Pretty old question, but maybe it's still worth adding to the comments given so far:

Type of weights: Spatial weights form a crucial part in estimating spatial autocorrelation. The choice of weights depends on a range of factors like the type of spatial behaviour you assume in the analysed process, the type of data you have at hand, the scale of your process, etc. Thus, there is no easy answer regarding an appropriate choice of weigths and it is ultimately up to a specific analytical task.

Software/different p-values: I'm not familiar with ape but have used spdep. spdep allows you to calculate distance-based weights. The function dnearneigh gives you binary weights indicating whether neighbours are located at a disc of radius dmax (dmin is also possible). If you need something like IDW weights, then you need to do some (not too extensive) R programming indeed, but it is still possible. In addition, spdep also provides functionality for creating k-nearest-neighbour weights through knearneigh.

Inference about Moran's I: There are two ways of drawing inference about Moran's I. One is called the Normal assumption (N), the other one is based on Randomisations (R). The N assumption is based on the so-called Pitman-Koopmans theorem that roughly states that Moran's I is independent of its denominator under iid normal variates. This assumption allows you to evaluate p-values of Moran's I from a normal distribution regardless of sample size, but under the (somewhat strict) assumption of normality. This is obviously a very efficient way of assessing p-values. In contrast, the R assumption is based on a permutation argument that assumes random reallocations of your values within the fixed set of spatial units. Therefore, the R assumption is a non-parametric one. While N is based on sampling with replacement, R corresponds to sampling without replacement, causing statistical power to be lower (because your decision is based on less information content). In the latter case you would construct a bootstrap from recurrently calculating Moran's I a certain number of times. The (pseudo) p-values are then assessed from that bootstrap distribution. However, even under R, Moran's I converges to normality rather quickly (though this is also influenced by the layout of your spatial units/geographic region). A valuable source for this is the series of seminal books published by Cliff and Ord (1973, 1981).

Hi Patric

Thank you for your suggestion. I found spdep - package is quite useful. If you had did any analysis and published related to spatial autocorrelation and residual analysis in species distribution modelling please share it.

you can also check "lctools" (http://cran.r-project.org/web/packages/lctools/index.html) which perhaps you find more user friendly!

There are other user fiendly alternatives as "ncf" and "pgirmess" (http://www.r-bloggers.com/spatial-correlograms-in-r-a-mini-overview) specially if you are interested in perform spatial correlograms instead of overall Moran's I.

Thanks for sharing!

Has anyone else noticed that the p-values from the Moran's I test results from the 'ape' and 'spdep' packages are not the same? Which one is correct?

Hi AT Hudak, I just did! They are quite different actually!

I think it has to do with the weights you are using to calculate Moran's I in each case. While in ape your weights are given by your distance matrix, in spdep you must specify spatial weights from a neighbors (nb) object, choosing a given style (binary, standardised, ect). Seems to me the latter approach is better, but would like to hear if someone else knows better!

Hi everybody,

There are two ways to calculate the p-values, one is by running a simulation using random data and the second by a couple of complex formulae based on either the resampling or randomisation hypothesis test. The latter is best described by M. Goodchild at the Catmog 47 book (available here https://alexsingleton.files.wordpress.com/2014/09/47-spatial-aurocorrelation.pdf). Another way to calculate the Moran's I and the corresponding p-values is by using the package lctools (an example is available here https://cran.r-project.org/web/packages/lctools/vignettes/SpatialAutocorrelation.pdf). Hope this helps!

Thank you Rodolfo and Stamatis for your helpful responses!

Thank you so much. This has been useful for me.

http://www.ats.ucla.edu/stat/r/faq/morans_i.htm

try this

Pretty old question, but maybe it's still worth adding to the comments given so far:

Type of weights: Spatial weights form a crucial part in estimating spatial autocorrelation. The choice of weights depends on a range of factors like the type of spatial behaviour you assume in the analysed process, the type of data you have at hand, the scale of your process, etc. Thus, there is no easy answer regarding an appropriate choice of weigths and it is ultimately up to a specific analytical task.

Software/different p-values: I'm not familiar with ape but have used spdep. spdep allows you to calculate distance-based weights. The function dnearneigh gives you binary weights indicating whether neighbours are located at a disc of radius dmax (dmin is also possible). If you need something like IDW weights, then you need to do some (not too extensive) R programming indeed, but it is still possible. In addition, spdep also provides functionality for creating k-nearest-neighbour weights through knearneigh.

Inference about Moran's I: There are two ways of drawing inference about Moran's I. One is called the Normal assumption (N), the other one is based on Randomisations (R). The N assumption is based on the so-called Pitman-Koopmans theorem that roughly states that Moran's I is independent of its denominator under iid normal variates. This assumption allows you to evaluate p-values of Moran's I from a normal distribution regardless of sample size, but under the (somewhat strict) assumption of normality. This is obviously a very efficient way of assessing p-values. In contrast, the R assumption is based on a permutation argument that assumes random reallocations of your values within the fixed set of spatial units. Therefore, the R assumption is a non-parametric one. While N is based on sampling with replacement, R corresponds to sampling without replacement, causing statistical power to be lower (because your decision is based on less information content). In the latter case you would construct a bootstrap from recurrently calculating Moran's I a certain number of times. The (pseudo) p-values are then assessed from that bootstrap distribution. However, even under R, Moran's I converges to normality rather quickly (though this is also influenced by the layout of your spatial units/geographic region). A valuable source for this is the series of seminal books published by Cliff and Ord (1973, 1981).

Hello everyone !

Of course, you have already found your information, but it is advisable to slip an additional answer for what in search:

Patrick Moran's index is nowadays calculated under multiple applications; R Pyhon, ArcGis. To consider this, it would appear at first sight that the phenomena studied spatially are similar.

The aim is to quantify the spatial interactions between the points in a well-defined field. Indeed, the distance matrix between these points will be calculated for the diagnosed, triangulated and to deduce the interactions between the stations.

Under R, this example will serve as a first start

Commande R:

library(spdep)

data(afcon)

View(afcon)

oid