Package 'MD2sample'

Create case studies

Description

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

Usage

case.studies(
  which,
  n = 200,
  nx = n,
  ny = n,
  nbins = -1,
  Ranges = matrix(c(-Inf, Inf, -Inf, Inf), 2, 2),
  ReturnCaseNames = FALSE
)

Arguments

which	name of the case study.
n	=200, sample size for both data sets
nx	=n, sample size for first data sets
ny	=n, sample size for second data sets
nbins	=-1, number of bins for chi-square test, 2D only
Ranges	= matrix(c(-Inf, Inf, -Inf, Inf), 2, 2), ranges of variables
ReturnCaseNames	=FALSE, should list of case studies be returned?

Value

a list of functions and vectors

---

This function does the chi square two sample test for continuous data in two dimensions

Description

This function does the chi square two sample test for continuous data in two dimensions

Usage

chisq2D_test_cont(
  dta_x,
  dta_y,
  Ranges = matrix(c(-Inf, Inf, -Inf, Inf), 2, 2),
  nbins = c(5, 5),
  minexpcount = 5,
  SuppressMessages = FALSE
)

Arguments

dta_x	a matrix of numbers
dta_y	a matrix of numbers
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, print informative messages?

Value

a list with statistics and p values

---

This function does the chi square two sample test for continuous data in two dimensions

Description

This function does the chi square two sample test for continuous data in two dimensions

Usage

chisq2D_test_disc(dta, minexpcount = 5)

Arguments

dta	a list with values and counts
minexpcount	=5 minimum counts required per bin

Value

a list with statistics and p values

---

Chi-square test for continuous data, example of user supplied function

Description

This function does the chi square two sample test for continuous data in two dimensions

Usage

chiTS.cont(x, y, TSextra)

Arguments

x	a matrix of numbers
y	a matrix of numbers
TSextra	list with some info

Value

either a test statistic or a p value

---

Chi-square test for discrete data, example of user supplied function

Description

This function does the chi square two sample test for discrete data in two dimensions

Usage

chiTS.disc(x, y, vals_x, vals_y, TSextra)

Arguments

x	a vector with counts
y	a vector with counts
vals_x	a vector with points
vals_y	a vector with points
TSextra	list with some info

Value

either a test statistic or a p value

---

This function does the tests by Chen and Friedman

Description

This function does the tests by Chen and Friedman

Usage

edge.tests(x, y)

Arguments

x	a matrix of numbers
y	a matrix of numbers

Value

a list with statistics and p values

---

Friedman-Rafsky (FR) test

Description

FR test is a multivariate generalization of nonparametric two-sample test. This function is an implementation with customized options, including a visualization of the minimum spanning tree (MST).

Usage

FR.test(
  samp1,
  samp2,
  use.cosine = FALSE,
  binary = FALSE,
  binary.cutoff = 2,
  plot.MST = FALSE,
  col = c("#F0E442", "#56B4E9"),
  label.names = c("Sample 1", "Sample 2"),
  vertex.size = 5,
  edge.width = 1,
  ...
)

Arguments

samp1	Numeric matrix or data frame for Sample 1. Rows are multivariate dimensions, and columns are samples. E.g. gene by cell.
samp2	Numeric matrix or data frame for Sample 2.
use.cosine	An option if to use cosine distance. Logical variable. By default (FALSE), Euclidean distance is used.
binary	An option if to use binary values. Logical variable. Default: FALSE. If TRUE, use binary.cutoff to dichotomize samp1 and samp2.
binary.cutoff	Numeric value for binary cutoff. Binary value = 1 if greater than binary.cutoff, 0 otherwise. Default: 2.
plot.MST	Boolean variable indicating if to plot the minimum spanning tree (MST). Default: FALSE.
col	Character vector of length two for customized colors of the nodes in MST. Default: c("#F0E442", "#56B4E9").
label.names	Character vector of length two for customized names of the two samples. Default: c("Sample 1","Sample 2").
vertex.size, edge.width, ...	Additional plotting parammeters passed to plot.igraph. Default: vertex.size=5, edge.width=1.

Value

Test statistics and p-values.

runs	Total number of subtrees.
runs.samp1	Number of subtrees of Sample 1.
runs.samp2	Number of subtrees of Sample 2.
stat	The standardized FR statistic.
p.value	P-value of the FR test.

---

power_studies_results

Description

the results of the included power studies

Usage

power_studies_results

Format

'power_studies_results'

A list of matrices with powers

---

Benchmarking for Multivariate Two-Sample Tests

Description

This function runs the case studies included in the package.

Usage

run.studies(
  Continuous = TRUE,
  study,
  TS,
  TSextra,
  With.p.value = FALSE,
  nsample = 200,
  alpha = 0.05,
  param_alt,
  SuppressMessages = FALSE,
  B = 1000,
  maxProcessor
)

Arguments

Continuous	=TRUE, run cases for continuous data.
study	either the name of the study, or its number in the list. If missing all the studies are run.
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	= 200, desired sample size. 200 is used in included case studies.
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	=FALSE, should informative messages be printed?
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="MD2sample")

Value

A (list of ) matrices of p.values.

Examples

#The new test is a (included) chi square test:
TSextra=list(which="pval", nbins=rbind(c(3,3), c(4,4)))
run.studies(Continuous=TRUE, study=c("NormalD2", "tD2"), 
          TS=MD2sample::chiTS.cont, TSextra=TSextra, 
          With.p.value=TRUE, B=100)

---

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 = 4)

Arguments

x	a list of two vectors
d	=4 number of digits to round to

Value

A list with rounded vectors

---

test function

Description

test function

Usage

timecheck(dta, TS, typeTS, TSextra)

Arguments

dta	data set
TS	test statistics
typeTS	format of TS
TSextra	additional info TS

Value

Mean computation time

---

This function runs a number of two sample tests which find their own p value.

Description

This function runs a number of two sample tests which find their own p value.

Usage

TS_cont_pval(x, y)

Arguments

x	a matrix of numbers if data is continuous or of counts if data is discrete.
y	a matrix of numbers if data is continuous or of counts if data is discrete.

Value

A list of two numeric vectors, the test statistics and the p values.

---

Power Estimation for Multivariate Two-Sample Tests

Description

Estimate the power of various two sample tests using Rcpp and parallel computing.

Usage

twosample_power(
  f,
  ...,
  TS,
  TSextra,
  alpha = 0.05,
  B = 1000,
  nbins = c(5, 5),
  minexpcount = 5,
  Ranges = matrix(c(-Inf, Inf, -Inf, Inf), 2, 2),
  samplingmethod = "Binomial",
  rnull,
  With.p.value = FALSE,
  DoTransform = TRUE,
  SuppressMessages = FALSE,
  LargeSampleOnly = FALSE,
  maxProcessor,
  doMethods = "all"
)

Arguments

f	function to generate a list with data sets x and y for continuous data or a matrix with columns vals_x, vals_y, x and y for discrete data.
...	additional arguments passed to f, up to 2.
TS	routine to calculate test statistics for new tests.
TSextra	additional info passed to TS, if necessary.
alpha	=0.05, the type I error probability of the hypothesis test.
B	=1000, number of simulation runs.
nbins	=c(5, 5), number of bins for chi square test if Dim=2.
minexpcount	=5, lowest required count for chi-square test.
Ranges	=matrix(c(-Inf, Inf, -Inf, Inf),2,2), a 2x2 matrix with lower and upper bounds.
samplingmethod	="Binomial" for Binomial sampling or "independence" for independence sampling in the discrete data case.
rnull	function to generate new data sets for parametric bootstrap.
With.p.value	=FALSE, does user supplied routine return p values?
DoTransform	=TRUE, should data be transformed to to unit hypercube?
SuppressMessages	=FALSE, should messages be printed?
LargeSampleOnly	=FALSE, should only methods with large sample theories be run?
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.
doMethods	="all", which methods should be included?

Details

For details consult vignette("MD2sample","MD2sample")

Value

A numeric matrix or vector of power values.

Examples

#Note that the resulting power estimates are meaningless because
#of the extremely low number of simulation runs B, required because of CRAN timing rule
#
#Power of tests when one data set comes from a standard normal multivariate distribution function
#and the other data set from a multivariate normal with correlation
#number of simulation runs is ridiculously small because of CRAN submission rules
f=function(a=0) {
 S=diag(2) 
 x=mvtnorm::rmvnorm(100, sigma = S)
 S[1,2]=a
 S[2,1]=a
 y=mvtnorm::rmvnorm(120, sigma = S)
 list(x=x, y=y)
}
twosample_power(f, c(0, 0.5), B=10, maxProcessor=1)
#Power of use supplied test. Example is a (included) chi-square test:
TSextra=list(which="statistics", nbins=rbind(c(3,3), c(4,4)))
twosample_power(f, c(0, 0.5), TS=chiTS.cont, TSextra=TSextra, B=10, maxProcessor=1)
#Same example, but this time the user supplied routine calculates p values:
TSextra=list(which="pvalues", nbins=c(4,4))
twosample_power(f, c(0, 0.5), TS=chiTS.cont, TSextra=TSextra, B=10, 
             With.p.value=TRUE, maxProcessor=1)
#Example for discrete data
g=function(p1, p2) {
  x = table(sample(1:4, size=1000, replace = TRUE))
  y = table(sample(1:4, size=500, replace = TRUE, prob=c(p1,p2,1,1)))
  cbind(vals_x=rep(1:2,2),  vals_y=rep(1:2, each=2), x=x, y=y)
}  
twosample_power(g, 1.5, 1.6, B=10, maxProcessor=1)

---

Multivariate Two-Sample Tests

Description

This function runs a number of two sample tests using Rcpp and parallel computing.

Usage

twosample_test(
  x,
  y,
  vals_x = NA,
  vals_y = NA,
  TS,
  TSextra,
  B = 5000,
  nbins = c(5, 5),
  minexpcount = 5,
  Ranges = matrix(c(-Inf, Inf, -Inf, Inf), 2, 2),
  DoTransform = TRUE,
  samplingmethod = "Binomial",
  rnull,
  SuppressMessages = FALSE,
  LargeSampleOnly = FALSE,
  maxProcessor,
  doMethods = "all"
)

Arguments

x	Continuous data: either a matrix of numbers, or a list with two matrices called x and y. if it is a matrix Observations are in different rows. Discrete data: a vector of counts or a matrix with columns named vals_x, vals_y, x and y.
y	a matrix of numbers if data is continuous or a vector of counts if data is discrete.
vals_x	=NA, a vector of values for discrete random variables, or NA if data is continuous.
vals_y	=NA, a vector of values for discrete random variables, or NA if data is continuous.
TS	user supplied routine to calculate test statistics for new tests.
TSextra	(optional) additional info passed to TS, if necessary.
B	=5000, number of simulation runs for permutation test.
nbins	=c(5,5), for chi square tests (2D only).
minexpcount	=5, lowest required count for chi-square test (2D only).
Ranges	=matrix(c(-Inf, Inf, -Inf, Inf),2,2), a 2x2 matrix with lower and upper bounds (2D only).
DoTransform	=TRUE, should data be transformed to unit hypercube?
samplingmethod	="Binomial" for Binomial sampling or "independence" for independence sampling.
rnull	function to generate new data sets for simulation as an alternative to the permutation method.
SuppressMessages	=FALSE, should informative messages be printed?
LargeSampleOnly	=FALSE, should only methods with large sample theories be run?
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.
doMethods	="all", Which methods should be included?

Details

For details consult vignette("MD2sample","MD2sample")

Value

A list of two numeric vectors, the test statistics and the p values.

Examples

#Two continuous data sets from a multivariate normal:
x = mvtnorm::rmvnorm(100, c(0,0))
y = mvtnorm::rmvnorm(120, c(0,0))
twosample_test(x, y, B=100, maxProcessor=1)
#Using a new test, this one is an (included) chi square test. 
#Also enter data as a list:
TSextra=list(which="statistics", nbins=rbind(c(3,3), c(4,4)))
dta=list(x=x, y=y)
twosample_test(dta, TS=chiTS.cont, TSextra=TSextra, B=100, maxProcessor=1)
#Two discrete data sets from some distribution:
x = table(sample(1:4, size=1000, replace = TRUE))
y = table(sample(1:4, size=1000, replace = TRUE, prob=c(1,2,1,1)))
vals_x=rep(1:2,2)
vals_y=rep(1:2, each=2)
twosample_test(x, y, vals_x, vals_y, B=100, maxProcessor=1)
#Run a discrete chi square test and enter the data as a matrix:
TSextra=list(which="statistics")
dta=cbind(x=x, y=y, vals_x=vals_x, vals_y=vals_y)
twosample_test(dta, TS=chiTS.disc, TSextra=TSextra, B=100, maxProcessor=1)

---

Adjusted p values

Description

This function runs a number of two sample tests using Rcpp and parallel computing and then finds the correct p value for the combined tests.

Usage

twosample_test_adjusted_pvalue(
  x,
  y,
  vals_x = NA,
  vals_y = NA,
  B = c(5000, 1000),
  nbins = c(5, 5),
  minexpcount = 5,
  samplingmethod = "Binomial",
  Ranges = matrix(c(-Inf, Inf, -Inf, Inf), 2, 2),
  DoTransform = TRUE,
  rnull,
  SuppressMessages = FALSE,
  maxProcessor,
  doMethods
)

Arguments

x	Continuous data: either a matrix of numbers, or a list with two matrices called x and y. if it is a matrix Observations are in different rows. Discrete data: a vector of counts or a matrix with columns named vals_x, vals_y, x and y.
y	a matrix of numbers if data if data is continuous or a vector of counts if data is discrete.
vals_x	=NA, a vector of values for discrete random variable, or NA if data is continuous.
vals_y	=NA, a vector of values for discrete random variable, or NA if data is continuous.
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.
samplingmethod	="Binomial" or "independence" for discrete data.
Ranges	=matrix(c(-Inf, Inf, -Inf, Inf),2,2) a 2x2 matrix with lower and upper bounds.
DoTransform	=TRUE, should data be transformed to interval (0,1)?
rnull	routine for parametric bootstrap.
SuppressMessages	= FALSE, print 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("MD2sample","MD2sample")

Value

NULL, results are printed out.

Examples

#Note that the number of simulation runs B is very small to
#satisfy CRAN's run time constraints. 
#Two continuous data sets from a multivariate normal:
x = mvtnorm::rmvnorm(100, c(0,0))
y = mvtnorm::rmvnorm(120, c(0,0))
twosample_test_adjusted_pvalue(x, y, maxProcessor=1, B=20)
#Two discrete data sets from some distribution:
x = table(sample(1:4, size=1000, replace = TRUE))
y = table(sample(1:4, size=500, replace = TRUE, prob=c(1, 1.5, 1, 1)))
twosample_test_adjusted_pvalue(x, y, rep(1:2,2), rep(1:2, each=2), maxProcessor=1, B=20)

---