Package 'MDgof'

Title: Various Methods for the Goodness-of-Fit Problem in D>1 Dimensions
Description: The routine gof_test() in this package runs the goodness-of-fit test using various test statistic for multivariate data. Models under the null hypothesis can either be simple or allow for parameter estimation. p values are found via the parametric bootstrap (simulation). The routine gof_test_adjusted_pvalues() runs several tests and then finds a p value adjusted for simultaneous inference. The routine gof_power() allows the estimation of the power of the tests. hybrid_test() and hybrid_power() do the same by first generating a Monte Carlo data set under the null hypothesis and then running a number of two-sample methods. The routine run.studies() allows a user to quickly study the power of a new method and how it compares to those included in the package via a large number of case studies. For details of the methods and references see the included vignettes.
Authors: Wolfgang Rolke [aut, cre] (ORCID: <https://orcid.org/0000-0002-3514-726X>)
Maintainer: Wolfgang Rolke <[email protected]>
License: GPL (>= 2)
Version: 1.0.1
Built: 2026-06-03 18:59:48 UTC
Source: https://github.com/cran/MDgof

Help Index

Run Bakshaev and Rudzkis Test

Description

Run Bakshaev and Rudzkis Test

Usage

bakshaev_rudzkis(dta, rnull, p, m_eval = 100L, nsim = 200L, nsim_mc = 1000L)

Arguments

dta

data matrix.
rnull

generate new data.
p

, parameters for parametric bootstrap.
m_eval

=100, number of evaluation points of kde.
nsim

=200, number of simulation runs.
nsim_mc

=1000, number of simulation runs.

Value

a list

Create various case studies

Description

This function creates the functions needed to run the various case studies.

Usage

case.studies(
  which,
  Continuous = TRUE,
  WithEstimation = FALSE,
  Dim = 2,
  nsample = 250,
  nbins = c(5, 5),
  ReturnCaseNames = FALSE
)

Arguments

which

name or number of the case study.
Continuous

= TRUE for continuous data
WithEstimation

=FALSE, with parameter estimation
Dim

=2 dimension of data
nsample

=250, sample size.
nbins

=c(5,5) number of bins in x and y direction
ReturnCaseNames

=FALSE, just return names of case studies?

Value

a list of functions

Create various case studies for continuous data without parameter estimation

Description

This function creates the functions needed to run the various case studies.

Usage

case.studies.cont(which, nsample = 250, ReturnCaseNames = FALSE)

Arguments

which

name of the case study.
nsample

=250, sample size.
ReturnCaseNames

=FALSE, just return names of case studies?

Value

a list of functions

Create various case studies for continuous data in 5 dimensions without parameter estimation

Description

This function creates the functions needed to run the various case studies.

Usage

case.studies.cont.D5(which, nsample = 250, ReturnCaseNames = FALSE)

Arguments

which

name of the case study.
nsample

=250, sample size.
ReturnCaseNames

=FALSE, just return names of case studies?

Value

a list of functions

Discretize 2D data from case studies

Description

This function provides the info necessary to run the case studies for discrete data.

Usage

case.studies.disc(
  which,
  WithEstimation = FALSE,
  nbins = c(5, 5),
  nsample = 250
)

Arguments

which

name or number of desired case study.
WithEstimation

= FALSE, case study with or without parameter estimation.
nbins

=c(5, 5) number of bins to use in x and y direction
nsample

= 250, required sample size

Value

a list with needed stuff

Create various case studies with parameter estimation

Description

This function creates the functions needed to run the various case studies that include parameter estimation.

Usage

case.studies.est(which, nsample = 250, ReturnCaseNames = FALSE)

Arguments

which

name of the case study.
nsample

=250, sample size.
ReturnCaseNames

=FALSE, just return names of case studies?

Value

a list of functions

Sanity Checks

Description

This function checks whether the inputs have the correct format

Usage

check.functions(pnull, rnull, phat = function(x) -99, x)

Arguments

pnull

cdf under the null hypothesis
rnull

routine to generate data under the null hypothesis
phat

=function(x) -99, function to estimate parameters from the data, or -99
x

matrix with data

Chi-square test for 2D data

Description

This function does the chi square goodness-of-fit test for continuous data in two dimensions.

Usage

chi_cont_test(
  dta,
  pnull,
  phat = function(x) -99,
  Ranges = matrix(c(-Inf, Inf, -Inf, Inf), 2, 2),
  nbins = c(5, 5),
  minexpcount = 5,
  SuppressMessages = TRUE
)

Arguments

dta

a matrix of numbers.
pnull

function to calculate expected counts.
phat

=function(x) -99, function to estimate parameters of pnull.
Ranges

=matrix(c(-Inf, Inf, -Inf, Inf),2,2), a 2x2 matrix with lower and upper bounds
nbins

=c(5,5) number of bins in x and y direction
minexpcount

=5 minimum counts required per bin
SuppressMessages

=FALSE, should info be shown?

Value

a matrix with statistics, p values and degree of freedoms

Chi-square test for discrete 2D data

Description

This function does the chi square goodness-of-fit test for discrete data in two dimensions.

Usage

chi_disc_test(
  dta,
  pnull,
  dnull,
  phat = function(x) -99,
  minexpcount = 5,
  SuppressMessages = FALSE
)

Arguments

dta

a matrix of numbers.
pnull

distribution function to calculate expected counts.
dnull

density to calculate expected counts.
phat

=function(x) -99, function to estimate parameters of pnull.
minexpcount

=5 minimum counts required per bin
SuppressMessages

=TRUE, should info be shown?

Value

a vector with statistic, p value and degree of freedom

Power Estimation of Chi Square Tests

Description

This function finds the power of various chi-square tests.

Usage

chi_power(
  pnull,
  ralt,
  param_alt,
  phat = function(x) -99,
  alpha = 0.05,
  Ranges = matrix(c(-Inf, Inf, -Inf, Inf), 2, 2),
  nbins = c(5, 5),
  rate = 0,
  minexpcount = 5,
  dnull = function(x) -99,
  Retry = TRUE,
  SuppressMessages = TRUE,
  B = 1000
)

Arguments

pnull

distribution function to find cdf under null hypothesis
ralt

function to generate data under alternative hypothesis
param_alt

vector of parameter values for distribution under alternative hypothesis
phat

=function(x) -99, function to estimate parameters
alpha

=0.05, the level of the hypothesis test
Ranges

=matrix(c(-Inf, Inf, -Inf, Inf),2,2), a 2x2 matrix with lower and upper bounds, if any
nbins

=c(5, 5), number of bins for chi square tests
rate

=0 rate of Poisson if sample size is random, 0 if sample size is fixed
minexpcount

=5 minimal expected bin count required
dnull

=function(x) -99, density function to find probabilities under null hypothesis, mostly used for discrete data, or -99 if missing.
Retry

=TRUE, retry if test fails?
SuppressMessages

=TRUE, should info be shown?
B

=1000 number of simulation runs to find power

Value

A numeric matrix of power values.

Compute M statistic for one dtaset

Description

Compute M statistic for one dtaset

Usage

compute_M_for_dtaset(dta, Eval, hs, rnull, p, nsim_mc)

Arguments

dta

data matrix.
Eval

matrix of evaluations
hs

bandwiths
rnull

generate new data
p

values for parametric bootstrap
nsim_mc

number of simulation runs

Value

a double

Bins continuous data

Description

Bins continuous data

Usage

discretize(x, Range, nbins, ChangeVals = FALSE)

Arguments

x

A numeric matrix with two columns.
Range

range of variables
nbins

number of bins.
ChangeVals

=FALSE, should values of discrete rv's be adjusted to midpoints?

Value

A numeric matrix

Create plot for any case study

Description

This function illustrates any of the case studies.

Usage

draw_case(
  which,
  Continuous = TRUE,
  WithEstimation = FALSE,
  Dim = 2,
  palt,
  nsample = 1000,
  Dms = c(1, 2),
  AltOnly = FALSE
)

Arguments

which

name or number of the case study.
Continuous

= TRUE for continuous data
WithEstimation

=FALSE, with parameter estimation
Dim

=2 dimension of data
palt

parameter for alternative. If missing value in study is used.
nsample

=250, sample size.
Dms

=c(1,2, which dimensions are to be shown (for 5D data).
AltOnly

= FALSE show only graph for alternative?

Value

a ggplot2 object

Estimate E and Var/n at Eval for given h, using MC from rnull

Description

Estimate E and Var/n at Eval for given h, using MC from rnull

Usage

estimateEV(rnull, p, Eval, h, nsim_mc, n)

Arguments

rnull

generate data under the null hypothesis.
p

values for rnull
Eval

matrix of evaluations
h

bandwith, a double
nsim_mc

number of simulation runs
n

sample size

Value

a matrix

examples.mdgof.vignette

Description

stuff needed to run vignette fast enough to pass CRAN

Usage

examples.mdgof.vignette

Format

'examples.mdgof.vignette'

A list

Find gaussian kernel pdf

Description

Find gaussian kernel pdf

Usage

gauss_kernel_matrix(Eval, S, h)

Arguments

Eval

a matrix.
S

a matrix
h

bandwith, a double

Value

a matrix

Find evaluation points

Description

Find evaluation points

Usage

gen_eval(rnull, p, m)

Arguments

rnull

a function that generate new data.
p

a vector of parameters for rnull.
m

size of matrix.

Value

a matrix

Create copula objects

Description

This function creates copula objects

Usage

gen.cop(family, p, d = 2)

Arguments

family

name of copula.
p

parameter of copula.
d

dimension

Value

a copula object

Power estimation of goodness-of-fit tests.

Description

Find the power of various goodness-of-fit tests.

Usage

gof_power(
  pnull,
  rnull,
  ralt,
  param_alt,
  phat = function(x) -99,
  dnull = function(x) -99,
  TS,
  TSextra,
  With.p.value = FALSE,
  alpha = 0.05,
  Ranges = matrix(c(-Inf, Inf, -Inf, Inf), 2, 2),
  nbins = c(5, 5),
  minexpcount = 5,
  rate = 0,
  SuppressMessages = FALSE,
  maxProcessor,
  B = 1000
)

Arguments

pnull

function to find cdf under null hypothesis
rnull

function to generate data under null hypothesis
ralt

function to generate data under alternative hypothesis
param_alt

vector of parameter values for distribution under alternative hypothesis
phat

=function(x) -99, function to estimate parameters from the data, or -99
dnull

=function(x) -99, density function under the null hypothesis, if available, or -99 if missing
TS

user supplied function to find test statistics
TSextra

list provided to TS (optional)
With.p.value

=FALSE does user supplied routine return p values?
alpha

=0.05, the level of the hypothesis test
Ranges

=matrix(c(-Inf, Inf, -Inf, Inf),2,2), a 2x2 matrix with lower and upper bounds, if any, for chi-square tests
nbins

=c(5, 5), number of bins for chi square tests.
minexpcount

=5 minimal expected bin count required for chi square tests.
rate

=0 rate of Poisson if sample size is random, 0 if sample size is fixed
SuppressMessages

=FALSE, should informative messages be shown?
maxProcessor

maximum of number of processors to use, 1 if no parallel processing is needed or number of cores-1 if missing
B

=1000 number of simulation runs

Details

For details on the usage of this routine consult the vignette with vignette("MDgof","MDgof")

Value

A numeric matrix of power values.

Examples

# All examples are run with B=10 and maxProcessor=1 to pass CRAN checks.
# This is obviously MUCH TO SMALL for any real usage.
# Power of tests if null hypothesis specifies a bivariate standard normal 
# distribution but data comes from a bivariate normal with different means, 
# without parameter estimation.
rnull=function() mvtnorm::rmvnorm(100, c(0, 0))
ralt=function(p) mvtnorm::rmvnorm(100, c(p, p))
pnull=function(x) {
  if(!is.matrix(x)) return(mvtnorm::pmvnorm(rep(-Inf, 2), x))
  apply(x, 1, function(x) mvtnorm::pmvnorm(rep(-Inf, 2), x))
}
gof_power(pnull, rnull, ralt, c(0, 1), B=10, maxProcessor = 1)
# Same as above, but now with density included
dnull=function(x) {
  if(!is.matrix(x)) return(mvtnorm::dmvnorm(x))
  apply(x, 1, function(x) mvtnorm::dmvnorm(x))
}
gof_power(pnull, rnull, ralt, c(0, 1), dnull=dnull, B=10, maxProcessor = 1)
# Power of tests when null hypothesis specifies a bivariate normal distribution, 
# with mean parameter estimated, wheras data comes from a t distribution
rnull=function(p) mvtnorm::rmvnorm(100, p)
ralt=function(df) mvtnorm::rmvt(100, sigma=diag(2), df=df)
pnull=function(x,p) {
  if(!is.matrix(x)) return(mvtnorm::pmvnorm(rep(-Inf, 2), x, mean=p))
  apply(x, 1, function(x) mvtnorm::pmvnorm(rep(-Inf, 2), x, mean=p))
}
dnull=function(x, p) {
  if(!is.matrix(x)) return(mvtnorm::dmvnorm(x, mean=p))
  apply(x, 1, function(x) mvtnorm::dmvnorm(x, mean=p))
}
phat=function(x) apply(x, 2, mean)
gof_power(pnull, rnull, ralt, c(50, 5), dnull=dnull, phat=phat, B=10, maxProcessor = 1)
# Example of a discrete model, with parameter estimation
# Under null hypothesis: X~Bin(10, p), Y|X=x~Bin(5, 0.5+x/100)
# Under alternative hypothesis: X~Bin(10, p), Y|X=x~Bin(5, K+x/100)
rnull=function(p=0.5) {
  x=stats::rbinom(1000, 10, p)
  y=stats::rbinom(1000, 5, 0.5+x/100)
  MDgof::sq2rec(table(x, y))
}
ralt=function(K=0.5) {
  x=stats::rbinom(1000, 10, 0.5)
  y=stats::rbinom(1000, 5, K+x/100)
  MDgof::sq2rec(table(x, y))
}
pnull=function(x, p) {
  f=function(x) sum(dbinom(0:x[1], 10, p[1])*pbinom(x[2], 5, 0.5+0:x[1]/100))
  if(!is.matrix(x)) x=rbind(x)
  apply(x, 1, f)
}
phat=function(x) {
  tx=tapply(x[,3], x[,1], sum)
  mean(rep(as.numeric(names(tx)), times=tx))/10
}
gof_power(pnull, rnull, ralt, c(0.5, 0.6), phat=phat, B=10, maxProcessor = 1)

Tests for the multivariate goodness-of-fit problem

Description

This function runs a number of goodness-of-fit tests using Rcpp and parallel computing.

Usage

gof_test(
  x,
  pnull,
  rnull,
  phat = function(x) -99,
  dnull = function(x) -99,
  TS,
  TSextra,
  rate = 0,
  nbins = c(5, 5),
  Ranges = matrix(c(-Inf, Inf, -Inf, Inf), 2, 2),
  minexpcount = 5,
  maxProcessor,
  doMethods,
  B = 5000,
  ReturnTSextra = FALSE
)

Arguments

x

a matrix with the data set
pnull

cdf under the null hypothesis
rnull

routine to generate data under the null hypothesis
phat

=function(x) -99, function to estimate parameters from the data, or -99 if no parameters are estimated
dnull

=function(x) -99, density function under the null hypothesis, if available, or -99 if missing
TS

user supplied function to find test statistics, if any.
TSextra

(optional) list passed to TS, if needed.
rate

=0 rate of Poisson if sample size is random, 0 if sample size is fixed
nbins

=c(5, 5) number of bins for chi-square tests
Ranges

=matrix(c(-Inf, Inf, -Inf, Inf),2,2), a 2x2 matrix with lower and upper bounds, if any, for chi-square tests
minexpcount

=5 minimal expected bin count required
maxProcessor

number of processors to use in parallel processing.
doMethods

a vector of codes for the methods to include. If ="all", it does all the included tests. #missing it runs a default selection. I
B

=5000 number of simulation runs. If B=0 the routine returns the test statistics.
ReturnTSextra

=FALSE, should setup info be returned?

Details

For details on the usage of this routine consult the vignette with vignette("MDgof","MDgof")

Value

A list with vectors of test statistics and p.values

Examples

# All examples are run with B=10 and maxProcessor=1 to pass CRAN checks.
# This is obviously MUCH TO SMALL for any real usage.
# Tests to see whether data comes from a bivariate standard normal distribution, 
# without parameter estimation.
rnull=function() mvtnorm::rmvnorm(100, c(0, 0))
x=rnull()
pnull=function(x) {
  if(!is.matrix(x)) return(mvtnorm::pmvnorm(rep(-Inf, 2), x))
  apply(x, 1, function(x) mvtnorm::pmvnorm(rep(-Inf, 2), x))
}
gof_test(x, pnull, rnull, B=10, maxProcessor = 1)
# Same as above, but now with density included
dnull=function(x) {
  if(!is.matrix(x)) return(mvtnorm::dmvnorm(x))
  apply(x, 1, function(x) mvtnorm::dmvnorm(x))
}
gof_test(x, pnull, rnull, dnull=dnull, B=20, maxProcessor = 1)
# Tests to see whether data comes from a standard normal distribution, 
# with mean parameter estimated.
rnull=function(p) mvtnorm::rmvnorm(100, p)
x=rnull(c(0,1))
pnull=function(x,p) {
  if(!is.matrix(x)) return(mvtnorm::pmvnorm(rep(-Inf, 2), x, mean=p))
  apply(x, 1, function(x) mvtnorm::pmvnorm(rep(-Inf, 2), x, mean=p))
}
dnull=function(x, p) {
  if(!is.matrix(x)) return(mvtnorm::dmvnorm(x, mean=p))
  apply(x, 1, function(x) mvtnorm::dmvnorm(x, mean=p))
}
phat=function(x) apply(x, 2, mean)
gof_test(x, pnull, rnull, dnull=dnull, phat=phat,B=20, maxProcessor = 1)
# Example of a discrete model, with parameter estimation
# X~Bin(10, p1), Y|X=x~Bin(5, p2+x/100)
rnull=function(p) {
  x=rbinom(1000, 10, p[1])
  y=rbinom(1000, 5, p[2]+x/100)
  MDgof::sq2rec(table(x, y))
}
pnull=function(x, p) {
  f=function(x) sum(dbinom(0:x[1], 10, p[1])*pbinom(x[2], 5, p[2]+0:x[1]/100))
  if(!is.matrix(x)) x=rbind(x)
  apply(x, 1, f)
}
phat=function(x) {
  tx=tapply(x[,3], x[,1], sum)
  p1=mean(rep(as.numeric(names(tx)), times=tx))/10
  ty=tapply(x[,3], x[,2], sum)
  p2=mean(rep(as.numeric(names(ty)), times=ty))/5-p1/10
  c(p1, p2)
}
x=rnull(c(0.5, 0.5))
gof_test(x, pnull, rnull, phat=phat,B=10, maxProcessor = 1)

Adjusted p values

Description

This function runs a number of goodness-f-fit tests using Rcpp and parallel computing and then finds the correct p value for the combined tests.

Usage

gof_test_adjusted_pvalue(
  x,
  pnull,
  rnull,
  phat = function(x) -99,
  dnull = function(x) -99,
  B = c(5000, 1000),
  nbins = c(5, 5),
  minexpcount = 5,
  Ranges = matrix(c(-Inf, Inf, -Inf, Inf), 2, 2),
  SuppressMessages = FALSE,
  maxProcessor,
  doMethods
)

Arguments

x

matrix with data
pnull

cdf under the null hypothesis
rnull

routine to generate data under the null hypothesis
phat

=function(x) -99, function to estimate parameters from the data, or -99 if no parameters are estimated
dnull

=function(x) -99, density function under the null hypothesis, if available, or -99 if missing
B

=c(5000, 1000), number of simulation runs for permutation test and for estimation of the empirical distribution function.
nbins

=c(5, 5), number of bins for chi square tests (2D only).
minexpcount

= 5, minimum required expected counts for chi-square tests.
Ranges

=matrix(c(-Inf, Inf, -Inf, Inf),2,2) a 2x2 matrix with lower and upper bounds.
SuppressMessages

= FALSE, show informative messages?
maxProcessor

number of cores for parallel processing.
doMethods

Which methods should be included? If missing a small number of methods that generally have good power are used.

Details

For details consult the vignette("MDgof","MDgof")

Value

a vector of p values.

Examples

# All examples are run with B=10 and maxProcessor=1 to pass CRAN checks.
# This is obviously MUCH TO SMALL for any real usage.
# Tests to see whether data comes from a bivariate standard normal distribution, 
# without parameter estimation.
rnull=function() mvtnorm::rmvnorm(100, c(0, 0))
x=rnull()
pnull=function(x) {
  if(!is.matrix(x)) return(mvtnorm::pmvnorm(rep(-Inf, 2), x))
  apply(x, 1, function(x) mvtnorm::pmvnorm(rep(-Inf, 2), x))
}
dnull=function(x) {
  if(!is.matrix(x)) return(mvtnorm::dmvnorm(x))
  apply(x, 1, function(x) mvtnorm::dmvnorm(x))
}
gof_test_adjusted_pvalue(x, pnull, rnull, dnull=dnull, B=10, maxProcessor = 1)

Find gradient of log(f) for a matrix of points

Description

Find gradient of log(f) for a matrix of points

Usage

grad_mat(x, f)

Arguments

x

point of evaluation
f

function

Value

a matrix of gradient vectors

Power Estimation for the multivariate goodness-of-fit problem via twosample tests

Description

This function estimates the power of goodness-of-fit/two-sample hybrid tests using Rcpp and parallel computing by generating a Monte Carlo data set and then running a twosample test.

Usage

hybrid_power(
  rnull,
  ralt,
  param_alt,
  phat = function(x) -99,
  nMC = 1,
  TS,
  TSextra,
  With.p.value = FALSE,
  alpha = 0.05,
  B = 1000,
  maxProcessor,
  doMethods = "all"
)

Arguments

rnull

routine to generate data under the null hypothesis.
ralt

routine to generate data under the alternative hypothesis.
param_alt

values passed to ralt.
phat

=function(x) -99 parameter estimation, if needed.
nMC

=1 sample size of Monte Carlo data set, if it is a number nMC<=10 sample size used will be nMC*sample size of x.
TS

user supplied function to find test statistics, if any.
TSextra

(optional) list passed to TS, if needed.
With.p.value

=FALSE, does user supplied method find its own p-values?
alpha

=0.05 type I error rate used in tests.
B

=5000 number of simulation runs. If B=0 the routine returns the test statistics.
maxProcessor

number of processors to use in parallel processing.
doMethods

="all", a vector of codes for the methods to include or all of them.

Details

For details on the usage of this routine consult the vignette with vignette("MDgof-hybrid","MDgof-hybrid")

Value

A list with vectors of test statistics and p.values

Examples

# All examples are run with B=20 and maxProcessor=1 to pass CRAN checks.
# Power of tests see whether data comes from a bivariate standard normal distribution, 
# without parameter estimation. True Distribution is bivariate normal with
# correlation r.
rnull=function() mvtnorm::rmvnorm(100, c(0, 0))
ralt=function(r) mvtnorm::rmvnorm(100, sigma=matrix(c(1,r,r,1),2,2))
hybrid_power(rnull, ralt, 0.3, B=20, maxProcessor = 1)
# Power of tests to see whether data comes from a standard normal distribution, 
# with mean parameter estimated. True data comes from t distribution.
rnull=function(p) mvtnorm::rmvnorm(100, p)
ralt=function(df) mvtnorm::rmvt(100, df=df)
phat=function(x) apply(x, 2, mean)  
hybrid_power(rnull, ralt, 5, phat, B=20, maxProcessor = 1)

Tests for the multivariate goodness-of-fit problem via twosample tests

Description

This function runs a number of goodness-of-fit tests using Rcpp and parallel computing by generating a Monte Carlo data set and then running a twosample test.

Usage

hybrid_test(
  x,
  rnull,
  phat = function(x) -99,
  nMC = 1,
  TS,
  TSextra,
  B = 1000,
  maxProcessor,
  doMethods = "all"
)

Arguments

x

a matrix with the data set
rnull

routine to generate data under the null hypothesis.
phat

=function(x) -99 parameter estimation, if needed.
nMC

=1 sample size of Monte Carlo data set, if it is a number nMC<=10 sample size used will be nMC*sample size of x.
TS

user supplied function to find test statistics, if any.
TSextra

(optional) list passed to TS, if needed.
B

=5000 number of simulation runs. If B=0 the routine returns the test statistics.
maxProcessor

number of processors to use in parallel processing.
doMethods

="all", a vector of codes for the methods to include or all of them.

Details

For details on the usage of this routine consult the vignette with vignette("MDgof-hybrid","MDgof-hybrid")

Value

A list with vectors of test statistics and p.values

Examples

# All examples are run with B=20 and maxProcessor=1 to pass CRAN checks.
# Tests to see whether data comes from a bivariate standard normal distribution, 
# without parameter estimation.
rnull=function() mvtnorm::rmvnorm(100, c(0, 0))
x=rnull()
hybrid_test(x, rnull, B=20, maxProcessor = 1)
# Tests to see whether data comes from a standard normal distribution, 
# with mean parameter estimated.
rnull=function(p) mvtnorm::rmvnorm(100, p)
phat=function(x) apply(x, 2, mean)  
x=rnull(c(0,1))
hybrid_test(x, rnull, phat, B=20, maxProcessor = 1)
# Example of a discrete model, without parameter estimation
# X~Bin(5, 0.5), Y|X=x~Bin(4, 0.5+x/100)
rnull=function() {
  x=rbinom(1000, 5, 0.5)
  y=rbinom(1000, 4, 0.5)
  MDgof::sq2rec(table(x, y))
}
x=rnull()
hybrid_test(x, rnull, B=50, maxProcessor = 1)
# Example of a discrete model, with parameter estimation
# X~Bin(5, p), Y|X=x~Bin(4, 0.5+x/100)
rnull=function(p) {
  x=rbinom(1000, 5, p)
  y=rbinom(1000, 4, 0.5+x/100)
  MDgof::sq2rec(table(x, y))
}
phat=function(x) {
  tx=tapply(x[,3], x[,1], sum)
  p1=mean(rep(as.numeric(names(tx)), times=tx))/5
  p1
}
x=rnull(0.5)
hybrid_test(x, rnull, phat, B=20, maxProcessor = 1)

hybrid.mdgof.vignette

Description

stuff needed to run vignette MDgof::hybrid fast enough to pass CRAN

Usage

hybrid.mdgof.vignette

Format

'hybrid.mdgof.vignette'

A list

Find test statistic for Kernel Stein Discrepancy test

Description

Find test statistic for Kernel Stein Discrepancy test

Usage

ksd(X, scf, p)

Arguments

X

data set.
scf

function to find scores
p

(possible) parameters

Value

a double (test statistic)

Create list with needed info

Description

This function creates a list with info needed in various parts of the package

Usage

makeTSextra(
  x,
  Continuous,
  pnull,
  rnull,
  phat = function(x) -99,
  dnull = function(x) -99,
  Ranges,
  TSextra
)

Arguments

x

data set
Continuous

=TRUE, is data continuous?
pnull

cdf under the null hypothesis
rnull

routine to generate data under the null hypothesis
phat

=function(x) -99, function to estimate parameters from the data, or -99 if no parameters are estimated
dnull

=function(x) -99, density function under the null hypothesis, if available, or -99 if missing
Ranges

Range of variables
TSextra

(optional) list passed to TS, if needed.

Value

A list with vectors of test statistics and p.values

Example for a new test

Description

This shows how a new test routine can be used with Mgof, based on chi square tests

Usage

newTS(x, pnull, p, TSextra)

Arguments

x

a data set.
pnull

function to calculate expected counts.
p

parameter for pnull, if needed
TSextra

a list with setup info

Value

a vector with either values of the test statistic, or p values

Find probabilities from cdf for discrete data

Description

Find probabilities from cdf for discrete data

Usage

p2dC(x, cdf, p, Fx = as.numeric(c(-1)))

Arguments

x

matrix with data
cdf

function to find distribution function
p

(possible) arguments for cdf
Fx

(if available) already calculated values of cdf

Value

a matrix with probabilities added

power_studies_cont_D5_hybrid_results

Description

the results of the included power studies for continuous data without estimation using two-sample methods in 5 dimensions

Usage

power_studies_cont_D5_hybrid_results

Format

'power_studies_cont_D5_hybrid_results'

A list of matrices with powers

power_studies_cont_D5_results

Description

the results of the included power studies for continuous data without estimation in 5 dimensions

Usage

power_studies_cont_D5_results

Format

'power_studies_cont_D5_results'

A list of matrices with powers

power_studies_cont_est_results

Description

the results of the included power studies for continuous data with estimation

Usage

power_studies_cont_est_results

Format

'power_studies_cont_est_results'

A list of matrices with powers

power_studies_cont_hybrid_results

Description

the results of the included power studies for continuous data without estimation using two-sample methods

Usage

power_studies_cont_hybrid_results

Format

'power_studies_cont_hybrid_results'

A list of matrices with powers

power_studies_cont_nMC5_D5_hybrid_results

Description

the results of the included power studies for continuous data without estimation using two-sample methods in 5 dimensions and five times sample size using two-sample methods and nMC=5

Usage

power_studies_cont_nMC5_D5_hybrid_results

Format

'power_studies_cont_nMC5_D5_hybrid_results'

A list of matrices with powers

power_studies_cont_nMC5_hybrid_results

Description

the results of the included power studies for continuous data without estimation using two-sample methods and nMC=5

Usage

power_studies_cont_nMC5_hybrid_results

Format

'power_studies_cont_nMC5_hybrid_results'

A list of matrices with powers

power_studies_cont_results

Description

the results of the included power studies for continuous data without estimation

Usage

power_studies_cont_results

Format

'power_studies_cont_results'

A list of matrices with powers

power_studies_disc_est_results

Description

the results of the included power studies for discrete data with estimation

Usage

power_studies_disc_est_results

Format

'power_studies_disc_est_results'

A list of matrices with powers

power_studies_disc_hybrid_results

Description

the results of the included power studies for discrete data without estimation using two-sample methods

Usage

power_studies_disc_hybrid_results

Format

'power_studies_disc_hybrid_results'

A list of matrices with powers

power_studies_disc_nMC5_hybrid_results

Description

the results of the included power studies for discrete data without estimation using two-sample methods and nMC=5

Usage

power_studies_disc_nMC5_hybrid_results

Format

'power_studies_disc_nMC5_hybrid_results'

A list of matrices with powers

power_studies_disc_results

Description

the results of the included power studies for discrete data without estimation

Usage

power_studies_disc_results

Format

'power_studies_disc_results'

A list of matrices with powers

Ripley's K function test

Description

this function calculates the test statistic of Ripley's K function test

Usage

RipleyK(x)

Arguments

x

matrix with data

Value

a number (test statistic)

Benchmarking for Multivariate Goodness-of-fit Tests

Description

This function runs the case studies included in the package.

Usage

run.studies(
  study,
  Continuous = TRUE,
  WithEstimation = FALSE,
  Hybrid = FALSE,
  nMC5 = FALSE,
  Dim = 2,
  TS,
  TSextra,
  With.p.value = FALSE,
  nsample = 250,
  nbins = c(5, 5),
  alpha = 0.05,
  param_alt,
  SuppressMessages = TRUE,
  ShowResult = TRUE,
  B = 1000,
  maxProcessor
)

Arguments

study

either the name of the study, or its number in the list. If missing all the studies are run.
Continuous

=TRUE, run cases for continuous data.
WithEstimation

=FALSE, run case studies with or without parameter estimation?
Hybrid

=FALSE run hybrid tests?
nMC5

=FALSE, sample size of hybrid test.
Dim

=2 two or five-dimensional continuous data sets?
TS

routine to calculate new test statistics.
TSextra

list passed to TS (optional).
With.p.value

=FALSE, does user supplied routine return p values?
nsample

= 250, desired sample size. 250 is used in included case studies.
nbins

=c(5,5) number of bins for discretized data.
alpha

=0.05, type I error probability of tests. 0.05 is used in included case studies.
param_alt

(list of) values of parameter under the alternative hypothesis. If missing included values are used.
SuppressMessages

=TRUE, should informative messages be shown?
ShowResult

=TRUE should result be shown in console?
B

= 1000, number of simulation runs.
maxProcessor

number of cores to use. If missing the number of physical cores-1 is used. If set to 1 no parallel processing is done.

Details

For details consult vignette(package="MDgof")

Value

A (list of ) matrices of p.values.

Examples

#Examples are run with a super small B=25 simulation runs to satisfy CRAN submission rules.
#Run a new test for studies 1-3 for continuous data and without estimation.
#The new test is an (included) chi square test that finds it's own p value.
TSextra=list(Continuous=TRUE, WithEstimation=FALSE, Withpvalue=TRUE)
MDgof::run.studies(Continuous=TRUE, WithEstimation=FALSE, 
           study=1:3, TS=MDgof::newTS, TSextra=TSextra, 
           With.p.value = TRUE, B=25, maxProcessor = 1)
#Run included tests for studies 1-3 for discrete data and without estimation,
#but with type I error alpha=0.1
p=MDgof::power_studies_disc_results[[3]][1:3,,drop=FALSE]    
MDgof::run.studies(Continuous=FALSE, WithEstimation=FALSE, 
           study=1:3, param_alt=p,alpha=0.1, B=25, maxProcessor = 1)

This function does some rounding to nice numbers

Description

This function does some rounding to nice numbers

Usage

## S3 method for class 'digits'
signif(x, d = 3)

Arguments

x

a list of two vectors
d

=4 number of digits to round to

Value

A list with rounded vectors

Rearrange 2D discrete data

Description

This function changes a discrete data set given as a nXm counting matrix to a nmX3 matrix

Usage

sq2rec(x)

Arguments

x

a matrix of discrete data.

Value

a rearranged matrix

estimate run time function

Description

estimate run time function

Usage

timecheck(dta, TS, typeTS, TSextra)

Arguments

dta

data set
TS

test statistic
typeTS

format of TS
TSextra

additional info TS

Value

Mean computation time

Find test statistics for continuous data

Description

Find test statistics for continuous data

Usage

TS_cont(x, pnull, param, TSextra)

Arguments

x

A numeric matrix.
pnull

cdf.
param

parameters for pnull in case of parameter estimation.
TSextra

list with additional info

Value

A numeric vector with test statistics

Find test statistics for discrete data

Description

Find test statistics for discrete data

Usage

TS_disc(x, pnull, param, TSextra)

Arguments

x

A numeric matrix.
pnull

cdf.
param

parameters for pnull in case of parameter estimation.
TSextra

list with additional info

Value

A numeric vector with test statistics