmp[1],input$nu.mle.cmp[2],
degree=heapeddat()[[1]])
} else if((!input$dataupload & input$distdat=="Delaporte") | (input$dataupload & input$distdat1=="Delaporte"))
{
max.loglik.del(input$alpha1.mle[1],input$alpha1.mle[2],input$alpha2.mle[1],input$alpha2.mle[2],
input$a.mle.del[1],input$a.mle.del[2],input$b.mle.del[1],input$b.mle.del[2],
input$c.mle.del[1],input$c.mle.del[2],degree=heapeddat()[[1]])
} else if((!input$dataupload & input$distdat=="Yule-Simon") | (input$dataupload & input$distdat1=="Yule-Simon"))
{
max.loglik.ys(input$alpha1.mle[1],input$alpha1.mle[2],input$alpha2.mle[1],input$alpha2.mle[2],
input$rho.mle.ys[1],input$rho.mle.ys[2],degree=heapeddat()[[1]])
}
}
})
})
})
mles = reactive({
ind = which.max(mleoptim()[[1]])[1]
mleoptim()[[3]][[ind]]
})
heapeddatmle = reactive({
input$startoptim
isolate({
dat = heapeddat()[[1]]
if((!input$dataupload & input$distdat=="Negative Binomial") | (input$dataupload & input$distdat1=="Negative Binomial"))
{
dens = dnbinom(min(dat):max(dat),size=round(mles()[3]),mu=mles()[4])
} else if((!input$dataupload & input$distdat=="Beta Binomial") | (input$dataupload & input$distdat1=="Beta Binomial"))
{
dens = dbetabinom(min(dat):max(dat),size=round(mles()[3]),prob=mles()[4],rho=mles()[5])
} else if((!input$dataupload & input$distdat=="Delaporte") | (input$dataupload & input$distdat1=="Delaporte"))
{
dens = ddelap(min(dat):max(dat),alpha=mles()[3],beta=mles()[4],lambda=mles()[5])
} else if((!input$dataupload & input$distdat=="Conway-Maxwell Poisson") | (input$dataupload & input$distdat1=="Conway-Maxwell Poisson"))
{
dens = dcom(min(dat):max(dat),lambda=mles()[3],nu=mles()[4])
} else if((!input$dataupload & input$distdat=="Yule-Simon") | (input$dataupload & input$distdat1=="Yule-Simon"))
{
dens = dyules(min(dat):max(dat),rho=mles()[3])
}
return(dens)
})
})
output$estdistplot = renderPlot({
input$startoptim
isolate({
if(input$startoptim>0)
{
if(input$dataupload)
{
dat1 = data.frame(x=heapeddat()[[1]])
dat2 = data.frame(x=min(heapeddat()[[1]]):max(heapeddat()[[1]]),
y=heapeddatmle())
g1 = ggplot() + geom_histogram(data=dat1, aes(x=x,y=..density..),fill="white",color="darkred",binwidth=1) +
xlab("Rounded values") + ylab("Relative frequency") + ggtitle("Histogram of rounded values with\nestimated distribution overlayed") +
theme_bw() + geom_point(data=dat2, aes(x=x,y=y), size=3, shape=1, color="darkseagreen4") +
scale_x_continuous(breaks=seq(min(dat1$x),max(dat1$x),by=5))
return(g1)
}else if(!input$dataupload)
{
dat1 = data.frame(x=heapeddat()[[1]])
dat2 = data.frame(x=min(heapeddat()[[1]]):max(heapeddat()[[1]]),
y=heapeddatmle())
g1 = ggplot() + geom_histogram(data=dat1, aes(x=x,y=..density..),fill="white",color="darkred",binwidth=1) +
xlab("Rounded values") + ylab("Relative frequency") + ggtitle("Histogram of rounded values with\nestimated distribution overlayed") +
theme_bw() + geom_point(data=dat2, aes(x=x,y=y), size=3, shape=1, color="darkseagreen4") +
scale_x_continuous(breaks=seq(min(dat1$x),max(dat1$x),by=5))
dat3 = data.frame(x=heapeddat()[[1]])
dat4 = data.frame(x=min(heapeddat()[[1]]):max(heapeddat()[[1]]),
y=heapeddat()[[2]])
g2 = ggplot() + geom_histogram(data=dat3, aes(x=x,y=..density..),fill="white",color="darkred",binwidth=1) +
xlab("Rounded values") + ylab("Relative frequency") + ggtitle("Histogram of rounded values with\nunderlying distribution overlayed") +
theme_bw() + geom_point(data=dat4, aes(x=x,y=y), size=3, shape=1) +
scale_x_continuous(breaks=seq(min(dat3$x),max(dat3$x),by=5))
graph = arrangeGrob(g1,g2,nrow=1,ncol=2)
return(graph)
}
}
})
})
output$loglikvalsplot = renderPlot({
input$startoptim
isolate({
if(input$startoptim>0)
{
loglik.dat = data.frame(lk=1:length(mleoptim()[[1]]), ll=mleoptim()[[1]])
ldat = data.frame(x=which.max(mleoptim()[[1]]), y=max(mleoptim()[[1]]))
g1 = ggplot() + geom_point(data=loglik.dat, aes(x=lk,y=ll), shape=19, size=3) +
geom_point(data=ldat, aes(x=x,y=y), color="tomato", size=5) +
xlab("Iteration number") + ylab("Loglikelihood value") + theme_bw() +
ggtitle(paste("Scatterplot of loglikelihood value\nversus iteration number ",
"(", length(mleoptim()[[1]]), " iterations)", sep=""))
return(g1)
}
})
})
output$loglikvalspop = renderUI({
if(input$startoptim>0)
return(bsPopover("loglikvalsplot","Optimization process","The iteration corresponding to the red point yielded the set of estimates that maximized the loglikelihood function. Thus, the set of estimates in the above table are called the maxmimum likelihood estimators.",
trigger="hover",placement="left"))
})
output$mlevalstable = renderTable({
input$startoptim
isolate({
if (input$startoptim>0)
{
if(input$dataupload)
{
if (input$distdat1=="Negative Binomial")
{
tab = matrix(nrow=1, ncol=4)
rownames(tab) = c("MLE")
colnames(tab) = c(HTML("&alpha;<sub>1</sub>"), HTML("&alpha;<sub>2</sub>"), "r", "&mu;")
tab[1,] = c(round(mles()[1], digits=2),
round(mles()[2], digits=2),
round(mles()[3], digits=2),
round(mles()[4], digits=2))
tab
} else if(input$distdat1=="Beta Binomial")
{
tab = matrix(nrow=1, ncol=5)
rownames(tab) = c("MLE")
colnames(tab) = c("&alpha;<sub>1</sub>", "&alpha;<sub>2</sub>", "r", "Pr", "&rho;")
tab[1,] = c(round(mles()[1], digits=2),
round(mles()[2], digits=2),
round(mles()[3], digits=2),
round(mles()[4], digits=2),
round(mles()[5], digits=2))
tab
} else if(input$distdat1=="Conway-Maxwell Poisson")
{
tab = matrix(nrow=1, ncol=4)
rownames(tab) = c("MLE")
colnames(tab) = c("&alpha;<sub>1</sub>", "&alpha;<sub>2</sub>", "&lambda;", "&nu;")
tab[1,] = c(round(mles()[1], digits=2),
round(mles()[2], digits=2),
round(mles()[3], digits=2),
round(mles()[4], digits=2))
tab
} else if(input$distdat1=="Delaporte")
{
tab = matrix(nrow=1, ncol=5)
rownames(tab) = c("MLE")
colnames(tab) = c("&alpha;<sub>1</sub>", "&alpha;<sub>2</sub>","&alpha;", "&beta;", "&lambda;")
tab[1,] = c(round(mles()[1], digits=2),
round(mles()[2], digits=2),
round(mles()[3], digits=2),
round(mles()[4], digits=2),
round(mles()[5], digits=2))
tab
} else if(input$distdat1=="Yule-Simon")
{
tab = matrix(nrow=1, ncol=3)
rownames(tab) = c("MLE")
colnames(tab) = c("&alpha;<sub>1</sub>", "&alpha;<sub>2</sub>", "&rho;")
tab[1,] = c(round(mles()[1], digits=2),
round(mles()[2], digits=2),
round(mles()[3], digits=2))
tab
}
}else if(!input$dataupload)
{
if (input$distdat=="Negative Binomial")
{
tab = matrix(nrow=2, ncol=4)
rownames(tab) = c("MLE","Underlying")
colnames(tab) = c(HTML("&alpha;<sub>1</sub>"), HTML("&alpha;<sub>2</sub>"), "r", "&mu;")
tab[2,] = c(input$alpha1,input$alpha2,input$size.dat,input$mu.dat)
tab[1,] = c(round(mles()[1], digits=2),
round(mles()[2], digits=2),
round(mles()[3], digits=2),
round(mles()[4], digits=2))
tab
} else if(input$distdat=="Beta Binomial")
{
tab = matrix(nrow=2, ncol=5)
rownames(tab) = c("MLE","Underlying")
colnames(tab) = c("&alpha;<sub>1</sub>", "&alpha;<sub>2</sub>", "r", "Pr", "&rho;")
tab[2,] = c(input$alpha1,input$alpha2,input$rbb.dat,input$pbb.dat,input$corbb.dat)
tab[1,] = c(round(mles()[1], digits=2),
round(mles()[2], digits=2),
round(mles()[3], digits=2),
round(mles()[4], digits=2),
round(mles()[5], digits=2))
tab
} else if(input$distdat=="Conway-Maxwell Poisson")
{
tab = matrix(nrow=2, ncol=4)
rownames(tab) = c("MLE","Underlying")
colnames(tab) = c("&alpha;<sub>1</sub>", "&alpha;<sub>2</sub>", "&lambda;", "&nu;")
tab[2,] = c(input$alpha1,input$alpha2,input$lam.dat,input$nu.dat)
tab[1,] = c(round(mles()[1], digits=2),
round(mles()[2], digits=2),
round(mles()[3], digits=2),
round(mles()[4], digits=2))
tab
} else if(input$distdat=="Delaporte")
{
tab = matrix(nrow=2, ncol=5)
rownames(tab) = c("MLE","Underlying")
colnames(tab) = c("&alpha;<sub>1</sub>", "&alpha;<sub>2</sub>","&alpha;", "&beta;", "&lambda;")
tab[2,] = c(input$alpha1,input$alpha2,input$adel.dat,input$bdel.dat,input$cdel.dat)
tab[1,] = c(round(mles()[1], digits=2),
round(mles()[2], digits=2),
round(mles()[3], digits=2),
round(mles()[4], digits=2),
round(mles()[5], digits=2))
tab
} else if(input$distdat=="Yule-Simon")
{
tab = matrix(nrow=2, ncol=3)
rownames(tab) = c("MLE","Underlying")
colnames(tab) = c("&alpha;<sub>1</sub>", "&alpha;<sub>2</sub>", "&rho;")
tab[2,] = c(input$alpha1,input$alpha2,input$rho.dat)
tab[1,] = c(round(mles()[1], digits=2),
round(mles()[2], digits=2),
round(mles()[3], digits=2))
tab
}
}
}
})
}, sanitize.text.function = function(x) x)
#################################################################
#################################################################
## Confidence Intervals
#################################################################
#################################################################
# g function
g = function(params,dist)
{
if(dist=="Negative Binomial")
return(c(expit(params[1]),expit(params[2]),exp(params[3]),exp(params[4])))
else if(dist=="Beta Binomial")
return(c(expit(params[1]),expit(params[2]),exp(params[3]),expit(params[4]),expit(params[5])))
else if(dist=="Conway-Maxwell Poisson")
return(c(expit(params[1]),expit(params[2]),exp(params[3]),exp(params[4])))
else if(dist=="Delaporte")
return(c(expit(params[1]),expit(params[2]),exp(params[3]),exp(params[4]),exp(params[5])))
else if(dist=="Yule-Simon")
return(c(expit(params[1]),expit(params[2]),exp(params[3])))
}
# grad.g function
grad.g = function(params,dist)
{
if(dist=="Negative Binomial")
{
mat = matrix(0, nrow=4, ncol=4)
diag(mat) = c((exp(params[1])/(1+exp(params[1]))^2),(exp(params[2])/(1+exp(params[2]))^2),exp(params[3]),exp(params[4]))
return(mat)
} else if(dist=="Beta Binomial")
{
mat = matrix(0, nrow=5, ncol=5)
diag(mat) = c((exp(params[1])/(1+exp(params[1]))^2),(exp(params[2])/(1+exp(params[2]))^2),exp(params[3]),
(exp(params[4])/(1+exp(params[4]))^2),(exp(params[5])/(1+exp(params[5]))^2))
return(mat)
} else if(dist=="Conway-Maxwell Poisson")
{
mat = matrix(0, nrow=4, ncol=4)
diag(mat) = c((exp(params[1])/(1+exp(params[1]))^2),(exp(params[2])/(1+exp(params[2]))^2),exp(params[3]),exp(params[4]))
return(mat)
} else if(dist=="Delaporte")
{
mat = matrix(0, nrow=5, ncol=5)
diag(mat) = c((exp(params[1])/(1+exp(params[1]))^2),(exp(params[2])/(1+exp(params[2]))^2),
exp(params[3]),exp(params[4]),exp(params[5]))
return(mat)
} else if(dist=="Yule-Simon")
{
mat = matrix(0, nrow=3, ncol=3)
diag(mat) = c((exp(params[1])/(1+exp(params[1]))^2),(exp(params[2])/(1+exp(params[2]))^2),exp(params[3]))
return(mat)
}
}
info.mat = reactive({
input$startci
isolate({
if(input$startci>0)
{
if(input$dataupload)
{
if(input$distdat1=="Negative Binomial")
{
mm = optim(par=c(logit(mles()[1]),logit(mles()[2]),log(mles()[3]),log(mles()[4])), loglik.nb,
degree=heapeddat()[[1]],control=list(fnscale=-1,maxit=10000), hessian=TRUE)
} else if(input$distdat1=="Beta Binomial")
{
mm = optim(par=c(logit(mles()[1]),logit(mles()[2]),log(mles()[3]),logit(mles()[4]),logit(mles()[5])), loglik.bb,
degree=heapeddat()[[1]],control=list(fnscale=-1,maxit=10000), hessian=TRUE)
} else if(input$distdat1=="Conway-Maxwell Poisson")
{
mm = optim(par=c(logit(mles()[1]),logit(mles()[2]),log(mles()[3]),log(mles()[4])), loglik.cmp,
degree=heapeddat()[[1]],control=list(fnscale=-1,maxit=10000), hessian=TRUE)
} else if(input$distdat1=="Delaporte")
{
mm = optim(par=c(logit(mles()[1]),logit(mles()[2]),log(mles()[3]),log(mles()[4]),log(mles()[5])), loglik.del,
degree=heapeddat()[[1]],control=list(fnscale=-1,maxit=10000), hessian=TRUE)
} else if(input$distdat1=="Yule-Simon")
{
mm = optim(par=c(logit(mles()[1]),logit(mles()[2]),log(mles()[3])), loglik.ys,
degree=heapeddat()[[1]],control=list(fnscale=-1,maxit=10000), hessian=TRUE)
}
# obtaining the Fisher info matrix
info.mat = -mm$hessian
return(list(info.mat,mm))
} else if(!input$dataupload)
{
if(input$distdat=="Negative Binomial")
{
mm = optim(par=c(logit(mles()[1]),logit(mles()[2]),log(mles()[3]),log(mles()[4])), loglik.nb,
degree=heapeddat()[[1]],control=list(fnscale=-1,maxit=10000), hessian=TRUE)
} else if(input$distdat=="Beta Binomial")
{
mm = optim(par=c(logit(mles()[1]),logit(mles()[2]),log(mles()[3]),logit(mles()[4]),logit(mles()[5])), loglik.bb,
degree=heapeddat()[[1]],control=list(fnscale=-1,maxit=10000), hessian=TRUE)
} else if(input$distdat=="Conway-Maxwell Poisson")
{
mm = optim(par=c(logit(mles()[1]),logit(mles()[2]),log(mles()[3]),log(mles()[4])), loglik.cmp,
degree=heapeddat()[[1]],control=list(fnscale=-1,maxit=10000), hessian=TRUE)
} else if(input$distdat=="Delaporte")
{
mm = optim(par=c(logit(mles()[1]),logit(mles()[2]),log(mles()[3]),log(mles()[4]),log(mles()[5])), loglik.del,
degree=heapeddat()[[1]],control=list(fnscale=-1,maxit=10000), hessian=TRUE)
} else if(input$distdat=="Yule-Simon")
{
mm = optim(par=c(logit(mles()[1]),logit(mles()[2]),log(mles()[3])), loglik.ys,
degree=heapeddat()[[1]],control=list(fnscale=-1,maxit=10000), hessian=TRUE)
}
# obtaining the Fisher info matrix
info.mat = -mm$hessian
return(list(info.mat,mm))
}
}
})
})
output$invert = renderUI({
input$startci
isolate({
if(input$startci>0)
{
if(det(info.mat()[[1]])==0)
{
return(code("Fisher information matrix is not invertible. Need to calculate CI's with bootstrapping."))
}
}
})
})
output$ci = renderTable({
input$startci
isolate({
if(input$startci>0)
{
if(input$dataupload & det(info.mat()[[1]])!=0)
{
cov.mat = solve(info.mat()[[1]])
se.vec = sqrt(diag(cov.mat))
# transformed estimates
t.est = g(info.mat()[[2]]$par,dist=input$distdat1)
# matrix
mat1 = grad.g(info.mat()[[2]]$par,dist=input$distdat1)
# covariance matrix
cov.mat1 = t(mat1)%*%cov.mat%*%mat1
# obtaining standard errors
se = sqrt(diag(cov.mat1))
# computing 95% CI's
ci=matrix(nrow=length(t.est),ncol=3)
i=0
while(i<length(t.est))
{
i=i+1
ci[i,] = c(t.est[i], t.est[i]-2*se[i],t.est[i]+2*se[i])
if(ci[i,2]<0) ci[i,2]=0
if(i==1 | i==2)
{
if(ci[i,3]>1) ci[i,3]=1
}
}
colnames(ci) = c("midpoint", "95% lower bound", "95% upper bound")
if(input$distdat1=="Negative Binomial")
rownames(ci) = c("&alpha;<sub>1</sub>", "&alpha;<sub>2</sub>", "r", "&mu;")
else if(input$distdat1=="Beta Binomial")
rownames(ci) = c("&alpha;<sub>1</sub>", "&alpha;<sub>2</sub>", "r", "Pr","&rho;")
else if(input$distdat1=="Conway-Maxwell Poisson")
rownames(ci) = c("&alpha;<sub>1</sub>", "&alpha;<sub>2</sub>", "&lambda;", "&nu;")
else if(input$distdat1=="Delaporte")
rownames(ci) = c("&alpha;<sub>1</sub>", "&alpha;<sub>2</sub>", "&alpha;", "&beta;", "&lambda;")
else if(input$distdat1=="Yule-Simon")
rownames(ci) = c("&alpha;<sub>1</sub>", "&alpha;<sub>2</sub>", "&rho;")
return(ci)
}else if(!input$dataupload & det(info.mat()[[1]])!=0)
{
cov.mat = solve(info.mat()[[1]])
se.vec = sqrt(diag(cov.mat))
# transformed estimates
t.est = g(info.mat()[[2]]$par,dist=input$distdat)
# matrix
mat1 = grad.g(info.mat()[[2]]$par,dist=input$distdat)
# covariance matrix
cov.mat1 = t(mat1)%*%cov.mat%*%mat1
# obtaining standard errors
se = sqrt(diag(cov.mat1))
# computing 95% CI's
ci=matrix(nrow=length(t.est),ncol=3)
i=0
while(i<length(t.est))
{
i=i+1
ci[i,] = c(t.est[i], t.est[i]-2*se[i],t.est[i]+2*se[i])
if(ci[i,2]<0) ci[i,2]=0
if(i==1 | i==2)
{
if(ci[i,3]>1) ci[i,3]=1
}
}
colnames(ci) = c("Midpoint", "95% Lower bound", "95% Upper bound")
if(input$distdat=="Negative Binomial")
rownames(ci) = c("&alpha;<sub>1</sub>", "&alpha;<sub>2</sub>", "r", "&mu;")
else if(input$distdat=="Beta Binomial")
rownames(ci) = c("&alpha;<sub>1</sub>", "&alpha;<sub>2</sub>", "r", "Pr","&rho;")
else if(input$distdat=="Conway-Maxwell Poisson")
rownames(ci) = c("&alpha;<sub>1</sub>", "&alpha;<sub>2</sub>", "&lambda;", "&nu;")
else if(input$distdat=="Delaporte")
rownames(ci) = c("&alpha;<sub>1</sub>", "&alpha;<sub>2</sub>", "&alpha;", "&beta;", "&lambda;")
else if(input$distdat=="Yule-Simon")
rownames(ci) = c("&alpha;<sub>1</sub>", "&alpha;<sub>2</sub>", "&rho;")
return(ci)
}
}
})
}, sanitize.text.function = function(x) x)
#################################################################
#################################################################
## Bootstrapped Confidence Intervals
#################################################################
#################################################################
createAlert(session, inputId = "boottime",
message = "Please be patient as the bootstrapping process may take a few minutes depending on the specified distribution and number of parameters in the model.",
type = "warning", dismiss = TRUE, block = FALSE,append = TRUE)
boot.est = reactive({
input$startciboot
withProgress(session, {
setProgress(message = "Bootstrapping...",value=1)
isolate({
if(input$startciboot>0)
{
if(input$dataupload)
{
if(input$distdat1=="Negative Binomial")
{
bootlist=matrix(nrow=500,ncol=4)
i=0
while(i<500)
{
i=i+1
new.dat = sample(heapeddat()[[1]],size=length(heapeddat()[[1]]),replace=TRUE)
res = optim(par=c(logit(mles()[1]),logit(mles()[2]),log(mles()[3]),log(mles()[4])), loglik.nb,
degree=new.dat,control=list(fnscale=-1,maxit=10000))
bootlist[i,] = c(expit(res$par[1:2]),exp(res$par[3:4]))
}
return(bootlist)
} else if(input$distdat1=="Beta Binomial")
{
bootlist=matrix(nrow=500,ncol=5)
i=0
while(i<500)
{
i=i+1
new.dat = sample(heapeddat()[[1]],size=length(heapeddat()[[1]]),replace=TRUE)
res = optim(c(logit(mles()[1]),logit(mles()[2]),log(mles()[3]),logit(mles()[4]),logit(mles()[5])), loglik.bb,
degree=new.dat,control=list(fnscale=-1,maxit=10000))
bootlist[i,] = c(expit(res$par[1:2]),exp(res$par[3]),expit(res$par[4:5]))
}
return(bootlist)
} else if(input$distdat1=="Conway-Maxwell Poisson")
{
bootlist=matrix(nrow=500,ncol=4)
i=0
while(i<500)
{
i=i+1
new.dat = sample(heapeddat()[[1]],size=length(heapeddat()[[1]]),replace=TRUE)
res = optim(par=c(logit(mles()[1]),logit(mles()[2]),log(mles()[3]),log(mles()[4])), loglik.cmp,
degree=new.dat,control=list(fnscale=-1,maxit=10000))
bootlist[i,] = c(expit(res$par[1:2]),exp(res$par[3:4]))
}
return(bootlist)
} else if(input$distdat1=="Delaporte")
{
bootlist=matrix(nrow=500,ncol=5)
i=0
while(i<500)
{
i=i+1
new.dat = sample(heapeddat()[[1]],size=length(heapeddat()[[1]]),replace=TRUE)
res = optim(par=c(logit(mles()[1]),logit(mles()[2]),log(mles()[3]),log(mles()[4]),log(mles()[5])), loglik.del,
degree=new.dat,control=list(fnscale=-1,maxit=10000))
bootlist[i,] = c(expit(res$par[1:2]),exp(res$par[3:5]))
}
return(bootlist)
} else if(input$distdat1=="Yule-Simon")
{
bootlist=matrix(nrow=500,ncol=3)
i=0
while(i<500)
{
i=i+1
new.dat = sample(heapeddat()[[1]],size=length(heapeddat()[[1]]),replace=TRUE)
res = optim(par=c(logit(mles()[1]),logit(mles()[2]),log(mles()[3])), loglik.ys,
degree=new.dat,control=list(fnscale=-1,maxit=10000))
bootlist[i,] = c(expit(res$par[1:2]),exp(res$par[3]))
}
return(bootlist)
}
} else if(!input$dataupload)
{
if(input$distdat=="Negative Binomial")
{
bootlist=matrix(nrow=500,ncol=4)
i=0
while(i<500)
{
i=i+1
new.dat = sample(heapeddat()[[1]],size=length(heapeddat()[[1]]),replace=TRUE)
res = optim(par=c(logit(mles()[1]),logit(mles()[2]),log(mles()[3]),log(mles()[4])), loglik.nb,
degree=new.dat,control=list(fnscale=-1,maxit=10000))
bootlist[i,] = c(expit(res$par[1:2]),exp(res$par[3:4]))
}
return(bootlist)
} else if(input$distdat=="Beta Binomial")
{
bootlist=matrix(nrow=500,ncol=5)
i=0
while(i<500)
{
i=i+1
new.dat = sample(heapeddat()[[1]],size=length(heapeddat()[[1]]),replace=TRUE)
res = optim(c(logit(mles()[1]),logit(mles()[2]),log(mles()[3]),logit(mles()[4]),logit(mles()[5])), loglik.bb,
degree=new.dat,control=list(fnscale=-1,maxit=10000))
bootlist[i,] = c(expit(res$par[1:2]),exp(res$par[3]),expit(res$par[4:5]))
}
return(bootlist)
} else if(input$distdat=="Conway-Maxwell Poisson")
{
bootlist=matrix(nrow=500,ncol=4)
i=0
while(i<500)
{
i=i+1
new.dat = sample(heapeddat()[[1]],size=length(heapeddat()[[1]]),replace=TRUE)
res = optim(par=c(logit(mles()[1]),logit(mles()[2]),log(mles()[3]),log(mles()[4])), loglik.cmp,
degree=new.dat,control=list(fnscale=-1,maxit=10000))
bootlist[i,] = c(expit(res$par[1:2]),exp(res$par[3:4]))
}
return(bootlist)
} else if(input$distdat=="Delaporte")
{
bootlist=matrix(nrow=500,ncol=5)
i=0
while(i<500)
{
i=i+1
new.dat = sample(heapeddat()[[1]],size=length(heapeddat()[[1]]),replace=TRUE)
res = optim(par=c(logit(mles()[1]),logit(mles()[2]),log(mles()[3]),log(mles()[4]),log(mles()[5])), loglik.del,
degree=new.dat,control=list(fnscale=-1,maxit=10000))
bootlist[i,] = c(expit(res$par[1:2]),exp(res$par[3:5]))
}
return(bootlist)
} else if(input$distdat=="Yule-Simon")
{
bootlist=matrix(nrow=500,ncol=3)
i=0
while(i<500)
{
i=i+1
new.dat = sample(heapeddat()[[1]],size=length(heapeddat()[[1]]),replace=TRUE)
res = optim(par=c(logit(mles()[1]),logit(mles()[2]),log(mles()[3])), loglik.ys,
degree=new.dat,control=list(fnscale=-1,maxit=10000))
bootlist[i,] = c(expit(res$par[1:2]),exp(res$par[3]))
}
return(bootlist)
}
}
}
})
})
})
output$bootdist = renderPlot({
input$startciboot
isolate({
if(input$startciboot>0)
{
cols = c("aquamarine3", "aquamarine3", "darksalmon", "darksalmon","darksalmon")
if((!input$dataupload & input$distdat=="Negative Binomial") | (input$dataupload & input$distdat1=="Negative Binomial"))
names = c(bquote(hat(alpha)[1]^MLE), bquote(hat(alpha)[2]^MLE), bquote(hat(r)^MLE), bquote(hat(mu)^MLE))
else if((!input$dataupload & input$distdat=="Beta Binomial") | (input$dataupload & input$distdat1=="Beta Binomial"))
names = c(bquote(hat(alpha)[1]^MLE), bquote(hat(alpha)[2]^MLE), bquote(hat(r)^MLE),
bquote(hat(Pr)^MLE), bquote(hat(rho)^MLE))
else if((!input$dataupload & input$distdat=="Conway-Maxwell Poisson") | (input$dataupload & input$distdat1=="Conway-Maxwell Poisson"))
names = c(bquote(hat(alpha)[1]^MLE), bquote(hat(alpha)[2]^MLE), bquote(hat(lambda)^MLE), bquote(hat(nu)^MLE))
else if((!input$dataupload & input$distdat=="Delaporte") | (input$dataupload & input$distdat1=="Delaporte"))
names = c(bquote(hat(alpha)[1]^MLE), bquote(hat(alpha)[2]^MLE), bquote(hat(alpha)^MLE),
bquote(hat(beta)^MLE), bquote(hat(lambda)^MLE))
else if((!input$dataupload & input$distdat=="Yule-Simon") | (input$dataupload & input$distdat1=="Yule-Simon"))
names = c(bquote(hat(alpha)[1]^MLE), bquote(hat(alpha)[2]^MLE), bquote(hat(rho)^MLE))
if(!input$dataupload & input$distdat=="Negative Binomial")
true = c(input$alpha1,input$alpha2,input$size.dat,input$mu.dat)
else if(!input$dataupload & input$distdat=="Beta Binomial")
true = c(input$alpha1,input$alpha2,input$rbb.dat,input$pbb.dat,input$corbb.dat)
else if(!input$dataupload & input$distdat=="Conway-Maxwell Poisson")
true = c(input$alpha1,input$alpha2,input$lam.dat,input$nu.dat)
else if(!input$dataupload & input$distdat=="Delaporte")
true = c(input$alpha1,input$alpha2,input$adel.dat,input$bdel.dat,input$cdel.dat)
else if(!input$dataupload & input$distdat=="Yule-Simon")
true = c(input$alpha1,input$alpha2,input$rho.dat)
plot=list()
i=0
while(i<dim(boot.est())[2])
{
i=i+1
boot.dat = data.frame(x = boot.est()[,i])
plot[[i]] = ggplot(boot.dat) + geom_histogram(aes(x=x), fill=cols[i], alpha=.7) +
xlab("") + ylab("") + theme_bw() +
geom_vline(aes(xintercept=quantile(x,.025)), color="gray") +
geom_vline(aes(xintercept=quantile(x,.975)), color="gray") +
ggtitle(substitute("Bootstrap distribution of" ~ name,list(name=names[[i]])))
if(!input$dataupload)
plot[[i]] = plot[[i]] + geom_vline(xintercept=true[i],color="navy")
}
if(dim(boot.est())[2]==3)
graph = arrangeGrob(plot[[1]], plot[[2]], plot[[3]], ncol=2)
else if(dim(boot.est())[2]==4)
graph = arrangeGrob(plot[[1]], plot[[2]], plot[[3]], plot[[4]], ncol=2)
else if(dim(boot.est())[2]==5)
graph = arrangeGrob(plot[[1]], plot[[2]], plot[[3]], plot[[4]], plot[[5]], ncol=2)
return(graph)
}
})
})
output$bootdistpop = renderUI({
if(input$startciboot>0 & !input$dataupload)
return(bsPopover("bootdist","Information","In each of the bootstrap distributions, the underlying parameter is shown by the navy line while the 2.5 and 97.5 percentiles are shown by the gray lines.",
trigger="hover",placement="left"))
else if(input$startciboot>0 & input$dataupload)
return(bsPopover("bootdist","Information","In each of the bootstrap distributions, the 2.5 and 97.5 percentiles are shown by the gray lines.",
trigger="hover",placement="left"))
})
output$boottable = renderTable({
input$startciboot
isolate({
if(input$startciboot>0)
{
ci=matrix(nrow=dim(boot.est())[2],ncol=3)
i=0
while(i<dim(boot.est())[2])
{
i=i+1
ci[i,] = c(mean(mles()[i]), quantile(boot.est()[,i],.025),quantile(boot.est()[,i],.975))
if(ci[i,2]<0) ci[i,2]=0
if(i==1 | i==2)
{
if(ci[i,3]>1) ci[i,3]=1
}
}
colnames(ci) = c("Mean", "2.5 Percentile", "97.5 Percentile")
if((!input$dataupload & input$distdat=="Negative Binomial") | (input$dataupload & input$distdat1=="Negative Binomial"))
rownames(ci) = c("&alpha;<sub>1</sub>", "&alpha;<sub>2</sub>", "r", "&mu;")
else if((!input$dataupload & input$distdat=="Beta Binomial") | (input$dataupload & input$distdat1=="Beta Binomial"))
rownames(ci) = c("&alpha;<sub>1</sub>", "&alpha;<sub>2</sub>", "r", "Pr","&rho;")
else if((!input$dataupload & input$distdat=="Conway-Maxwell Poisson") | (input$dataupload & input$distdat1=="Conway-Maxwell Poisson"))
rownames(ci) = c("&alpha;<sub>1</sub>", "&alpha;<sub>2</sub>", "&lambda;", "&nu;")
else if((!input$dataupload & input$distdat=="Delaporte") | (input$dataupload & input$distdat1=="Delaporte"))
rownames(ci) = c("&alpha;<sub>1</sub>", "&alpha;<sub>2</sub>", "&alpha;", "&beta;", "&lambda;")
else if((!input$dataupload & input$distdat=="Yule-Simon") | (input$dataupload & input$distdat1=="Yule-Simon"))
rownames(ci) = c("&alpha;<sub>1</sub>", "&alpha;<sub>2</sub>", "&rho;")
return(ci)
}
})
}, sanitize.text.function = function(x) x)
##############################################
##############################################
## Method Validation Panel
##############################################
##############################################
createAlert(session, inputId = "simtime",
message = "Please be patient as the simulation process may take a few minutes depending on the specified distribution and number of simulations.",
type = "warning", dismiss = TRUE, block = FALSE,append = TRUE)
sim.mles = reactive({
input$startvalid
withProgress(session, {
setProgress(message = "Running simulations...", value=1)
isolate({
if(input$startvalid>0)
{
if(input$dataupload)
{
if(input$distdat1=="Negative Binomial")
{
nb.sim(n=input$nsim.mv, a1=mles()[1], a2=mles()[2], size=round(mles()[3]), mu=mles()[4],
sample.size=input$nsim.dat)
} else if(input$distdat1=="Beta Binomial")
{
bb.sim(n=input$nsim.mv, a1=mles()[1], a2=mles()[2], size=round(mles()[3]), prob=mles()[4],
rho=mles()[5], sample.size=input$nsim.dat)
} else if(input$distdat1=="Conway-Maxwell Poisson")
{
cmp.sim(n=input$nsim.mv, a1=mles()[1], a2=mles()[2], lam=mles()[3], nu=mles()[4],
sample.size=input$nsim.dat)
} else if(input$distdat1=="Delaporte")
{
del.sim(n=input$nsim.mv, a1=mles()[1], a2=mles()[2], alpha=mles()[3], beta=mles()[4],
lambda=mles()[5], sample.size=input$nsim.dat)
} else if(input$distdat1=="Yule-Simon")
{
ys.sim(n=input$nsim.mv, a1=mles()[1], a2=mles()[2], rho=mles()[3],
sample.size=input$nsim.dat)
}
} else if(!input$dataupload)
{
if(input$distdat=="Negative Binomial")
{
nb.sim(n=input$nsim.mv, a1=input$alpha1, a2=input$alpha2, size=input$size.dat, mu=input$mu.dat,
sample.size=input$nsim.dat)
} else if(input$distdat=="Beta Binomial")
{
bb.sim(n=input$nsim.mv, a1=input$alpha1, a2=input$alpha2, size=input$rbb.dat, prob=input$pbb.dat,
rho=input$corbb.dat, sample.size=input$nsim.dat)
} else if(input$distdat=="Conway-Maxwell Poisson")
{
cmp.sim(n=input$nsim.mv, a1=input$alpha1, a2=input$alpha2, lam=input$lam.dat, nu=input$nu.dat,
sample.size=input$nsim.dat)
} else if(input$distdat=="Delaporte")
{
del.sim(n=input$nsim.mv, a1=input$alpha1, a2=input$alpha2, alpha=input$adel.dat, beta=input$bdel.dat,
lambda=input$cdel.dat, sample.size=input$nsim.dat)
} else if(input$distdat=="Yule-Simon")
{
ys.sim(n=input$nsim.mv, a1=input$alpha1, a2=input$alpha2, rho=input$rho.dat,
sample.size=input$nsim.dat)
}
}
}
})
})
})
output$simplots = renderPlot({
input$startvalid
isolate({
if(input$startvalid>0)
{
cols = c("aquamarine3", "aquamarine3", "darksalmon", "darksalmon", "darksalmon")
if(input$dataupload)
{
true=mles()
} else if(!input$dataupload)
{
if(input$distdat=="Negative Binomial")
{
true=c(input$alpha1,input$alpha2,input$size.dat,input$mu.dat)
} else if(input$distdat=="Beta Binomial")
{
true=c(input$alpha1,input$alpha2,input$rbb.dat,input$pbb.dat,input$corbb.dat)
} else if(input$distdat=="Conway-Maxwell Poisson")
{
true=c(input$alpha1,input$alpha2,input$lam.dat,input$nu.dat)
} else if(input$distdat=="Delaporte")
{
true=c(input$alpha1,input$alpha2,input$adel.dat,input$bdel.dat,input$cdel.dat)
} else if(input$distdat=="Yule-Simon")
{
true=c(input$alpha1,input$alpha2,input$rho.dat)
}
}
if((!input$dataupload & input$distdat=="Negative Binomial") | (input$dataupload & input$distdat1=="Negative Binomial"))
{
names = c(bquote(hat(alpha)[1]^MLE), bquote(hat(alpha)[2]^MLE), bquote(hat(r)^MLE), bquote(hat(mu)^MLE))
plot=list()
i=0
while(i<4)
{
i=i+1
sim.dat = data.frame(x = sim.mles()[,i])
plot[[i]] = ggplot(sim.dat) + geom_histogram(aes(x=x), fill=cols[i], alpha=.7) + xlab("") + ylab("") +
ggtitle(substitute("Simulated distribution of"~name,list(name=names[[i]]))) + theme_bw() +
geom_vline(xintercept=true[i],color="navy") + geom_vline(aes(xintercept=mean(x)),color="gold2")
}
print(arrangeGrob(plot[[1]], plot[[2]], plot[[3]], plot[[4]], ncol=2))
} else if((!input$dataupload & input$distdat=="Beta Binomial") | (input$dataupload & input$distdat1=="Beta Binomial"))
{
names = c(bquote(hat(alpha)[1]^MLE), bquote(hat(alpha)[2]^MLE), bquote(hat(r)^MLE),
bquote(hat(Pr)^MLE), bquote(hat(rho)^MLE))
plot=list()
i=0
while(i<5)
{
i=i+1
sim.dat = data.frame(x = sim.mles()[,i])
plot[[i]] = ggplot(sim.dat) + geom_histogram(aes(x=x), fill=cols[i], alpha=.7) + xlab("") + ylab("") +
ggtitle(substitute("Simulated distribution of"~name,list(name=names[[i]]))) + theme_bw() +
geom_vline(xintercept=true[i],color="navy") + geom_vline(aes(xintercept=mean(x)),color="gold2")
}
print(arrangeGrob(plot[[1]], plot[[2]], plot[[3]], plot[[4]], plot[[5]], ncol=2))
} else if((!input$dataupload & input$distdat=="Conway-Maxwell Poisson") | (input$dataupload & input$distdat1=="Conway-Maxwell Poisson"))
{
names = c(bquote(hat(alpha)[1]^MLE), bquote(hat(alpha)[2]^MLE), bquote(hat(lambda)^MLE), bquote(hat(nu)^MLE))
plot=list()
i=0
while(i<4)
{
i=i+1
sim.dat = data.frame(x = sim.mles()[,i])
plot[[i]] = ggplot(sim.dat) + geom_histogram(aes(x=x), fill=cols[i], alpha=.7) + xlab("") + ylab("") +
ggtitle(substitute("Simulated distribution of"~name,list(name=names[[i]]))) + theme_bw() +
geom_vline(xintercept=true[i],color="navy") + geom_vline(aes(xintercept=mean(x)),color="gold2")
}
print(arrangeGrob(plot[[1]], plot[[2]], plot[[3]], plot[[4]], ncol=2))
} else if((!input$dataupload & input$distdat=="Delaporte") | (input$dataupload & input$distdat1=="Delaporte"))
{
names = c(bquote(hat(alpha)[1]^MLE), bquote(hat(alpha)[2]^MLE), bquote(hat(alpha)^MLE),
bquote(hat(beta)^MLE), bquote(hat(lambda)^MLE))
plot=list()
i=0
while(i<5)
{
i=i+1
sim.dat = data.frame(x = sim.mles()[,i])
plot[[i]] = ggplot(sim.dat) + geom_histogram(aes(x=x), fill=cols[i], alpha=.7) + xlab("") + ylab("") +
ggtitle(substitute("Simulated distribution of"~name,list(name=names[[i]]))) + theme_bw() +
geom_vline(xintercept=true[i],color="navy") + geom_vline(aes(xintercept=mean(x)),color="gold2")
}
print(arrangeGrob(plot[[1]], plot[[2]], plot[[3]], plot[[4]], plot[[5]], ncol=2))
} else if((!input$dataupload & input$distdat=="Yule-Simon") | (input$dataupload & input$distdat1=="Yule-Simon"))
{
names = c(bquote(hat(alpha)[1]^MLE), bquote(hat(alpha)[2]^MLE), bquote(hat(rho)^MLE))
plot=list()
i=0
while(i<3)
{
i=i+1
sim.dat = data.frame(x = sim.mles()[,i])
plot[[i]] = ggplot(sim.dat) + geom_histogram(aes(x=x), fill=cols[i], alpha=.7) + xlab("") + ylab("") +
ggtitle(substitute("Simulated distribution of"~name,list(name=names[[i]]))) + theme_bw() +
geom_vline(xintercept=true[i],color="navy") + geom_vline(aes(xintercept=mean(x)),color="gold2")
}
print(arrangeGrob(plot[[1]], plot[[2]], plot[[3]], ncol=2))
}
}
})
})
output$plots.sim.pop = renderUI({
if(input$startvalid>0)
return(bsPopover("simplots","Information","In each of the simulated distributions, the underlying parameter is shown by the navy line while the mean is shown by the yellow line.",
trigger="hover",placement="left"))
})
output$means.sim.tab = renderTable({
input$startvalid
isolate({
if(input$startvalid>0)
{
if(input$dataupload)
{
if(input$distdat1=="Negative Binomial")
{
sim.mat = matrix(nrow=2, ncol=4)
sim.mat[2,] = c(mles()[1], mles()[2], mles()[3], mles()[4])
sim.mat[1,] = c(mean(sim.mles()[,1]), mean(sim.mles()[,2]), mean(sim.mles()[,3]), mean(sim.mles()[,4]))
colnames(sim.mat) = c("&alpha;<sub>1</sub>", "&alpha;<sub>2</sub>", "r", "&mu;")
rownames(sim.mat) = c("Mean","Underlying")
return(sim.mat)
} else if(input$distdat1=="Beta Binomial")
{
sim.mat = matrix(nrow=2, ncol=5)
sim.mat[2,] = c(mles()[1], mles()[2], mles()[3], mles()[4], mles()[5])
sim.mat[1,] = c(mean(sim.mles()[,1]), mean(sim.mles()[,2]), mean(sim.mles()[,3]), mean(sim.mles()[,4]), mean(sim.mles()[,5]))
colnames(sim.mat) = c("&alpha;<sub>1</sub>", "&alpha;<sub>2</sub>", "r", "Pr", "&rho;")
rownames(sim.mat) = c("Mean","Underlying")
return(sim.mat)
} else if(input$distdat1=="Conway-Maxwell Poisson")
{
sim.mat = matrix(nrow=2, ncol=4)
sim.mat[2,] = c(mles()[1], mles()[2], mles()[3], mles()[4])
sim.mat[1,] = c(mean(sim.mles()[,1]), mean(sim.mles()[,2]), mean(sim.mles()[,3]), mean(sim.mles()[,4]))
colnames(sim.mat) = c("&alpha;<sub>1</sub>", "&alpha;<sub>2</sub>", "&lambda;", "&nu;")
rownames(sim.mat) = c("Mean","Underlying")
return(sim.mat)
} else if(input$distdat1=="Delaporte")
{
sim.mat = matrix(nrow=2, ncol=5)
sim.mat[2,] = c(mles()[1], mles()[2], mles()[3], mles()[4], mles()[5])
sim.mat[1,] = c(mean(sim.mles()[,1]), mean(sim.mles()[,2]), mean(sim.mles()[,3]), mean(sim.mles()[,4]), mean(sim.mles()[,5]))
colnames(sim.mat) = c("&alpha;<sub>1</sub>", "&alpha;<sub>2</sub>", "&alpha;", "&beta;", "&lambda;")
rownames(sim.mat) = c("Mean","Underlying")
return(sim.mat)
} else if(input$distdat1=="Yule-Simon")
{
sim.mat = matrix(nrow=2, ncol=3)
sim.mat[2,] = c(mles()[1], mles()[2], mles()[3])
sim.mat[1,] = c(mean(sim.mles()[,1]), mean(sim.mles()[,2]), mean(sim.mles()[,3]))
colnames(sim.mat) = c("&alpha;<sub>1</sub>", "&alpha;<sub>2</sub>", "&rho;")
rownames(sim.mat) = c("Mean","Underlying")
return(sim.mat)
}
}else if(!input$dataupload)
{
if(input$distdat=="Negative Binomial")
{
sim.mat = matrix(nrow=2, ncol=4)
sim.mat[2,] = c(input$alpha1, input$alpha2, input$size.dat, input$mu.dat)
sim.mat[1,] = c(mean(sim.mles()[,1]), mean(sim.mles()[,2]), mean(sim.mles()[,3]), mean(sim.mles()[,4]))
colnames(sim.mat) = c("&alpha;<sub>1</sub>", "&alpha;<sub>2</sub>", "r", "&mu;")
rownames(sim.mat) = c("Mean","Underlying")
return(sim.mat)
} else if(input$distdat=="Beta Binomial")
{
sim.mat = matrix(nrow=2, ncol=5)
sim.mat[2,] = c(input$alpha1, input$alpha2, input$rbb.dat, input$pbb.dat, input$corbb.dat)
sim.mat[1,] = c(mean(sim.mles()[,1]), mean(sim.mles()[,2]), mean(sim.mles()[,3]), mean(sim.mles()[,4]), mean(sim.mles()[,5]))
colnames(sim.mat) = c("&alpha;<sub>1</sub>", "&alpha;<sub>2</sub>", "r", "Pr", "&rho;")
rownames(sim.mat) = c("Mean","Underlying")
return(sim.mat)
} else if(input$distdat=="Conway-Maxwell Poisson")
{
sim.mat = matrix(nrow=2, ncol=4)
sim.mat[2,] = c(input$alpha1, input$alpha2, input$lam.dat, input$nu.dat)
sim.mat[1,] = c(mean(sim.mles()[,1]), mean(sim.mles()[,2]), mean(sim.mles()[,3]), mean(sim.mles()[,4]))
colnames(sim.mat) = c("&alpha;<sub>1</sub>", "&alpha;<sub>2</sub>", "&lambda;", "&nu;")
rownames(sim.mat) = c("Mean","Underlying")
return(sim.mat)
} else if(input$distdat=="Delaporte")
{
sim.mat = matrix(nrow=2, ncol=5)
sim.mat[2,] = c(input$alpha1, input$alpha2, input$adel.dat, input$bdel.dat, input$cdel.dat)
sim.mat[1,] = c(mean(sim.mles()[,1]), mean(sim.mles()[,2]), mean(sim.mles()[,3]), mean(sim.mles()[,4]), mean(sim.mles()[,5]))
colnames(sim.mat) = c("&alpha;<sub>1</sub>", "&alpha;<sub>2</sub>", "&alpha;", "&beta;", "&lambda;")
rownames(sim.mat) = c("Mean","Underlying")
return(sim.mat)
} else if(input$distdat=="Yule-Simon")
{
sim.mat = matrix(nrow=2, ncol=3)
sim.mat[2,] = c(input$alpha1, input$alpha2, input$rho.dat)
sim.mat[1,] = c(mean(sim.mles()[,1]), mean(sim.mles()[,2]), mean(sim.mles()[,3]))
colnames(sim.mat) = c("&alpha;<sub>1</sub>", "&alpha;<sub>2</sub>", "&rho;")
rownames(sim.mat) = c("Mean","Underlying")
return(sim.mat)
}
}
}
})
}, sanitize.text.function = function(x) x)
})
# -----------------------------------------------------------------
# App Title: Heaped Distribution Estimation
# Author: Jimmy Wong
# -----------------------------------------------------------------
##############################################
##############################################
## Libraries
##############################################
##############################################
if (!require("shinyBS")) install.packages("shinyBS")
if (!require("devtools")) install.packages("devtools")
if (!require("shinyIncubator")) devtools::install_github("rstudio/shiny-incubator")
library(devtools)
library(shinyBS)
library(shinyIncubator)
##############################################################################################################
##############################################################################################################
## Shiny user interface
##############################################################################################################
##############################################################################################################
shinyUI(fluidPage(
tags$head(tags$link(rel = "icon", type = "image/x-icon",
href = "https://webresource.its.calpoly.edu/cpwebtemplate/5.0.1/common/images_html/favicon.ico")),
progressInit(),
titlePanel("Heaped Distribution Estimation"),
tabsetPanel(type="tabs",
tabPanel("Simulate Data",
column(12,
p("The goal of this study is to apply a", code("Mixture Model",style = "color:firebrick"), "to", code("Heaped",style = "color:firebrick"), "data.
Heaped data is defined to be data in which irregular peaks exist in the distribution due to some form of bias.
For example, a social network analysis study asked subjects to report the number of contacts on a given day.
Interviewers were told to instruct subjects to round to the nearest multiple of 5. However, not all subjects
rounded to 5 after analyzing the distribution of number of contacts. Therefore, there were peaks at multiples of
5 and less frequencies at non-multiples of 5."),tags$hr()),
column(5,
p("Let",strong("C = actual value"), "from the underlying distribution."),
p("To begin this study, please select an underlying distribution to randomly generate data to be used in
subsequent sections. If you choose to upload your own data, the distribution of C is unknown and will be
estimated by accounting for heaping."),
checkboxInput("dataupload", "Upload data", FALSE),br(),
conditionalPanel(
condition="!input.dataupload",
uiOutput("distselect"),
selectInput("distdat", strong("Distribution:"),
choices=list("Negative Binomial","Beta Binomial","Conway-Maxwell Poisson","Delaporte", "Yule-Simon"),
selected="Negative Binomial"),
conditionalPanel(
condition="input.distdat=='Negative Binomial'",
sliderInput("size.dat", "\\(r\\):", min=0, max=100, value=3, step=1),
sliderInput("mu.dat", "\\(\\mu\\):", min=0, max=100, value=10, step=1)),
conditionalPanel(
condition="input.distdat=='Beta Binomial'",
sliderInput("rbb.dat", "\\(r\\):", min=0, max=500, value=40, step=20),
sliderInput("pbb.dat", "\\(Pr\\):", min=0, max=1, value=.25, step=.05),
sliderInput("corbb.dat", "\\(\\rho\\):", min=0, max=1, value=.1, step=.05)),
conditionalPanel(
condition="input.distdat=='Conway-Maxwell Poisson'",
sliderInput("lam.dat", "\\(\\lambda\\):", min=1, max=100, value=7, step=.05),
sliderInput("nu.dat", "\\(\\nu\\):", min=1, max=10, value=1, step=.05)),
conditionalPanel(
condition="input.distdat=='Delaporte'",
sliderInput("adel.dat", "\\(\\alpha\\):", min=0, max=100, value=1, step=.5),
sliderInput("bdel.dat", "\\(\\beta\\):", min=0, max=100, value=7, step=.5),
sliderInput("cdel.dat", "\\(\\lambda\\):", min=0, max=100, value=1, step=.5)),
conditionalPanel(
condition="input.distdat=='Yule-Simon'",
sliderInput("rho.dat", "\\(\\rho\\):", min=0, max=100, value=2, step=1)),
sliderInput("nsim.dat", "\\(sample\\,size\\):", min=100, max=5000, value=500, step=100),br(),
actionButton("beginstudy", strong("Simulate data"))),
conditionalPanel(
condition="input.dataupload",
column(3,
fileInput("file", "",accept=c("text/csv", "text/comma-separated-values,text/plain", ".csv")),
checkboxInput("header", "Header", TRUE),
radioButtons("sep", "Separator:", choices=c(Comma=",",Semicolon=";",Tab="\t"), selected=","),
radioButtons("quote", "Quote", choices=c(None="","Double Quote"='"',"Single Quote"="'"),selected="")),br(),br())),
column(7,
plotOutput("simdatplot"))),
tabPanel("Heaping Process",
withMathJax(), br(),
column(4,
p("Let", strong("Y = observed value"), "from the heaped (rounded) distribution."),
p("Consider two rounding probabilities \\(\\alpha_1\\) and \\(\\alpha_2\\) such that:"),
uiOutput("prob1"),
bsPopover("prob1","Interpretation","&alpha;<sub>1</sub>: probability of rounding to 5, given that the actual value is either 1, 2, 3, or 4",
trigger="hover",placement="right"),
uiOutput("prob2"),
bsPopover("prob2","Interpretation","&alpha;<sub>2</sub>: probability of rounding to the nearest multiple of 5, given that the actual value is greater than 5 and not a multiple of 5",
trigger="hover",placement="right"),br(),
em("Hoover over above for more info"),
conditionalPanel(
condition="!input.dataupload",
tags$hr(),
p("To begin the rounding process, select values for the two rounding probabilities. The result is a distribution
with heaping present."),
strong("Rounding probabilities:"),br(),
sliderInput("alpha1", p("\\(\\alpha_1\\):"), min=0, max=1, value=.3, step=.05),
sliderInput("alpha2", p("\\(\\alpha_2\\):"), min=0, max=1, value=.6, step=.05),br(),
actionButton("beginround", strong("Round data")),br(),br())),
column(8,
plotOutput("heapeddatplot"),
uiOutput("heapedpop")),
column(12)),
tabPanel("Maximum Likelihood Estimation",
column(4,br(),
p("Based on the heaped data,", code("Maximum Likelihood Estimation",style = "color:navy"), "is used to obtain the
estimates of the underlying distribution's parameters and of the two rounding probabilities."),tags$hr(),
p("To start the optimization process, please select a range of starting values for each parameter
of interest."),
bsAlert(inputId="optimtime"),
conditionalPanel(
condition="input.dataupload",
selectInput("distdat1", strong("Distribution:"),
choices=list("Negative Binomial","Beta Binomial","Conway-Maxwell Poisson","Delaporte", "Yule-Simon"),
selected="Negative Binomial")),
strong("Starting values:"),br(),
sliderInput("alpha1.mle", "\\(\\alpha_1\\):", min=0, max=1, value=c(.2,.4), step=.1),
sliderInput("alpha2.mle", "\\(\\alpha_2\\):", min=0, max=1, value=c(.5,.7), step=.1),
conditionalPanel(
condition="(!input.dataupload && input.distdat=='Negative Binomial') ||
(input.dataupload && input.distdat1=='Negative Binomial')",
sliderInput("size.mle.nb", "\\(r\\):", min=0, max=100, value=c(0,3), step=1),
sliderInput("mu.mle.nb", "\\(\\mu\\):", min=0, max=100, value=c(7,10), step=1)),
conditionalPanel(
condition="(!input.dataupload && input.distdat=='Beta Binomial') ||
(input.dataupload && input.distdat1=='Beta Binomial')",
sliderInput("size.mle.bb", "\\(r\\):", min=0, max=100, value=c(39,43), step=1),
sliderInput("prob.mle.bb", "\\(Pr\\):", min=0, max=1, value=c(.4,.5), step=.05),
sliderInput("rho.mle.bb", "\\(\\rho\\):", min=0, max=1, value=c(.05,.15), step=.05)),
conditionalPanel(
condition="(!input.dataupload && input.distdat=='Conway-Maxwell Poisson') ||
(input.dataupload && input.distdat1=='Conway-Maxwell Poisson')",
sliderInput("lam.mle.cmp", "\\(\\lambda\\):", min=1, max=100, value=c(3,10), step=1),
sliderInput("nu.mle.cmp", "\\(\\nu\\):", min=1, max=10, value=c(1,4), step=1)),
conditionalPanel(
condition="(!input.dataupload && input.distdat=='Delaporte') ||
(input.dataupload && input.distdat1=='Delaporte')",
sliderInput("a.mle.del", "\\(\\alpha\\):", min=0, max=100, value=c(.5,4), step=.5),
sliderInput("b.mle.del", "\\(\\beta\\):", min=0, max=100, value=c(4,9), step=.5),
sliderInput("c.mle.del", "\\(\\lambda\\):", min=0, max=100, value=c(.5,4), step=.5)),
conditionalPanel(
condition="(!input.dataupload && input.distdat=='Yule-Simon') ||
(input.dataupload && input.distdat1=='Yule-Simon')",
sliderInput("rho.mle.ys", "\\(\\rho\\):", min=0, max=100, value=c(1,5), step=1)),br(),
actionButton("startoptim", strong("Start optimization")),br(),br()),
column(8,
conditionalPanel(
condition="input.startoptim>0",
plotOutput("estdistplot"),br(),
tableOutput("mlevalstable"),tags$hr(),
plotOutput("loglikvalsplot"))),
column(12)),
tabPanel("Confidence Intervals",
br(),
column(4,
p(strong("Confidence intervals based on"), code("Inverse Fisher info matrix",style = "color:navy")),
HTML("Using the asymptotic normality of the MLE:
<ol> <li> Invert the Fisher information matrix </li> </ol>"),
p("Calculate CI's using the diagonal of the inverted matrix as the SE's.",style="color:navy"), br(),
actionButton("startci", strong("Calculate confidence intervals"))),
column(8,
tableOutput("ci"),
uiOutput("invert")),
column(1),
column(12,tags$hr()),
column(4,br(),
p(strong("Confidence intervals based on"), code("Bootstrapping",style = "color:navy")),
HTML("In each of the 500 iterations:
<ol> <li> Resample from the heaped data </li>
<li> Use the original MLE's as starting values to find the MLE's for the resampled data </li> </ol>"),
p("Calculate CI's using the 2.5 and 97.5 percentiles of the bootstrap distributions.",style="color:navy"),br(),
actionButton("startciboot", strong("Calculate bootstrap confidence intervals")),br(),br(),
bsAlert(inputId="boottime")),
column(8,br(),
tableOutput("boottable"),br(),
plotOutput("bootdist"),
uiOutput("bootdistpop"))),
tabPanel("Method Validation",
column(4,br(),
p("To verify the validity of this statistical method, a simulation study is performed. The purpose is to ensure the correct
parameters are being estimated."),
HTML("In each iteration:
<ol> <li> Randomly generate data from the specified distribution (in first tab)</li>
<li> Perform the heaping process on the data based on the specified rounding probabilities (in second tab)</li>
<li> Use the specified underlying parameters as starting values to optimize the loglikelihood function </li> </ol>"),
p("If data were uploaded, the MLE's are used as the underlying parameters."),
p("The means of the MLE distributions should be close to the specified underlying parameters.",style = "color:navy"),tags$hr(),
sliderInput("nsim.mv", "Number of simulations:", min=10, max=500, value=10, step=10),
actionButton("startvalid", strong("Start simulations")),br(),br(),
bsAlert(inputId="simtime"),br(),br()),
column(8,
plotOutput("simplots"),
uiOutput("plots.sim.pop"),br(),
tableOutput("means.sim.tab"))))
))
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