Type: Package
Title: Sample Size and Power for Comparing Inequality Constrained Hypotheses
Version: 0.2.3
Author: Fayette Klaassen
Maintainer: Fayette Klaassen <klaassen.fayette@gmail.com>
Description: A collection of methods to determine the required sample size for the evaluation of inequality constrained hypotheses by means of a Bayes factor. Alternatively, for a given sample size, the unconditional error probabilities or the expected conditional error probabilities can be determined. Additional material on the methods in this package is available in Klaassen, F., Hoijtink, H. & Gu, X. (2019) <doi:10.31219/osf.io/d5kf3>.
License: LGPL-3
Encoding: UTF-8
LazyData: true
RoxygenNote: 7.1.0
Suggests: knitr, rmarkdown, testthat
VignetteBuilder: knitr
NeedsCompilation: no
Packaged: 2020-06-22 08:07:44 UTC; 31643
Repository: CRAN
Date/Publication: 2020-06-22 08:40:16 UTC

Determine the unconditional error probabilities for a set of simulated Bayes factors.

Description

Determine the unconditional error probabilities for a set of simulated Bayes factors.

Usage

bayes_error(BFs1, BFs2, bound1 = 1, bound2 = 1/bound1)

Arguments

BFs1

A vector. Simulated BF12 under H1 for a given n

BFs2

A vector. Simulated BF12 under H2 for a given n

bound1

A number. The boundary above which BF12 favors H1

bound2

A number. The boundary below which BF12 favors H2

Value

A named vector. The Type 1, Type 2, Decision error and Area of Indecision probabilities and the median Bayes factors under H1 and H2

Determine the 'power' for a Bayesian hypothesis test

Description

Determine the 'power' for a Bayesian hypothesis test

Usage

bayes_power(
  n,
  h1,
  h2,
  m1,
  m2,
  sd1 = 1,
  sd2 = 1,
  scale = 1000,
  bound1 = 1,
  bound2 = 1/bound1,
  datasets = 1000,
  nsamp = 1000,
  seed = 31
)

Arguments

n

A number. The sample size

h1

A constraint matrix defining H1

h2

A constraint matrix defining H2

m1

A vector of expected population means under H1

m2

A vector of expected populations means under H2 m2 must be of same length as m1

sd1

A vector of standard deviations under H1. Must be a single number (equal standard deviation under all populations), or a vector of the same length as m1

sd2

A vector of standard deviations under H2. Must be a single number (equal standard deviation under all populations), or a vector of the same length as m2

scale

A number specifying the prior scale

bound1

A number. The boundary above which BF12 favors H1

bound2

A number. The boundary below which BF12 favors H2

datasets

A number. The number of datasets to compute the error probabilities

nsamp

A number. The number of prior or posterior samples to determine the fit and complexity

seed

A number. The random seed to be set

Value

The Type 1, Type 2, Decision error and Area of Indecision probability and the median BF12s under H1 and H2

Examples

# Short example WITH SMALL AMOUNT OF SAMPLES
h1 <- matrix(c(1,-1,0,0,1,-1), nrow= 2, byrow= TRUE)
h2 <- "c"
m1 <- c(.4,.2,0)
m2 <- c(.2,0,.1)
bayes_power(40, h1, h2, m1, m2, datasets = 50, nsamp = 50)

Determine the required sample size for a Bayesian hypothesis test

Description

Determine the required sample size for a Bayesian hypothesis test

Usage

bayes_sampsize(
  h1,
  h2,
  m1,
  m2,
  sd1 = 1,
  sd2 = 1,
  scale = 1000,
  type = 1,
  cutoff,
  bound1 = 1,
  bound2 = 1/bound1,
  datasets = 1000,
  nsamp = 1000,
  minss = 2,
  maxss = 1000,
  seed = 31
)

Arguments

h1

A constraint matrix defining H1.

h2

A constraint matrix defining H2.

m1

A vector of expected population means under H1 (standardized).

m2

A vector of expected populations means under H2 (standardized). m2 must be of same length as m1

sd1

A vector of standard deviations under H1. Must be a single number (equal standard deviation under all populations), or a vector of the same length as m1

sd2

A vector of standard deviations under H2. Must be a single number (equal standard deviation under all populations), or a vector of the same length as m2

scale

A number specifying the prior scale

type

A character. The type of error to be controlled options are: "1", "2", "de", "aoi", "med.1", "med.2"

cutoff

A number. The cutoff criterion for type. If type is "1", "2", "de", "aoi", cutoff must be between 0 and 1 If type is "med.1" or "med.2", cutoff must be larger than 1

bound1

A number. The boundary above which BF12 favors H1

bound2

A number. The boundary below which BF12 favors H2

datasets

A number. The number of datasets to compute the error probabilities

nsamp

A number. The number of prior or posterior samples to determine the fit and complexity

minss

A number. The minimum sample size to consider

maxss

A number. The maximum sample size to consider

seed

A number. The random seed to be set

Value

The sample size for which the chosen type of error probability is at the set cutoff, and the according error probabilities and median Bayes factors

Examples

# Short computation example NOT SUFFICIENT SAMPLES
h1 <- matrix(c(1,-1), nrow= 1, byrow= TRUE)
h2 <- 'c'
m1 <- c(.4, 0)
m2 <- c(0, .1)
bayes_sampsize(h1, h2, m1, m2, sd1 = 1, sd2 = 1, scale = 1000,
type = "de", cutoff = .125, nsamp = 50, datasets = 50,
minss = 40, maxss = 70)

Compute a Bayes factor

Description

Compute a Bayes factor

Usage

calc_bf(data, h1, h2, scale, nsamp = 1000)

Arguments

data

A matrix. The dataset for which the BF must be computed

h1

A constraint matrix defining H1.

h2

A constraint matrix defining H2.

scale

A number specifying the prior scale.

nsamp

A number. The number of prior or posterior samples to determine the

Value

BF12, that is, the evidence for H1 relative to H2

Compute the complexity or fit for two hypotheses.

Description

Compute the complexity or fit for two hypotheses.

Usage

calc_fc(hyp, hyp2, means, sds, nsamp = 1000)

Arguments

hyp

A constraint matrix defining H1.

hyp2

A constraint matrix defining H2 OR a character 'u' or 'c' specifying an unconstrained or complement hypothesis

means

A vector of posterior or prior means

sds

A vector or posterior or prior standard deviation

nsamp

A number. The number of prior or posterior samples to determine the fit and complexity

Value

A vector. The proportion of posterior samples in agreement with H1 and with H2

Evaluate a constraint matrix for a set of prior/posterior samples

Description

Evaluate a constraint matrix for a set of prior/posterior samples

Usage

eval_const(hyp, samples)

Arguments

hyp

A constraint matrix defining a hypothesis.

samples

A matrix. Prior or posterior samples, the number of columns corresponds to the number of groups, the number of rows the number of samples

Value

A number between 0 and 1. The proportion of samples in which the constraints are met.

Sample multiple datasets and compute the Bayes factor in each

Description

Sample multiple datasets and compute the Bayes factor in each

Usage

samp_bf(datasets, n, ngroup, means, sds, h1, h2, scale, nsamp)

Arguments

datasets

A number. The number of datasets to simulate for each sample size n

n

A number. The group sample size to be used in data simulation

ngroup

A number. The number of groups.

means

A vector of expected population means.

sds

A vector of expected population standard deviations Note, when standardized, this is a vector of 1s

h1

A constraint matrix defining H1.

h2

A constraint matrix defining H2.

scale

A number specifying the prior scale.

nsamp

A number. The number of samples for the fit and complexity See ?BayesianPower::calc_fc

Value

A vector of Bayes factors BF12 for each of the simulated datasets

Sample from prior or posterior distribution

Description

Sample from prior or posterior distribution

Usage

samp_dist(nsamp, means, sds)

Arguments

nsamp

A number. The number of prior or posterior samples to determine the fit and complexity

means

A vector. The prior or posterior means for each group

sds

A number or a vector. The standard deviations for each group If a number is used, the same prior or posterior standard deviation is used for each group.

Value

A matrix of nsamp rows and as many columns as the length of means.