Generates the suite of functions related to the one sample binomial experiment
with a one-sided alternative hypothesis of interest.
Usage
binom1.1sided(p0, a, b)
Arguments
p0
Scalar. The upper bound of p under null hypothesis Ho: p<=p0.
a
Scalar. Shape1 parameter for prior Beta distribution. See documentation for
dbeta.
b
Scalar. Shape2 parameter for prior Beta distribution. See documentation for
dbeta.
Details
binom1.1sided is used to generate a suite of functions for a one-sample
binomial experiment with a one-sided alternative hypothesis. That is, when
X ~ Binomial(n,p)
H0: p <= p0 vs. H1: p > p0
using the following prior on p
p ~ Beta(a,b).
The functions that are generated are useful in examining the prior and
posterior densities of the parameter p, as well as constructing the
Bayes Factor and determining the sample size via an average error based
approach.
The arguments of binom1.1sided are passed to each of the additional
functions upon their creation as default values. That is, if p0 is
set to 0.5 in the call to binom1.1sided, each of the functions returned
will have the defaualt value of 0.5 for p0. If an argument is not
specified in the call to binom1.1sided, then it remains a required
parameter in all functions created.
Value
binom1.1sided returns a list of 4 functions. These functions are
useful for either visualizing the problem, or computing the required sample
size:
logm
The function returns a list of three vectors: the log marginal density under
the null hypothesis (logm0), the log marginal density under the
alternative hypothesis (logm1), and the log marginal density
(logm). Each are evaluated at the observed data provided. This
function is also passed to ssd.binom to calculate required
sample sizes. This function has the following usage:
logm(x, n, p0, a, b)
x: Vector. Number of successes observed, out of n
independent Bernoulli trials.
n: Scalar. Sample size, the number of independent
Bernoulli trials.
Remaining parameters are specified above for binom1.1sided.
logbf
Returns a vector: the value of the log Bayes Factor given the observed
data provided and the prior parameters specified. This function has the
following usage:
logbf(x, n, p0, a, b)
For details on the parameters for this function, see the above description
for logm.
prior
Returns a vector: the value of the prior density at the specified value of
p with parameters a and b. This function has the
following usage:
prior(p, a, b)
p: Vector. Quantiles at which to evaluate the prior
distribution.
Remaining parameters are specified above for binom1.1sided.
post
Returns a vector: the value of the posterior density. This function has
the following usage:
post(p, x, n, a, b)
p: Vector. Quantiles at which to evaluate the posterior
distribution.
x: Scalar. Number of successes observed, out of n
independent Bernoulli trials.
n: Scalar: The number of independent Bernoulli trials.
Remaining parameters are specified above for binom1.1sided.
############################################################
# Generate the suite of functions for a one-sample binomial
# with a one-sided test. Consider the hypothesis
# H0: p<=0.5 vs. H1: p>0.5
#
# with a uniform prior on p.
# generate suite
f1 <- binom1.1sided(p0=0.5,a=1,b=1)
# attach suite
attach(f1)
# plot prior and posterior given x = 25, n = 30
ps <- seq(0.01,0.99,0.01)
p1 <- prior(ps)
p2 <- post(ps,x=25,n=30)
plot(c(p1,p2)~rep(ps,2),type="n",ylab="Density",xlab="p",main="")
lines(p1~ps,lty=1,lwd=2)
lines(p2~ps,lty=2,lwd=2)
# perform sample size calculation with TE bound of 0.25 and weight 0.5
ssd.binom(alpha=0.25,w=0.5,logm=logm)
# detain suite
detach(f1)
Results
R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)
R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.
R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.
Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.
> library(BAEssd)
Loading required package: mvtnorm
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/BAEssd/binom1.1sided.Rd_%03d_medium.png", width=480, height=480)
> ### Name: binom1.1sided
> ### Title: Binomial Suite: One Sample, One Sided
> ### Aliases: binom1.1sided
>
> ### ** Examples
>
> ############################################################
> # Generate the suite of functions for a one-sample binomial
> # with a one-sided test. Consider the hypothesis
> # H0: p<=0.5 vs. H1: p>0.5
> #
> # with a uniform prior on p.
>
> # generate suite
> f1 <- binom1.1sided(p0=0.5,a=1,b=1)
Loading the 'binom1.1sided' suite...
This suite contains functions pertaining to a one sample experiment
with a binary outcome. The hypothesis of interest has a one-sided
alternative.
>
> # attach suite
> attach(f1)
>
> # plot prior and posterior given x = 25, n = 30
> ps <- seq(0.01,0.99,0.01)
> p1 <- prior(ps)
> p2 <- post(ps,x=25,n=30)
>
> plot(c(p1,p2)~rep(ps,2),type="n",ylab="Density",xlab="p",main="")
> lines(p1~ps,lty=1,lwd=2)
> lines(p2~ps,lty=2,lwd=2)
>
> # perform sample size calculation with TE bound of 0.25 and weight 0.5
> ssd.binom(alpha=0.25,w=0.5,logm=logm)
Bayesian Average Error Sample Size Determination
Call: ssd.binom(alpha = 0.25, w = 0.5, logm = logm)
Sample Size: 9
Total Average Error: 0.2460938
Acceptable sample size determined!
>
> # detain suite
> detach(f1)
>
>
>
>
>
> dev.off()
null device
1
>