15

Learning by doing is my preferred way. And when it comes to spatial statistics, R is getting seriously powerful tool. So if this is an option browse through some course materials, download the data and try it yourself. Few starting points covering spatial autocorrelation (SA) (and generally speaking handling spatial stuff in R): Center for Studies in ...


13

What these procedures are Although OLS and GWR share many aspects of their statistical formulation, they are used for different purposes: OLS formally models a global relationship of a particular sort. In its simplest form, each record (or case) in the dataset consists of a value, x, set by the experimenter (often called an "independent variable"), and ...


11

The expected value of Moran's I is -1/(N-1), which for your sample of 38 cases equals -1/(38-1) = -0.02702703. This is what the software spit out, so that is a good start! So this means that there is really no evidence of negative auto-correlation here, as with random data you would expect it to be a negative value more often than positive. You interpret ...


8

The formula for global Moran's I is: where i is an index of analysis units (basically, measurement units of of your map, or in your case pixels in the raster) and j is an index of the neighbors of each map unit. The formula for local Moran's I is extremely similar, except that since local Moran's I is calculated separately for each analysis unit indexed by ...


7

Moran's I ranges between -1 (perfectly dispersed) and 1 (perfectly clustered), with a value of 0 indicating random distribution. While 0.003 isn't "perfectly" random, it's much, much closer to random than to dispersed or clustered. The question of whether it's random enough depends on your discipline, personal standards, and research question. I'd ...


5

You cannot use the Moran's I on an unmarked process. The values, at each location, are what the statistic is based on and therefore cannot be absent or uniform. Your only real option, in ArcGIS, for evaluating the spatial process (dispersion/clustering) of an unmarked point process is the Nearest Neighbor Index (Average Nearest Neighbor Tool).


5

Given an inevitable nonparametric model structure, a residual in the traditional sense is not possible. You could approximate the response, Pearson's or deviance (likelihood ratio chi-squared) residual error using standard methods found in the logistic regression literature, eg., response = [y - y-hat], Pearson's = [(y - y-hat) / sqrt(y-hat)] where; y = ...


5

One does have to question the why here. What do you hope to achieve in evaluating multivariate autocorrelation? What hypothesis are you, in fact, testing? If this is in the context of a linear multivariate model then there is no real insight to be gained in evaluating the autocorrelation structure of the entire design matrix. You want to draw inference at ...


4

It may be prudent to back up a step and explore the "spdep" package in more detail and not just try to recreate an analysis that you do not entirely understand. Bivand's code is irrelevant if we can not see the structure and intent of your analysis. A .gal file is a weights matrix produced by the software GeoDa. The code provide is intended to demonstrate ...


4

Hello Moran's I and Geary's C are in fact inversely related to one another. So the general pattern that you're observing seems consistent. However, the possible range of values for Moran's I is -1 to 1 (where -1 indicates a perfect negatively spatial autocorrelation--think of a chess board pattern--and 1 indicates a perfect positive spatial autocorrelation). ...


4

I am wondering if someone can explain why the nugget seems so high? Does this mean that even at similar locations, there is still a relatively high degree of difference? Yes, a high nugget effect (high semivariance at origin) tells there is a weak (or none) spatial dependence (autocorrelation) among sample data at small distances. It could be the case the ...


4

Eventually, with the help of Serge Rey's answer and this link in the documentation, I ended up using pysal's implementation as follows: import pysal as ps w = ps.lat2W(input_img.shape[0],input_img.shape[1], rook=False, id_type="int") np.random.seed(12345) lm = ps.Moran_Local(input_img,w) moran_significance = np.reshape(lm.p_sim, input_img.shape) In the ...


4

Yes. If I_A > I_B for two data sets A and B, then there's greater spatial autocorrelation, where spatial autocorrelation is defined by the formula for the Moran I (other measures of spatial autocorrelation exist and may give different results). In short, neighbours of region i are more similar to i in data set A than in B, averaged all over. Usually the ...


4

In terms of a local autocorrelation (nonstationarity) statistics, there really is not one. Join-counts is adequate for hypothesis testing of global clustering in binary process, albeit very scale dependent, but not for multinomial data. I am not even sure what the underlying hypothesis test would be here, especially with ordinal data. One has to ask, how ...


3

Interesting finding, and thanks for the perfectly prepared reproducible example! Both variograms you mention are meant to prepare for linear kriging in the next step, and you may not want that. The robust variogram was (IIRC) deviced for normal data with some pollution (outliers), but not for count data. I would advice to look at model-based geostatistics, ...


3

Rsquared should not be used to compare models. Use log likihood or AIC values. If your residuals in GWR are random, or I guess appear to be random (not statistically sig.) than you might have a specified model. It at least suggests that you don't have correlated residuals and should suggest that you do not have any omitted variables.


3

We can run through some straight-forward approaches starting with looking at the modified z-score on the variable of interest (a-spatial) then move to calculating the local z-score and variance within a specified distance and finally calculate the local Moran's-I statistic. Our final example is evaluating the autocorrelation and heteroskedasticity in the ...


3

I myself am still learning as much as I can about Moran's I, but I think I help figure out the answer to this question. There is a great video on coursera about spatial correlation: Based on the Z-score, a statistical test is feasible to check if a given variable is spatially autocorrelated or not. The statistical test can be formulated like this, ...


2

Apologies for the double answer here, but since posting my first suggestion I came across a more-comprehensive toolkit for doing all sorts of analyses like this (including both global and local Moran's I): Crankshaft, a Python/PostGIS module by Carto. I've been using it for production analyses similar to your use case for a few months now and it works ...


2

Art Lembo has a simple example of a pseudo-Moran's I for PostGIS: SELECT corr(a.pctwhite, b.pctwhite) FROM cleveland AS a, cleveland AS b WHERE st_touches(a.geometry, b.geometry) AND a."OID" <> b."OID" The key here is that - as he puts it . . . [Moran's I] is really nothing more than Pearsons Correlation Coefficient tricked into a spatial context ...


2

I have no idea how to perform your QGIS/PostgreSQL idea but the following software can calculate measures for autocorrelation GeoDa http://geodacenter.asu.edu/ogeoda Passage 2 http://www.passagesoftware.net/ SAM (Spatial Analysis in Macroecology) http://www.ecoevol.ufg.br/sam/ PAST http://folk.uio.no/ohammer/past/ SAGA GIS http://www.saga-gis.org/...


2

I am assuming that you would like an AR(II) process term to account for serial autocorrelation. Here is example WinBUGS code for running a Simultaneous Autoregressive model with an AR(II) term that could be adapted for your problem. model; { # Defines likelihood for(i in 1:I){ D[i, 2:(I+2)] ~ dmulti(C[i,], D[i, 1]); } for(i in 1:(I-1)){ lphi[i] <-...


2

It would be good if you provided a bit more detail to your question and indicated what you have already tried. Working examples are always appreciated. Here is a function that calculates a correlogram on point data. You could, in theory, modify it to operate on a raster or on a subsample of a raster. Although, I wonder about the computational tractability ...


2

You might want to take a look at this question (How to implement Spatial Autocorrelation using QGIS or PostgreSQL (or any free application)?) and look at programmatic solutions like R. QGIS may be another option as well. This website outlines different formulas and measures for spatial autocorrelation that may also be of interest to you


2

I see a different output, namely: > m2 <- update( m1, corr = corExp(c(300, 0.7), form = ~ x + y, nugget = T) ) Error in lme.formula(fixed = log(zinc) ~ 1, data = meuse, random = ~1 | : nlminb problem, convergence error code = 1 message = false convergence (8) this is nlme_3.1-119 on R version 3.1.2 (2014-10-31) Platform: x86_64-pc-linux-gnu (...


2

I don't think there is any limit (mathematically speaking) to the z-score. I've got results up to 100-200 in some occasions. Just google search images of the morans zscore results and you will see a lot of cases with scores greater than 40.


2

Spatial Correlation (autocorrelation) is a very broad field. You could look at the Arc help on Global Moran's I, for example. There's a very good primer on this at: http://gisgeography.com/spatial-autocorrelation-moran-i-gis/... However, if you want to consider what attributes may be influencing the clusters - something like Luc Anselin's LISA might ...


2

Not sure if this suits your problem, because your data consists of non-discrete data. What I suggest is probably a brute force approach and maybe not very elegant. Anyways, there are some standard solutions in spatial cluster analysis e.g. DBSCAN (https://de.wikipedia.org/wiki/DBSCAN) which is an unsupervised machine learning approach for agglomerative ...


2

You need to put some thought into your experimental design and talk with somebody well versed in statistical analysis. In what you are describing, your experimental units are the transects and not the observations along them. This severely limits the types of analysis that can be applied and power is likely an issue. In terms of autocorrelation effects on a ...


2

The autocorrelation of covariates is not the problem in itself. What may be a problem is if there is correlation of covariates at the position of data observations. In that case, there will be identifiability issues to estimate the parameters of your SDM model. What people usually do is to test for correlation between covariates at observation points. When ...


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