Performing the Analysis
This package offers two ways to rectify Moran’s I. The first method is a Procrustes method, and the second one is a rectifying through Pearson correlation. We provided a straight forward way to perform both techniques.
Rectification method 1. Three-point anisometric scaling (3-PAS)
invited every passer-by to spend the night. If the guess were too short, Procrustes would stretch him to fit, or If the guest proved too tall, Procrustes would amputate the excess length. Keeping Procrustes’s myth in mind, what this technique does is to stretch or cut as necessary to make the Moran’s I null distribution to fit a Normal Curve, making the max and min or 99.99% - 0.1% quantile, values to match.
The package offers, as stated before, a direct way to apply the Procrustes technique to a data set. The function rescaleI requires an input file path, the number of samples to create the null distribution, and a parameter that establishes up to which value the Moran’s I value will be stretch.
The Loading data section explains the required format of the input file. The parameter scalingUpTo accepts two string values, “MaxMin” and “Quantile.” The first value is self-explanatory, while the second one refers to the quantiles 0.1% and 99.99%. The default value is “Quantile”, meaning that, if something different to “MaxMin” or “Quantile” is sent, the iCorrection function will apply “Quantile”.
library(Irescale)
fileInput<-system.file("testdata", "chen.csv", package="Irescale")
data<-loadFile(fileInput)
scaledI<-rescaleI(data,samples=1000, scalingUpTo="MaxMin")
fn = file.path(tempdir(),"output.csv",fsep = .Platform$file.sep)
saveFile(fn,scaledI)
if (file.exists(fn))
#Delete file if it exists
file.remove(fn)
#> [1] TRUERectified Correlation
Three-point anisometric scaling (3-PAS) method of rectification eliminated negative bias and more closely approached the theoretical distribution of regular (Pearson, Spearman) correlations, hence intuitive expectations for such; however, distribution shape depended upon choice of critical percentiles and did not conform to intuitive expectations for Gaussian shape. These results inspired development of a second approach which mapped $ $ values, based on their quantiles, to the theoretical values of regular correlations expected for each quantile. This latter method yielded perfectly repeatable null distributions that were Gauss-like but with definitive limits at $ 1$
fileInput <- system.file("testdata", "chen.csv", package="Irescale")
data <- loadFile(fileInput)
rectifiedI<-rectifyIrho(data,1000)
fn = file.path(tempdir(),"output.csv",fsep = .Platform$file.sep)
saveFile(fn,rectifiedI)
if (file.exists(fn))
#Delete file if it exists
file.remove(fn)
#> [1] TRUE
