Package 'GeneF'

A Flexible Order Restricted Hypothesis Testing

Description

These functions test the hypothesis regarding population means from ordered sample groups. Restrictions like a weakly/general/strongly isotonic/monotonic order as well as a lower bound for the location can be imposed on the population means. A partition of sample groups and the corresponding estimates of population means are also provided.

Usage

flexisoreg(y, x, lambda = 0, alpha.location = 1, alpha.adjacency = 0.5)
flexisoreg.stat(y, x, lambda = 0, alpha.location = 1, alpha.adjacency = 0.5)
flexmonoreg(y, x, lambda = 0, alpha.location = 1, alpha.adjacency = 0.5)
flexmonoreg.stat(y, x, lambda = 0, alpha.location = 1, alpha.adjacency = 0.5)

Arguments

y	a vector of observed data
x	a vector of ordinal group labels correponding to y but not necessarily sorted
lambda	a lower location bound for partitioned groups other than the first one
alpha.location	$\alpha$ level for the upper-tailed one-sample $t$-test with lower bound lambda
alpha.adjacency	$\alpha$ level for the upper-tailed two-sample $t$-test to evaluate the magnitude of nondecreasing order

Details

flexisoreg is used for flexible nondecreasing order restricted hypothesis testing. flexmonoreg is used for flexible nondecreasing or nonincreasing order restricted hypothesis testing. flexisoreg.stat and flexmonoreg.stat only return an $F$-statistic, which is convenient for multiple comparison.

Value

groups	A partition of sample groups
estimates	estimated population means
statistic	an $F$-type statistic from the test

Note

Since the $p$-value of test has to be evaluated by permutation method, these functions will not return any $p$-value. For the permutation $p$-value of an individual test, see flexisoreg.pvalue and flexmonoreg.pvalue. For the pooled permutation $p$-values of multiple tests, see flexisoreg.poolpvalues and flexmonoreg.poolpvalues.

Author(s)

Yinglei Lai [email protected]

References

Yinglei Lai (2007) A flexible order restricted hypothesis testing and its application to gene expression data. Technical Report

Examples

#generate ordinal group lables x
x <- runif(100)*6
x <- round(x,0)/3
#generate true values z
z <- round(x^2,0)
#generate observed values y
y <- z + rnorm(100)


#print default results
print(rbind(x,z,y))
print(flexisoreg(y,x))
print(flexisoreg.stat(y,x))
print(flexisoreg(y,0-x))
print(flexisoreg.stat(y,0-x))
print(flexmonoreg(y,x))
print(flexmonoreg.stat(y,x))


     #plots for illustration
     par(mfrow=c(2,3), mai=c(0.6, 0.6, 0.3, 0.1))
     plot(x,y, main="True Model",cex.axis=1.5, cex.lab=1.5, cex.main=1.5, cex=1.5)
     lines(x, z, type="p", pch=15, col="black", cex=2.5)

     results <- flexisoreg(y, x, lambda=1, alpha.location=0.05, alpha.adjacency=1)
     plot(x,y, main="Location Restriction",cex.axis=1.5, cex.lab=1.5, cex.main=1.5, cex=1.5)
     lines(x, results$estimate, type="p", pch=15, col="black", cex=2.5)

     results <- flexisoreg(y, x, lambda=1, alpha.location=0.05, alpha.adjacency=0.05)
     plot(x,y, main="Location and Strong Order Restrictions", 
     cex.axis=1.5, cex.lab=1.5, cex.main=1.5, cex=1.5)
     lines(x, results$estimate, type="p", pch=15, col="black", cex=2.5)

     results <- flexisoreg(y, x, lambda=0, alpha.location=1, alpha.adjacency=0.95)
     plot(x,y, main="Weak Order Restriction",cex.axis=1.5, cex.lab=1.5, cex.main=1.5, cex=1.5)
     lines(x, results$estimate, type="p", pch=15, col="black", cex=2.5)

     results <- flexisoreg(y, x, lambda=0, alpha.location=1, alpha.adjacency=0.5)
     plot(x,y, main="General Order Restriction",cex.axis=1.5, cex.lab=1.5, cex.main=1.5, cex=1.5)
     lines(x, results$estimate, type="p", pch=15, col="black", cex=2.5)

     results <- flexisoreg(y, x, lambda=0, alpha.location=1, alpha.adjacency=0.05)
     plot(x,y, main="Strong Order Restriction",cex.axis=1.5, cex.lab=1.5, cex.main=1.5, cex=1.5)
     lines(x, results$estimate, type="p", pch=15, col="black", cex=2.5)

---

Significance Assessment for the Flexible Order Restricted Hypothesis Testing

Description

These functions evaluate the $p$-values from an individual or multiple flexible order restricted hypothesis testing.

Usage

flexisoreg.pvalue(y, x, lambda=0, alpha.location=1, alpha.adjacency=0.5, B=100)
flexisoreg.poolpvalues(m, x, lambda=0, alpha.location=1, alpha.adjacency=0.5, B=100)
flexmonoreg.pvalue(y, x, lambda=0, alpha.location=1, alpha.adjacency=0.5, B=100)
flexmonoreg.poolpvalues(m, x, lambda=0, alpha.location=1, alpha.adjacency=0.5, B=100)

Arguments

m	a matrix of observed data, where samples are in columns and variables are in rows
y	a vector of observed data
x	a vector of ordinal group labels correponding to y or rows of m but not necessarily sorted
lambda	a lower location bound for partitioned groups other than the first one
alpha.location	$\alpha$ level for the upper-tailed one-sample $t$-test with lower bound lambda
alpha.adjacency	$\alpha$ level for the upper-tailed two-sample $t$-test to evaluate the magnitude of nondecreasing order
B	the number of permutations for $p$-value assessment

Details

flexisoreg.pvalue and flexmonoreg.pvalue provide the permutation $p$-value for an individual flexible order restricted hypothesis testing. flexisoreg.poolpvalues and flexmonoreg.poolpvalues provide the pooled permutation $p$-values for multiple flexible order restricted hypothesis testing.

Value

flexisoreg.pvalue and flexmonoreg.pvalue return a permutation $p$-value. flexisoreg.poolpvalues and flexmonoreg.poolpvalues return a vector of pooled permutation $p$-values.

Note

These functions are used in conjunction with flexisoreg, flexisoreg.stat, flexmonoreg and flexmonoreg.stat.

Author(s)

Yinglei Lai [email protected]

References

Yinglei Lai (2007) A flexible order restricted hypothesis testing and its application to gene expression data. Technical Report

Examples

#generate ordinal group lables x
x <- runif(100)*6
x <- round(x,0)/3
#generate true values z
z <- round(x^2,0)
#generate 6 vectors in a matrix for observed values, some noises and some not
m <- array(double(6*100), dim=c(6,100))
for(k in 1:3)
m[k,] <- rnorm(100)
for(k in 4:6)
m[k,] <- z + rnorm(100)


#print default results
par(mfrow=c(2,3))
for(k in 1:6){
print(paste("The ", k, "-th vector", sep=""))
y <- m[k,]
plot(x,y,main=k)
print(flexisoreg.stat(y,x))
print(flexisoreg.pvalue(y,x,B=20))
print(flexisoreg.stat(y,0-x))
print(flexisoreg.pvalue(y,0-x,B=20))
print(flexmonoreg.stat(y,x))
print(flexmonoreg.pvalue(y,x,B=20))
}

flexisoreg.poolpvalues(m, x, B=20)
flexmonoreg.poolpvalues(m, x, B=20)

---

Package for Generalized F-Statistics

Description

Implementation of several generalized $F$-statistics. The current version includes a generalized $F$-statistic based on the flexible isotonic/monotonic regression or order restricted hypothesis testing. Based on: Y. Lai (2011) <doi:10.1371/journal.pone.0019754>.

Details

Package:	GeneF
Type:	Package
Version:	1.0.1
Date:	2022-05-06
License:	GPL version 2 or newer

Author(s)

Yinglei Lai

Maintainer: [email protected]

---

Internal GeneF Functions

Description

Internal functions to support generalized $F$-statistics.

Usage

get.numbers(x)
t1p1(v, n)
t1p2(v, n1, n2)

Arguments

x	a vector of ordered groups of numbers
v	a vector of real numbers
n	the sample size of one-sample data
n1	the first sample size of two-sample data
n2	the second sample size of two-sample data

Value

get.numbers	a vector of culmulative sample sizes from ordered groups
t1p1	a $p$-value from one-sample $t$-test
t1p2	a $p$-value from two-sample $t$-test

Author(s)

Yinglei Lai [email protected]

---