flexorhtest | R Documentation |
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.
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)
y |
a vector of observed data |
x |
a vector of ordinal group labels correponding to |
lambda |
a lower location bound for partitioned groups other than the first one |
alpha.location |
α level for the upper-tailed one-sample t-test with lower bound |
alpha.adjacency |
α level for the upper-tailed two-sample t-test to evaluate the magnitude of nondecreasing order |
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.
groups |
A partition of sample groups |
estimates |
estimated population means |
statistic |
an F-type statistic from the test |
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
.
Yinglei Lai ylai@gwu.edu
Yinglei Lai (2007) A flexible order restricted hypothesis testing and its application to gene expression data. Technical Report
#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)
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