EOT analysis of a predictor and (optionally) a response RasterStack
Description
Calculate a given number of EOT modes either internally or between RasterStacks.
Usage
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Arguments
x 
a RasterStack used as predictor 
y 
a RasterStack used as response. If 
n 
the number of EOT modes to calculate 
standardised 
logical. If 
write.out 
logical. If 
path.out 
the file path for writing results if 
prefix 
optional prefix to be used for naming of results if

reduce.both 
logical. If 
type 
the type of the link function. Defaults to 
verbose 
logical. If 
... 
not used at the moment 
Details
For a detailed description of the EOT algorithm and the mathematics behind it, see the References section. In brief, the algorithm works as follows: First, the temporal profiles of each pixel xp of the predictor domain are regressed against the profiles of all pixels xr in the response domain. The calculated coefficients of determination are summed up and the pixel with the highest sum is identified as the 'base point' of the first/leading mode. The temporal profile at this base point is the first/leading EOT. Then, the residuals from the regression are taken to be the basis for the calculation of the next EOT, thus ensuring orthogonality of the identified teleconnections. This procedure is repeated until a predefined amount of n EOTs is calculated. In general, remote implements a 'brute force' spatial data mining approach to identify locations of enhanced potential to explain spatiotemporal variability within the same or another geographic field.
Value
if n = 1 an EotMode, if n > 1 an EotStack of n
EotModes. Each EotMode has the following components:

mode  the number of the identified mode (1  n)

eot  the EOT (time series) at the identified base point. Note, this is a simple numeric vector, not of class
ts

coords_bp  the coordinates of the identified base point

cell_bp  the cell number of the indeified base point

cum_exp_var  the (cumulative) explained variance of the considered EOT

r_predictor  the RasterLayer of the correlation coefficients between the base point and each pixel of the predictor domain

rsq_predictor  as above but for the coefficient of determination

rsq_sums_predictor  as above but for the sums of coefficient of determination

int_predictor  the RasterLayer of the intercept of the regression equation for each pixel of the predictor domain

slp_predictor  same as above but for the slope of the regression equation for each pixel of the predictor domain

p_predictor  the RasterLayer of the significance (pvalue) of the the regression equation for each pixel of the predictor domain

resid_predictor  the RasterBrick of the reduced data for the predictor domain
Apart from rsq_sums_predictor, all *_predictor fields are also returned for the *_response domain, even if predictor and response domain are equal. This is due to that fact, that if not both fields are reduced after the first EOT is found, these RasterLayers will differ.
References
Empirical Orthogonal Teleconnections
H. M. van den Dool, S. Saha, A. Johansson (2000)
Journal of Climate, Volume 13, Issue 8, pp. 14211435
http://journals.ametsoc.org/doi/abs/10.1175/15200442%282000%29013%3C1421%3AEOT%3E2.0.CO%3B2
Empirical methods in shortterm climate prediction
H. M. van den Dool (2007)
Oxford University Press, Oxford, New York
https://global.oup.com/academic/product/empiricalmethodsinshorttermclimateprediction9780199202782?cc=de&lang=en&
Examples
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