| Title: | Exact or Asymptotic Permutation Tests |
|---|---|
| Description: | Perform Exact or Asymptotic permutation tests [see Fay and Shaw <doi:10.18637/jss.v036.i02>]. |
| Authors: | Michael Fay |
| Maintainer: | Michael P. Fay <[email protected]> |
| License: | GPL |
| Version: | 1.0-0.4 |
| Built: | 2024-11-17 06:42:58 UTC |
| Source: | CRAN |
This package gives several methods for performing permutation tests.
The package has three main functions, to perform linear permutation tests.
These tests are tests where the test statistic is the sum of the product of a covariate (usually group indicator) and the
scores. The three tests are: permTS to perform two sample permutation tests,
permKS to perform K-sample permutation tests,
permTREND to perform trend permutation tests on numeric values.
By using suitable scores one can create
for example, the permutation t-test (general scores), the Wilcoxon rank sum test (rank scores),
the logrank test (need to use other functions to create these scores). The two sample test uses either
exact (network algorithm, complete enumeration, or Monte Carlo) or asymptotic calculations (using permutational
central limit theorem [pclt]), while the other tests use only the exact Monte Carlo or the pclt.
Most (if not all) of the tests here are also implemented in the coin package.
This package provides an independent validation of that package.
The perm package used by the interval package, and perm is described in Fay and Shaw (2010, Section 5).
Michael Fay
Maintainer: Michael Fay <[email protected]>
Fay, MP and Shaw, PA (2010). Exact and Asymptotic Weighted Logrank Tests for Interval Censored Data: The interval R package. Journal of Statistical Software. doi:10.18637/jss.v036.i02. 36 (2):1-34.
Create a choose(n,m) by n matrix. The matrix has unique rows with m ones in each row and the rest zeros.
chooseMatrix(n, m)chooseMatrix(n, m)
n |
an integer |
m |
an integer<=n |
A matrix with choose(n,m) rows n columns. The matrix has unique rows with m ones in each row and the rest zeros.
Used for complete enumeration when method='exact.ce' in permTS
M.P.Fay
chooseMatrix(5,2)chooseMatrix(5,2)
This is the default function which determines which method to use in permKS.
methodRuleKS1(x, group, exact, Nbound = c(5))methodRuleKS1(x, group, exact, Nbound = c(5))
x |
vector of response scores |
group |
group membership vector |
exact |
logical, TRUE=exact method chosen, FALSE=pclt |
Nbound |
gives 'pclt' if minimum sample size of any group > Nbound |
This function determines which of two methods will be used in permKS;
see that help for description of methods.
When exact=FALSE then returns 'pclt'. When exact=TRUE then returns 'exact.mc'. When exact=NULL then returns either 'exact.mc' if the minimum sample size for any group is less than or equal to Nbound, otherwise returns 'pclt'.
a character vector with one of the following values: "pclt","exact.mc"
This is the default function which determines which method to use in permTREND.
methodRuleTREND1(x, y, exact, Nbound = c(20))methodRuleTREND1(x, y, exact, Nbound = c(20))
x |
vector of response scores |
y |
group membership vector |
exact |
logical, TRUE=exact method chosen, FALSE=pclt |
Nbound |
gives 'pclt' if length(x) > Nbound |
This function determines which of two methods will be used in permTREND;
see that help for description of methods.
When exact=FALSE then returns 'pclt'. When exact=TRUE then returns 'exact.mc'. When exact=NULL then returns either 'exact.mc' if length(x) is less than or equal to Nbound, otherwise returns 'pclt'.
a character vector with one of the following values: "pclt","exact.mc"
This is the default function which determines which method to use in permTS.
methodRuleTS1(x, group, exact, Nbound = c(1000, 200, 100, 50, 16))methodRuleTS1(x, group, exact, Nbound = c(1000, 200, 100, 50, 16))
x |
vector of response scores |
group |
group membership vector |
exact |
logical, TRUE=exact method chosen, FALSE=pclt |
Nbound |
vector of bounds (see details) |
This function determines which of several methods will be used in permTS;
see that help for description of methods.
When exact=FALSE then returns 'pclt'. When exact=TRUE then returns either 'exact.network' if the estimated time of calculation is not too large or 'exact.mc' otherwise. When exact=NULL then returns either 'exact.network' if the estimated time is not too large or 'pclt' otherwise. The estimation of the calculation time is as follows: if the smallest number of unique values in one of the two groups is equal to kmin, then calculation time is large if the sample size <=Nbound[kmin-1], if Nbound[kmin-1] exists, or is large if the sample size <= min(Nbound) otherwise.
a character vector with one of the following values: "pclt","exact.network","exact.mc"
N<-100 set.seed(1) methodRuleTS1(x=sample(1:2,N,replace=TRUE),group=sample(c(0,1),N,replace=TRUE),exact=NULL) N<-100 methodRuleTS1(sample(1:500,N,replace=TRUE),sample(c(0,1),N,replace=TRUE),TRUE)N<-100 set.seed(1) methodRuleTS1(x=sample(1:2,N,replace=TRUE),group=sample(c(0,1),N,replace=TRUE),exact=NULL) N<-100 methodRuleTS1(sample(1:500,N,replace=TRUE),sample(c(0,1),N,replace=TRUE),TRUE)
These functions perform either: two-sample permutation tests (permTS),
k-sample permutation tests (permKS), or trend permutation tests (permTREND).
The test function can be transformed to a linear function of the scores times the covariate, where the covariate
may be either a factor or character vector with two (permTS) or more (permKS) levels or a
numeric vector (permTREND). By using suitable scores one can create
for example, the permutation t-test (general scores), the Wilcoxon rank sum test (rank scores),
the logrank test (need to use other functions to create these scores). It performs either
exact (network algorithm, complete enumeration, or Monte Carlo) asymptotic calculations (using permutational
central limit theorem).
permTS(x, ...) ## Default S3 method: permTS(x, y, alternative = c("two.sided", "less", "greater"), exact = NULL, method = NULL, methodRule = methodRuleTS1, control=permControl(), ...) ## S3 method for class 'formula' permTS(formula, data, subset, na.action, ...) permKS(x,...) ## Default S3 method: permKS(x, g, exact = NULL, method = NULL, methodRule = methodRuleKS1, control=permControl(), ...) ## S3 method for class 'formula' permKS(formula,data,subset, na.action,...) permTREND(x,...) ## Default S3 method: permTREND(x, y, alternative = c("two.sided", "less", "greater"), exact = NULL, method = NULL, methodRule = methodRuleTREND1, control=permControl(),...) ## S3 method for class 'formula' permTREND(formula,data,subset,na.action,...)permTS(x, ...) ## Default S3 method: permTS(x, y, alternative = c("two.sided", "less", "greater"), exact = NULL, method = NULL, methodRule = methodRuleTS1, control=permControl(), ...) ## S3 method for class 'formula' permTS(formula, data, subset, na.action, ...) permKS(x,...) ## Default S3 method: permKS(x, g, exact = NULL, method = NULL, methodRule = methodRuleKS1, control=permControl(), ...) ## S3 method for class 'formula' permKS(formula,data,subset, na.action,...) permTREND(x,...) ## Default S3 method: permTREND(x, y, alternative = c("two.sided", "less", "greater"), exact = NULL, method = NULL, methodRule = methodRuleTREND1, control=permControl(),...) ## S3 method for class 'formula' permTREND(formula,data,subset,na.action,...)
x |
numeric vector of respose scores for the first group |
y |
numeric vector of either response scores for the second group (for permTS) or trend scores for each observation (for permTREND) |
g |
a factor or character vector denoting group membership |
alternative |
a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater","less" (see details) |
exact |
a logical value, TRUE denotes exact test, ignored if method is not NULL |
method |
a character value, one of 'pclt','exact.network','exact.ce','exact.mc'. If NULL method chosen by methodRule |
methodRule |
a function used to choose the method (see details) |
control |
a list with arguments that control the algortihms, see |
formula |
a formula of the form lhs~rhs where lhs is a numeric variable giving the response scores and rhs a factor with two levels giving the corresponding groups. |
data |
an optional matrix or data frame containing the variables in the formula |
subset |
an optional vector specifying a subset of observations to be used. |
na.action |
a function which indicates what should happen when the data contain NAs. Defaults to getOption("na.action"). |
... |
further arguments to be passed to or from methods. |
There are 4 different methods for deciding how to determine the p-value by defining which test statistics are extreme.
For alternative there are 3 choices, "two.sided", "less" or "greater", but within alternative="two.sided" there are 2 methods defined by the
tsmethod given within control, see permControl. If Ti is a vector of test statistics, and T0 is the observed test statistic, then
alternative="less" gives p.lte=Pr[Ti<=T0], alternative="greater" gives p.gte=Pr[Ti>=T0],
alternative="two.sided" with tsmethod="central" (default) gives p.twosided=max(1, 2*min(p.lte,p.gte)), and alternative="two.sided"
with tsmethod="abs" gives p.twosidedAbs=Pr[abs(Ti - mean(Ti) ) >=abs(T0-mean(Ti))]. For permTS the test statistic
is equivalent to the mean of one group minus the mean of the other group. For permTREND the test
statistic is equivalent to the correlation between the response (x) and the trend scores (y).
For permKS only a twosided pvalue based on Pr[Ti>=T0] is allowed, where the test statistic, Ti, is the
weighted sum of the square of the mean within group, where the weights are the sample size for each group. This will
give for example, the usual Kruskal-Wallis test when the ranks are used on the responses.
Many standard statistical tests may be put into the form of the permutation test (see Graubard and Korn, 1987).
There is a choice of four different methods to calculate the p-values (the last two are only available for
permTS):
pclt: using permutational central limit theorem (see e.g., Sen, 1985).
exact.mc:exact using Monte Carlo.
exact.network: exact method using a network algorithm (see e.g., Agresti, Mehta, and Patel, 1990). Currently the network method does not implement many of the time saving suggestions such as clubbing.
exact.ce: exact using complete enumeration. This is good for very small sample sizes and when doing simulations, since the cm need only be calculated once for the simulation.
The exact.network and exact.ce may give errors related to running out of memory when the sample size is not small and will depend on the system you are using (e.g., about 15 in each group for exact.network or
14 in each group for exact.ce).
These associated functions for the above methods (e.g., twosample.pclt, twosample.exact.network, etc),
are internal and are not to be called directly.
The methodRule is a function which takes the first two objects of the default implementation, and returns the
method. This function can be used to appropriately choose the method based on the size of the data.
For explanation of the default method rules see methodRuleTS1, methodRuleKS1, or
methodRuleTREND1.
For more details see Fay and Shaw (2010, Section 5).
An object of class htest or for 'exact.mc' of class mchtest,
a list with the following elements:
p.value |
p value associated with alternative |
alternative |
description of alternative hypothesis |
p.values |
a vector giving lower, upper, and two-sided p-values as well as p.equal which is the proportion equal to the observed test statistic |
method |
a character vector describing the test |
estimate |
an estimate of the test statistic |
statistic |
statistic used for asymptotics, either Z statistics or chi square statistic, output if method="pclt" |
parameter |
degrees of freedom for chi square statistic, output if 'statistic' is the chi square statistic |
data.name |
character vector describing the response and group variables |
p.conf.int |
a confidence interval on the p-value if method='exact.mc'
(see |
nmc |
number of Monte Carlo replications if method='exact.mc', NULL otherwise |
Michael Fay
Agresti, A, Mehta, CR, Patel, NR (1990). JASA 85: 453-458.
Fay, MP and Shaw, PA (2010). Exact and Asymptotic Weighted Logrank Tests for Interval Censored Data: The interval R package. Journal of Statistical Software. doi:10.18637/jss.v036.i02. 36 (2):1-34.
Graubard, BI, and Korn, EL (1987). Biometrics 43: 471-476.
Sen, PK (1985) ‘Permutational central limit theorems’ in Encyclopedia of Statistics, Vol 6.
## Example from StatExact manual dBP<-c(94,108,110,90,80,94,85,90,90,90,108,94,78,105,88) treatment<-c(rep("treated",4),rep("control",11)) permTS(dBP~treatment,alternative="less",method="pclt") result<-permTS(dBP[treatment=="treated"],dBP[treatment=="control"],alternative="greater") result result$p.values## Example from StatExact manual dBP<-c(94,108,110,90,80,94,85,90,90,90,108,94,78,105,88) treatment<-c(rep("treated",4),rep("control",11)) permTS(dBP~treatment,alternative="less",method="pclt") result<-permTS(dBP[treatment=="treated"],dBP[treatment=="control"],alternative="greater") result result$p.values
A function to create a list of arguments for permTS, permKS or
permTREND.
permControl(cm=NULL,nmc=10^3-1,seed=1234321,digits=12, p.conf.level=.99,setSEED=TRUE,tsmethod="central")permControl(cm=NULL,nmc=10^3-1,seed=1234321,digits=12, p.conf.level=.99,setSEED=TRUE,tsmethod="central")
cm |
a choose(n,m) by n matrix, used if method='exact.ce', ignored otherwise |
nmc |
number of Monte Carlo replications, used if method='exact.mc', ignored otherwise |
seed |
value used in |
setSEED |
logical, set to FALSE when performing simulations that use method='exact.mc' |
p.conf.level |
confidence level for p value estimate, used if method='exact.mc', ignored otherwise |
digits |
number of digits to use in |
tsmethod |
method for calculating two-sided p-values, character, either 'central' or 'abs' (see details) |
When cm=NULL the resulting matrix is created by chooseMatrix, it may be optionally provided here
only so that chooseMatrix does not need to be repeatedly called in simulations. Also when doing simulations with
method='exact.mc', use setSEED=FALSE so that the seed is not reset to the same value each time you call the permutation test
function.
See calcPvalsMC for description of how p.conf.level is used.
The two-sided method is given by tsmethod. The default 'central' two-sided method is
just p=min(1, 2*min(pless,pgreater)), where pless and pgreater are the one-sided
p-values. The name 'central' follows the convention of the exact2x2 and
exactci packages; so that for example, a two-sample permutation test on a binary
response with tsmethod='central' will match the Central Fisher's Exact test (see
Fay, 2010). The option tsmethod='abs' defines another method for defining the two-sided p-value. We define it for complete enumeration,
but the algorithms may differ. Let Tj be the vector of length N of all possible values of the test statistic under each of N possible permutations.
The p-value with tsmethod='abs' is defined as 1/N times the number of times abs(Tj-mean(Tj)) >= abs(T0-mean(Tj)), where T0 is the observed value of the
test statistic. This option matches the default two-sided method for the coin package.
An list with the arguments as components.
Fay, M.P. (2010). Confidence intervals that match Fisher's exact or Blaker's exact tests. Biostatistics 11(2):373-373.