SpatialPack (version 0.4)

modified.Ftest: Modified F test

Description

Performs a modified version of the F test to assess the multiple correlation between one spatial processes and several others.

Usage

modified.Ftest(x, y, coords, nclass = 13)

Value

A list with class "mod.Ftest" containing the following components:

corr

the sample correlation coefficient.

ESS

the estimated effective sample size.

Fstat

the value of the (unscaled) F-statistic.

df1,df2

degrees of freedom for the F-statistic.

p.value

the p-value for the test.

upper.bounds

upper bounds of the intervals constructed to compute Moran's I.

card

number of elements in each interval generated to compute Moran's I.

imoran

a matrix containing Moran's index for each interval associated with the response and predicted variables.

The generic functions print and summary are used to obtain and print additional details about the modified F test.

Arguments

x

an \(n\)-by-\(q\) matrix of data values.

y

an \(n\)-dimensional vector of data values.

coords

an \(n\)-by-2 matrix containing coordinates of the \(n\) data locations in each row.

nclass

a single number giving the number of cells for Moran's index. The default is 13. If this argument is NULL Sturges' formula us used.

Details

The methodology implemented is a modified F test for assessing the multiple correlation between one spatial process and several others. The test is based on corrections of the multiple correlation coefficient between the two spatially correlated sequences and required the estimation of an effective sample size. This factor takes into account the spatial association of both processes.

References

Dutilleul, P., Pelletier, B., Alpargu, G. (2008). Modified F tests for assessing the multiple correlation between one spatial process and several others. Journal of Statistical Planning and Inference 138, 1402-1415.

Examples

# The Pinus Radiata data set
data(radiata)

# defining the response and predictor variables from the radiata data set
y <- radiata$height
x <- radiata[c("basal","altitude","slope")]

# extracting the coordinates from the radiata data set
coords <- radiata[c("xpos","ypos")]

# computing the modified F-test of spatial association
z <- modified.Ftest(x, y, coords)
z

# display the upper bounds, cardinality and the computed Moran's index
summary(z)