Using nparcomp with user-defined contrasts - r

Question

I would like to test the hypothesis H0: a2 - a1 = b2 - b1 on the following data:
data.csv
a1,a2,b1,b2
0.439,0.066,0.0,0.001
0.451,0.07,0.0,0.0
0.446,0.06,0.0,0.0
0.34,0.056,0.0,0.0
0.294,0.008,0.0,0.0
0.284,0.002,0.001,0.0
1.0,1.0,0.002,0.0
First, I tried ANOVA:
library(car)
data = read.csv('data.csv')
labels = factor(rep(c('a1','a2','b1','b2'),
c(nrow(data['a1']), nrow(data['a2']), nrow(data['b1']), nrow(data['b2']))))
x = C(labels, c(-1, 1, 1, -1), 1)
y = c(data[['a1']], data[['a2']], data[['b1']], data[['b2']])
l = lm(y ~ x)
a = Anova(l)
print(a$`Pr(>F)`)
which gives p = 0.1891837.
However, since I cannot assume that the data comes from a normal distribution, I would like to use a non-parametric test instead. I tried using nparcomp with a user-defined contrast matrix:
library(nparcomp)
data = read.csv('data.csv')
x = factor(rep(c('a1','a2','b1','b2'),
c(nrow(data['a1']), nrow(data['a2']), nrow(data['b1']), nrow(data['b2']))))
y = c(data[['a1']], data[['a2']], data[['b1']], data[['b2']])
nparcomp(y ~ x, data=data.frame(x, y), type="UserDefined", contrast.matrix=t(matrix(c(-1, 1, 1, -1))))
This failed with the error:
Error in nparcomp(y ~ x, data = data.frame(x, y), type =
"UserDefined", : Sums of positive contrast coefficients must be 1!
which I fixed by rescaling the contrast matrix to t(matrix(c(-0.5, 0.5, 0.5, -0.5))). However, this failed with another error:
Error in logit.dev %*% cov.bf : non-conformable arguments
What is the correct way to use nparcomp with user-defined contrasts?
P.S. I am a newcomer to R, so apologies for the bad coding style.

Answer 1

Let me preface this by saying that I'm not familiar with this particular area of statistics at all, so although my code does run without errors, my modification may have completely changed the design of what you are trying to test - let me know if this is the case. Anyways, I looked through the definition of nparcomp to see what was causing the first error, Sums of positive contrast coefficients must be 1! -
if (type == "UserDefined") {
if (is.null(contrast.matrix)) {
stop("Please eanter a contrast matrix!")
}
Con <- contrast.matrix
rownames(Con) <- paste("C", 1:nrow(Con))
for (rc in 1:nrow(Con)) {
if (sum(Con[rc, ][Con[rc, ] > 0]) != 1) {
stop("Sums of positive contrast coefficients must be 1!")
}
}
colnames(Con) <- fl
}
In the case of your original contrast.matrix of t(matrix(c(-1, 1, 1, -1))) this evaluates to 2; whereas your second attempt of t(matrix(c(-0.5, 0.5, 0.5, -0.5))) clearly evaluates to 1 in the above block of code (since it doesn't produce this error).
Your second error, Error in logit.dev %*% cov.bf : non-conformable arguments, seems to be arising from trying to multiply matrices of incompatible dimensions. I didn't trace the root of this particular error (the body of this function is pretty lengthy), but it gave me the idea to try passing t(matrix(c(-0.5, 0.5, 0.5, -0.5))) as a symmetric matrix:
contrVec <- t(matrix(c(-1, 1, 1, -1)))
contrMat <- -1*(matrix(
outer(contrVec,
t(contrVec)),
ncol=4)/2)
##
> contrMat
[,1] [,2] [,3] [,4]
[1,] -0.5 0.5 0.5 -0.5
[2,] 0.5 -0.5 -0.5 0.5
[3,] 0.5 -0.5 -0.5 0.5
[4,] -0.5 0.5 0.5 -0.5
Passing this to contrast.matrix does not produce any errors, but as I've said, I am unfamiliar with this particular procedure / function, so I may have completely changed the hypothesis you are trying to test. Here's the full code:
library(car)
library(nparcomp)
##
data <- data.frame(
a1=c(.439,.451,.446,
.340,.294,.284,1.00),
a2=c(.066,.07,.06,.056,
.008,.002,1.00),
b1=c(rep(0.0,5),
.001,.002),
b2=c(.001,
rep(0.0,6)))
##
x <- factor(
rep(names(data),
each=nrow(data)))
##
y <- c(data[['a1']], data[['a2']],
data[['b1']], data[['b2']])
##
contrVec <- t(matrix(c(-1, 1, 1, -1)))
contrMat <- -1*(matrix(
outer(contrVec,
t(contrVec)),
ncol=4)/2)
##
nprce <- nparcomp(
y ~ x,
data=data.frame(x, y),
type="UserDefined",
contrast.matrix=contrMat)
##
> summary(nprce)
#------------Nonparametric Multiple Comparisons for relative contrast effects----------#
- Alternative Hypothesis: True relative contrast effect p is less or equal than 1/2
- Estimation Method: Global Pseudo ranks
- Type of Contrast : UserDefined
- Confidence Level: 95 %
- Method = Logit - Transformation
- Estimation Method: Pairwise rankings
#---------------------------Interpretation--------------------------------------------#
p(a,b) > 1/2 : b tends to be larger than a
#-------------------------------------------------------------------------------------#
#----Data Info-------------------------------------------------------------------------#
Sample Size
1 a1 7
2 a2 7
3 b1 7
4 b2 7
#----Contrast--------------------------------------------------------------------------#
a1 a2 b1 b2
C 1 -0.5 0.5 0.5 -0.5
C 2 0.5 -0.5 -0.5 0.5
C 3 0.5 -0.5 -0.5 0.5
C 4 -0.5 0.5 0.5 -0.5
#----Analysis--------------------------------------------------------------------------#
Comparison Estimator Lower Upper Statistic p.Value
1 C 1 0.429 0.345 0.517 -1.593593 0.1110273
2 C 2 0.571 0.483 0.655 1.593593 0.1110273
3 C 3 0.571 0.483 0.655 1.593593 0.1110273
4 C 4 0.429 0.345 0.517 -1.593593 0.1110273
#----Overall---------------------------------------------------------------------------#
Quantile p.Value
1 1.959966 0.1110273
#--------------------------------------------------------------------------------------#