Pearson corelation and p-value for matrix

-----Original Message-----
From: Liaw, Andy [mailto:andy_liaw at merck.com] 
Sent: Monday, April 18, 2005 2:40 PM
To: 'John Fox'; 'Dren Scott'
Cc: 'R-Help'
Subject: RE: [R] Pearson corelation and p-value for matrix

I believe this will do:

cor.pval2 <- function(x,  alternative="two-sided") {
    corMat <- cor(x, use=if (any(is.na(x))) 
"pairwise.complete.obs" else
"all")
    df <- crossprod(!is.na(x)) - 2
    STATISTIC <- sqrt(df) * corMat / sqrt(1 - corMat^2)
    p <- pt(STATISTIC, df)
    p <- if (alternative == "less") {
        p
    } else if (alternative == "greater") {
        1 - p
    } else 2 * pmin(p, 1 - p)
    p
}

Some test:

set.seed(1)
x <- matrix(runif(2e3 * 1e2), 2e3)
system.time(res1 <- cor.pval(t(x)), gcFirst=TRUE)

[1] 17.28  0.77 18.16    NA    NA

system.time(res2 <- cor.pval2(t(x)), gcFirst=TRUE)

[1] 19.51  1.05 20.70    NA    NA

max(abs(res1 - res2))

[1] 0

x[c(1, 3, 6), c(2, 4)] <- NA
x[30, 61] <- NA
system.time(res2 <- cor.pval2(t(x)), gcFirst=TRUE)

[1] 24.48  0.71 25.28    NA    NA

This is a bit slower because of the extra computation for 
"df".  One can try to save some computation by only computing 
with the lower (or upper) triangular part.

Cheers,
Andy

From: John Fox

Dear Dren,

Since cor(), on which Andy's solution is based, can compute 
pairwise-present correlations, you could adapt his function 

-- you'll 

have to adjust the df for each pair. Alternatively, you 

could probably 

save some time (programming time + computer time) by just using my 
solution:

R <- diag(100)
R[upper.tri(R)] <- R[lower.tri(R)] <- .5
library(mvtnorm)
X <- rmvnorm(6000, sigma=R)
system.time(for (i in 1:50) cor.pvalues(X), gc=TRUE)

[1] 518.19   1.11 520.23     NA     NA

I know that time is money, but nine minutes (on my machine) 

probably 

won't bankrupt anyone.

Regards,
 John

--------------------------------
John Fox
Department of Sociology
McMaster University
Hamilton, Ontario
Canada L8S 4M4
905-525-9140x23604
http://socserv.mcmaster.ca/jfox
--------------------------------

-----Original Message-----
From: r-help-bounces at stat.math.ethz.ch 
[mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Dren Scott
Sent: Monday, April 18, 2005 12:41 PM
To: 'R-Help'
Subject: RE: [R] Pearson corelation and p-value for matrix

Hi all,
 
Thanks Andy, Mark and John for all the help. I really 

appreciate it. 

I'm new to both R and statistics, so please excuse any 

gaffes on my 

part.
 
Essentially what I'm trying to do, is to evaluate for 

each row, how 

many other rows would have a p-value < 0.05. So, after I 

get my N x 

N p-value matrix, I'll just filter out values that are > 0.05.
 
Each of my datasets (6000 rows x 100 columns) would 

consist of some 

NA's. The iterative procedure (cor.pvalues) proposed by 

John would 

yield the values, but it would take an inordinately long time (I 
have 50 of these datasets to process). The solution proposed by 
Andy, although fast, would not be able to incorporate the NA's.
 
Is there any workaround for the NA's? Or possibly do you think I 
could try something else?
 
Thanks very much. 
 
Dren


"Liaw, Andy" <andy_liaw at merck.com> wrote:

From: John Fox

Dear Andy,

That's clearly much better -- and illustrates an

effective strategy

for vectorizing (or "matricizing") a computation. I think

I'll add

this to my list of programming examples. It might be a little 
dangerous to pass ...
through to cor(), since someone could specify

type="spearman", for

example.

Ah, yes, the "..." isn't likely to help here! Also, it will only 
work correctly if there are no NA's, for example (or else 

the degree 

of freedom would be wrong).

Best,
Andy

Thanks,
John

--------------------------------
John Fox
Department of Sociology
McMaster University
Hamilton, Ontario
Canada L8S 4M4
905-525-9140x23604
http://socserv.mcmaster.ca/jfox
--------------------------------

-----Original Message-----
From: Liaw, Andy [mailto:andy_liaw at merck.com]
Sent: Friday, April 15, 2005 9:51 PM
To: 'John Fox'; MSchwartz at medanalytics.com
Cc: 'R-Help'; 'Dren Scott'
Subject: RE: [R] Pearson corelation and p-value for matrix

We can be a bit sneaky and `borrow' code from 

cor.test.default:

cor.pval <- function(x, alternative="two-sided", ...) {

corMat <-

cor(x, ...) n <- nrow(x) df <- n - 2 STATISTIC <-

sqrt(df) * corMat

/ sqrt(1 - corMat^2) p <- pt(STATISTIC, df) p <- if

(alternative ==

"less") { p } else if (alternative == "greater") {
1 - p
} else 2 * pmin(p, 1 - p)
p
}

The test:

system.time(c1 <- cor.pvals(X), gcFirst=TRUE)

[1] 13.19 0.01 13.58 NA NA

system.time(c2 <- cor.pvalues(X), gcFirst=TRUE)

[1] 6.22 0.00 6.42 NA NA

system.time(c3 <- cor.pval(X), gcFirst=TRUE)

[1] 0.07 0.00 0.07 NA NA

Cheers,
Andy

From: John Fox

Dear Mark,

I think that the reflex of trying to avoid loops in R

is often

mistaken, and so I decided to try to time the two

approaches (on a

3GHz Windows XP system).

I discovered, first, that there is a bug in your

function -- you

appear to have indexed rows instead of columns; fixing that:

cor.pvals <- function(mat)
{
cols <- expand.grid(1:ncol(mat), 1:ncol(mat))

matrix(apply(cols,

1,
function(x) cor.test(mat[, x[1]], mat[,

x[2]])$p.value), ncol =

ncol(mat)) }


My function is cor.pvalues and yours cor.pvals. This is

for a data

matrix with 1000 observations on 100 variables:

R <- diag(100)
R[upper.tri(R)] <- R[lower.tri(R)] <- .5
library(mvtnorm)
X <- rmvnorm(1000, sigma=R)
dim(X)

[1] 1000 100

system.time(cor.pvalues(X))

[1] 5.53 0.00 5.53 NA NA

system.time(cor.pvals(X))

[1] 12.66 0.00 12.66 NA NA

I frankly didn't expect the advantage of my approach to be

this large,

but there it is.

Regards,
John

-------------------------------- John Fox Department of 
Sociology McMaster University Hamilton, Ontario 

Canada L8S 4M4

905-525-9140x23604
http://socserv.mcmaster.ca/jfox
--------------------------------

-----Original Message-----
From: Marc Schwartz [mailto:MSchwartz at MedAnalytics.com]
Sent: Friday, April 15, 2005 7:08 PM
To: John Fox
Cc: 'Dren Scott'; R-Help
Subject: RE: [R] Pearson corelation and p-value for matrix

Here is what might be a slightly more efficient way to

get to John's

question:

cor.pvals <- function(mat)
{
rows <- expand.grid(1:nrow(mat), 1:nrow(mat)) 

matrix(apply(rows, 

1,
function(x) cor.test(mat[x[1], ], mat[x[2], 

])$p.value), ncol = 

nrow(mat)) }

HTH,

Marc Schwartz

On Fri, 2005-04-15 at 18:26 -0400, John Fox wrote:

Dear Dren,

How about the following?

cor.pvalues <- function(X){
nc <- ncol(X)
res <- matrix(0, nc, nc)
for (i in 2:nc){
for (j in 1:(i - 1)){
res[i, j] <- res[j, i] <- cor.test(X[,i],

X[,j])$p.value

}
}
res
}

What one then does with all of those 

non-independent test

is another

question, I guess.

I hope this helps,
John

-----Original Message-----
From: r-help-bounces at stat.math.ethz.ch 
[mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of

Dren Scott

Sent: Friday, April 15, 2005 4:33 PM
To: r-help at stat.math.ethz.ch
Subject: [R] Pearson corelation and p-value for matrix

Hi,

I was trying to evaluate the pearson correlation and

the p-values

for an nxm matrix, where each row represents 

a vector. 

One way to do

it would be to iterate through each row, and find its

correlation

value( and the p-value) with respect to the 

other rows. 

Is there

some function by which I can use the matrix as input? 

Ideally, the

output would be an nxn matrix, containing the p-values

between the

respective vectors.

I have tried cor.test for the iterations, but

couldn't find a

function that would take the matrix as input.

Thanks for the help.

Dren

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