Hello!

I want to make a permutation test between two variables, whereas the
dependent variable is a set of raster images (remote sensing index). In
total, I only have 7 observation dates. As this is a very small number, a
permutation test enables to simulate a high number of observations and
obtain a more robust statistic. - I am interested in getting the p-value
from a correlation between the two variables. The important thing: The
output should be a raster image with every pixel holding a prober value. 

Data Overview: 
independent variable (single value)         dependent variable (raster
image) 
x1                                                    y1  -
y1<-raster(raster image), raster func. in raster package
x2                                                    y2
x3                                                    y3
x4                                                    y4
x5                                                    y5
x6                                                    y6
x7                                                    y7

One raster image contains i rows and j columns. The permutation hast to be
executed for every single pixel during all obervation dates, in other words
seven values from every single pixel (one per observation date) have to be
permuted by the seven values of the independent variable x. This process has
to be repeated for every single pixel. It is important to keep the pixels,
as the output should be a map, where every pixel is assigned the p-value
(from the statistic). 

So far I used the 'lmp' function from the lmPerm package. Therefore, all
data have to be in one table. I ordered every pixel side by side to the one
pixel before and obtained the entire number of pixels in one row (pixel
number= number of columns). For every observation date I made one row
resulting in 7 rows. The first column was reserved for the independent
variable x. 

         V1  V2  V3  V4...
date1: x1 px1 px2 px3...
date2: x2 px1 px2 px3...
...
date7: x7 px1 px2 px3...

I then did the permutation test using 'lmp':
permutationTest <- lmp (V243606~V1, data=tableOfData, sep="", header=TRUE) #
here for the pixel in row243606
summary(permutationTest)

the Problem: the test has to be done for every singel pixel and i have more
than 1 million of it! that is not possible. 


I tried another method using the raster package: 
Raster package has the calc function, which allows to apply any formula to
every single pixel. E.g. I introduced the formula for the Pearson
correlation coefficient and the density function for a student
t-distribution to get the p-value into the 'calc' function. I was thinking
to introduce the 'lmp' formula into the 'calc' function, but was not
successful as I have to use 7 raster images and 7 numeric values, that this
function does not take. Does anybody know how to solve this problem?

I will very much appreciate any help for this problem!

Thanks! 







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