I have been successfully applying the Local Moran's Index (and Gi*) as part of my PhD, but I want to know exactly how the calculation is achieved. I am an archaeologist and I will be writing this in my thesis, so I must present it in a way other non-statisticians can understand it. I decided to produce a worked example, for Gi* it was simple but I'm having difficulty calculating a single instance of the Local Moran's i (Li).
Thank you in advance for any help you can give me, I really want to crack this as I am just starting my writing up phase (and it's bugging me)!
Here is the local neighbourhood (of a larger dataset 11x11 cells), the target cell is 100.
73|96|82 96|100|92 87|93|82
Neighbourhood average = 87.63
Here is my workings, there is an error which I point out as you go through it.
To get Si^2 sum of al the neighbours minus the mean then squared this is divided by the number of neighbouring cells minus 1 (the target cell) this calculation is then subtracted from the mean squared
so: �??(73-87.63)�??^2+ �??(96-87.63)�??^2+ �??(87-87.63)�??^2+ �??(96-87.63)�??^2+ �??(93-87.63)�??^2+ �??(82-87.63)�??^2+ �??(92-87.63)�??^2+ �??(82-87.63)�??^2 =465.88
then...
Si^2 = 465.88/(8-1)-7678.14= -7611.59
We have to take the value of a neighbour and subtract this from the average of neighbours and multiplied by the search radius (wij)
