I have some aggregated data for 20 geographical places and would like to understand Moran results based on the data. I know that the cluster field corresponds to low P-values and higher z-scores as well as positive Moran index, however I am not sure why the cluster gives number 2 for each clustered place. And how can I interpret the results for non-spatial statisticians:
Place Ii Ei Zi p.value Xi wXj Cluster
1 0.527153 -0.05263 1.521057 0.128245 1.099403 0.818118 0
2 1.169842 -0.05263 3.207143 0.001341 -1.69534 -1.63654 2
3-0.14793 -0.05263 -0.25003 0.802567 0.24454 -1.45796 0
4 1.169842 -0.05263 3.207143 0.001341 -1.69534 -1.63654 2
5 1.169842 -0.05263 3.207143 0.001341 -1.69534 -1.63654 2
6 1.169842 -0.05263 3.207143 0.001341 -1.69534 -1.63654 2
Many thanks,
Eiman
R is not a single software program, it is a programming language but also there are a large number of "packages" available, which one did you use and how did you use it?
All of the published R packages come with some tutorial material, try doing a search on Google for "******* R package tutorial material" where ****** is the name of the package.
You say you have aggregated data, how exactly is it aggregated? You need to look at the Moran algorithm to see how it is affected by aggregated data
How do we know if we have SA in a continuous geospatial data like NPP, precipitation
or other continuous geospatial variables? First, for regression, we calculate the residuals (Eq.1)
and then map the residuals: If we see any spatial patterns, we have a problem. Secondly, we
calculate Moran’s I for the residuals and if it is statistically significant, we have a problem.
Yi − Ŷi = Actual (Yi ) – Predicted (Ŷi ) (Eq. 1)
The next step is testing statistical significance for autocorrelation using MORAN’s I.
MORAN’s I is the most common measure of spatial autocorrelation (Briggs, 2010). It measures
the correlation between variable, X, and the “spatial lag” of X formed by averaging all the values
of X for the neighboring locations. (Net Primary Productivity) .
After Z scores are collected, we test the statistical significance using the normal curve for
Z. At Confidence level α = 0.95; we define the null and alternative hypothesis as:Null
hypothesis, H0 =There is no spatial autocorrelation (MORAN’s I = 0). Alternative hypothesis, H1
= There is spatial autocorrelation (MORAN’s I ≠ 0). In a statistical test, the null hypothesis is
rejected if the p-value is less than (p
In other words, if there is spatial correlation, then your samples are not independent of each other.
Several observations
1. Morans"I is an empirical measure of spatial correlation and is based on "randomization" (in contrast with a spatial autocorrelation function)
2.It is not a question of whether the "samples" are independent, first of all independence is a theoretical property of random variables (not of data)
3. Don't mix up confidence level and significance in a test of hypotheses. Significance is the probability of a Type I error (incorrect rejection of the null hypothesis) whereas confidence level is the related to whether the true but unknown parameter (the one being estimated) is inside the confidence interval (a confidence level is not a probability but is related to the probability that the estimatOR value is inside of an specified interval) You also have to be careful about the distinction between a one sided confidence interval and a two sided confidence interval.
4. The phrase " the correlation between variable, X, and the “spatial lag” of X formed by averaging all the values " doesn't make any sense. It is completely wrong
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