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I am confused about some aspects of spatial autocorrelation usind survey data (survey which is repeated every year). I have data from 1991 to 2012 with sampling region pretty consistent every year. I am studying the species distribtion of two species in the area, in this goal I used binomial GLM. After running the GLM, I noted that they were some spatial autocorrelation in the model error residuals (Moran's I index from 0.2 to 0.05 significant on 6 first lags). Therefore I decided to take in account the spatial autocorrelation using Moran's Eingenvector Mapping. However this method is generally described for dataset over 1 year. As the eigenvector are calculated using the coordinates (longitude and latitude) of my points in function of the neighbourhood response I assumed it should take in account the different distribution over the years. Thus I applied a 10 factor on longitude and lagitude to artificially separate points at the same location but sampled at different years (point A year 1 will have (1,1) coordinate; point B year 2 will have (10,10) coordinate.

My first question is to know if this is valid? If not what would you advise?

The outcomes of this method is that I have different eigenvector value for a point at the same position but at different years.

Is this not a problem for the model including MEM variables power of prediction?

Indeed following a question not answered yet I posted here (Spatial autocorrelation -- GLM, autocovariate, MEM (Moran's eigenvector mapping)), it appears that my GLM including MEM suffer a loss of 0.25 or more power of prediction (ROC Curve - AUC value). I am digging since one week to understand what is happening and why spatial autocorrelation included using MEM method are so unefficient while they seems to be the best method following litteratur.

Any clue or help will be really appreciated,

Thank you,

Xochitl C.

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The problem was indeed the artificial separation of the year using the 10 factor on latitude and longitudes:

First : this factor was to small for the are studied (the North Sea) so some of the southern and northern points of different years had the same latitudes/longitudes values. Second : this separation is not valid using MEMs because depending of the year Moran's eigenvectors values of the actually same coordinates were positive or negatives, which while selecting MEMs significance created a problem for the models.

The solution is to create a grid of coordinates including all the points covered in the time-series and to generate an unique connectivity matrix from which the different Moran's eigenvectors will be computed. The method will not allow to differentiate the different years but is suitable for taking in account spatial arrangement underlying in the data, which create spatial auto-correlation.

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