[R-sig-Geo] Spatial autocorrelation help

[Dechen Lham]

Hi Orcun

I am not quite sure if im doing this correctly but I do understand that i first need to check spatial autocorrelation occurs in my data. so i did this below steps and after that checked it again in best model residuals

# Another approach to find SAC by creating neighbors first, then get distances between each point and neighbors, then
# inverse the distance and then check the SAC using mora's I
coord <- cbind(data$long, data$lat)
coords <- coordinates(coord)

# creates a matrix of nn indexes - knearneigh to get nearest neighbors
nn5 <- knearneigh(coords, k=5)  
mi5.nlist <- knn2nb(nn5, row.names = NULL, sym=FALSE)

# creates a sp weights matrix
mi5.sw <- nb2listw(mi5.nlist) 

# cal moran's I using distance as weights
# calculates the distance
mi5.dist <- nbdists(mi5.nlist, coords) 

# now invert the distnace to determine weights (closer =higher)
mi5.dist1 <- lapply(mi5.dist, function(x){ifelse(is.finite(1/x), (1/x), (1/0.001))})
mi5.dist2 <- lapply(mi5.dist, function(x){ifelse(is.finite(1/x^2), (1/x^2), (1/0.001^2))})

# check the distance between the distribution
summary(unlist(mi5.dist1)) 

# now create sp weights matrix weighted on distance
mi5.d1sw <- nb2listw(mi5.nlist, glist=mi5.dist1)
mi5.d2sw <- nb2listw(mi5.nlist, glist=mi5.dist2)

# morans test
moran.test(as.numeric(data$response), mi5.d1sw)
moran.test(as.numeric(data$response), mi5.d2sw)

This first moran’s test gives :
Moran I statistic standard deviate = 2.0328, p-value = 0.02104
alternative hypothesis: greater
sample estimates:
Moran I statistic       Expectation          Variance 
      0.105850408      -0.004608295       0.002952729 

Second morans test gives:

Moran I statistic standard deviate = 2.3848, p-value = 0.008545
alternative hypothesis: greater
sample estimates:
Moran I statistic       Expectation          Variance 
      0.154097396      -0.004608295       0.004428848 

And both indicates presence of spatial autocorrelation in the raw data.

Should i account for this in all models or if i perform logistic mixed model it is fine……help is much appreciated. Difficult to understand what the problem is and how to solve it



> On 11 Jul 2018, at 7:01 PM, Orcun Morali <orcunmorali using gmail.com> wrote:
> 
> Hi Dechen,
> 
> As for measuring spatial autocorrelation, one thing I noticed about your output is that you are using the randomization assumption in spdep::moran.test. Randomization assumption is not appropriate for Moran's I of regression residuals and spdep::lm.morantest is the function to correctly calculate moments of the measure for regression residuals anyway. Before using lm.morantest though, if I were you, I would check whether its inference applies to logistic regression residuals as well, since the theory was initially based on the classical regression.
> 
> As for fitting a spatial logistic model if you need it, McSpatial package in R might help you.
> 
> Best Regards,
> 
> Orcun
> 
> On 10/07/18 20:46, Dechen Lham wrote:
>> Hello all,
>> 
>> I would like some help in my problem below:
>> 
>> I am running a logistic regression and my best model residuals has spatial autocorrelation  (SAC) when checked as below and also on the raw data of the response type. My response is binary 0 and 1 (type of prey and to be predicted by several predictors). These type of prey are obtained from  a total of  200 locations (where the faecal samples are collected from).   In order to account for this SAC , I used the auto_covdist function from spdep package. But when i use this as a new predictor in my model, and then check for spatial autocorrelation in the residues of the model, there is still spatial autocorrelation,…..could u see if i am doing something wrong please?
>> 
>> #account for SAC in the model using weights
>> # auto_covariate is a distance weighted covariate
>> data$response <- as.numeric(data$response)
>> auto_weight <- autocov_dist(data$prey.type, xy=coords, nbs=1, type="inverse", zero.policy = TRUE,style="W", longlat = TRUE)
>> 
>> m5_auto <- glm(response ~  predictor1 + predictor2 + predictor3 + predictor4 + predictor1:predictor4, weight=auto_weight, family=quasibinomial("logit"), data=data)
>> 
>> # check spatial autocorrelation - first convert data to spatial points dataframe
>> dat <- SpatialPointsDataFrame(cbind(data$long, data$lat), data)
>> lstw  <- nb2listw(knn2nb(knearneigh(dat, k = 2)))
>> 
>> # check SAC in model residuals
>> moran.test(residuals.glm(m5_auto), lstw) # and gives the below:
>> 
>> Moran I test under randomisation
>> 
>> data:  residuals.glm(m5)
>> weights: lstw
>> 
>> Moran I statistic standard deviate = 1.9194, p-value = 0.02747
>> alternative hypothesis: greater
>> sample estimates:
>> Moran I statistic       Expectation          Variance
>>      0.160824328      -0.004608295       0.007428642
>> 
>> -Someone said its stupid to account for spatial autocorrelation in a logistic regression when you have a significant SAC using moran’s I. So i am now wondering how this can be solved? or does a SAC in a logistic regression be just ignored?
>> 
>> I am new to spatial statistics and now idea how to move with such. I only know that my data has spatial
>>  autocorrelation (which i hope to have checked correctly using morans I as above) and now need to account for this in my analysis. Some advice would be greatly appreciated by people who have used to account for SAC in their logistic models.  Is a logistic mixed models an option to consider?especially if your covariates are spatial in nature,…i read somewhere that if you cant account for SAC in glm then you can move to mixed models esp if your covariates are spatial which is expected to digest the SAC.
>> 
>> Help and advice would be greatly appreciated.
>> 
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