# Questions tagged [spatial]

The field of study concerning statistical methods that use space and spatial relationships (such as distance, area, volume, length, height, orientation, centrality and/or other spatial characteristics of data) directly in their mathematical computations.

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### Specify correlation structure for different groups in mixed-effects model (lme4/nlme)

I am trying to account for spatial autocorrelation in a linear mixed-effects model in R with measurements repeated in time. BodyMass has been collected once per <...
134 views

### Test whether cross-sectional dependence in panel data follows known (network/spatial) structure

I want to test whether cross-sectional dependence in one specific variable (y) in panel data format follows a known structure (W) (e.g. network, spatial dependence), after controlling for individual ...
1k views

### How to deal with underdispersion with binomial data

I'm working with a pretty large dataset (n = 4,500) where 10% of my points (pixels in a GIS landscape) are 1s and the rest are 0s. The full model for my data looks something like this: ...
692 views

### Endogeneity in spatially lagged regression model

The standard convention in Spatial Statistic is that the spatial lag term in a regression model will be biased due to simultaneity. Looking at the following model, it would be difficult to argue with ...
91 views

### Territories from observations

I have a number of animal observations, and want to deduce the number of territories (i.e. the number of individual animals) from this. More formally, the problem can be stated as follows: Each ...
301 views

### How can I do a t-test on 2D data?

How can I do a t-test on 2D data with latitude and longitude attributes? I have 2 clusters of similar coordinates but in different time, I want to do a t-test to see if they are statistically ...
112 views

### Correlation in Distances of Points Within a Circle from Centre and One Other Point

Background The travel cost method, a method used in economics to estimate the value of parks and other recreational sites, requires (as one step) estimating the relation between $VR_i$, the visit ...
75 views

### Arbitrary spatial autocorrelation

A spatial autoregressive model includes a spatial lag of the dependent variable. $$y = \rho W y + x\beta$$ Where $W$ describes the spatial relationship between elements of the model. I have heard (...
270 views

### How to impose spatial continuity constraint onto clustering?

Statistics version: I have a few measurements of a function that takes three inputs and produces a few 2D fields of outputs: $f(a,b,c;x,y)$, with $f$ being a vector of several quantities. I would like ...
209 views

### How to do multiple imputation for spatial models?

I'm trying to estimate various spatial models such as spatial autoregressive regression (SAR), Spatial Durbin Model (SDM), and Spatial Error Model (SEM) but have missing data throughout my variables. ...
74 views

### What is the distribution of edge lengths for a Euclidean minimal spanning tree?

Suppose that you have a Poisson point process in $\mathbb{R}^d$ with rate (density) parameter $\rho$; I particularly care about $d=2$ if there is a solution in this special case. Given a finite ...
1k views

### CAR spatial models in JAGS

WinBUGS comes with the GeoBUGS add-on, which contains a number of predefined model structures that are suitable for modelling spatial data structures e.g. geostatical structures (spatial.exp), ...
694 views

### Spatial autocorrelation of non-homogeneous point data in irregularly shaped sample plots

Let's assume we registered the position of all individuals of different plant species within 3 irregularly shaped sample plots that are very close the each other. As an example, I put 2 pictures with ...
120 views

### Help with designing the analysis of a radio telemetry study

I was wondering if there are any spatial ecologists out there who can provide some insight on the trouble I'm having with my Masters research. I am looking at the association a bat species to high ...
2k views

### Examples of spatial generalized linear models

I've been reading some materials on Spatial data analysis, and I've a good background in GLMs. Right now I'm looking to find an example in spatial generalized linear models, but so far I've not found ...
69 views

### Optimal block size for spatial bootstrapping

Take a regression model: $$y_s = X_s\beta + \epsilon$$ Where $E[\epsilon|X] = 0$, but $cor(\epsilon_s, \epsilon_{near}) > cor(\epsilon_s, \epsilon_{far})> 0$. In other words, $X$ is ...
437 views

### What is the difference between Kamb and 1% area contours?

I have been doing a bunch of spherical statistics using Stereonet and there is a function for producing contour plots of data density. One of the options in this function is a choice between Kamb ...
36 views

### Algorithm that preserves the order of the predicted variable

Hi all, I need some advice on possible algorithms that I can apply to the following problem (if possible with pointers to implementations of these algorithms). The dataset: I have some dataset ...
51 views

### How to measure the asymmetry of data distribution in a convex?

I have some 2d points data and I generated a convex hull mesh. Looking by eye, it seems that the points are not uniformly distributed inside the convex. I wonder what is the best way to characterize ...
169 views

### Implementing a hierarchical bayesian graphical model in R

The shorter version: 1. Bayesian graphical models are new to me. 2. I want to use R to model spatial variation in county level crime using a BGN. I have been working with bnlearn, and would ideally ...
907 views

### Spatial Autoregressive Poisson model in R

I am estimating a gravity model of migration on cross-sectional data. The Moran I statistic indicates a positive and significant spatial autocorrelation in the residuals of the non-spatial model, and ...
599 views

### Difference between spatially autocorrelated logit methods

I am seeking advice on different methods to account for spatial autocorrelation in logit models. I've seen a lot of different models attempt to address all of the issues with spatial logit models (...
976 views

### How can I evaluate spatial autocorrelation in a binomial GLMM?

Following Dormann et al 2007 Ecography, I have employed a GLMM approach in R to account for spatial autocorrelation in a binomial regression model (logistic regression) that does not have random terms....
47 views

### Is it necessary to sample a raster for spatial regression?

I'm looking to model land cover change using a variety of environmental predictors (e.g. elevation, rainfall, etc.) stored as raster layers. In most similar studies I've found in the literature the ...
70 views

### Which groups of results is the closest to a central point?

I'm building an application where a specific location is chosen, multiple services are polled to return results for that specific location and shown on a map. I have the results from the different ...
2k views

### How to calculate spatial correlation between two variables?

I have a dataset of point coordinates of individuals and different variables of these individuals. I want to calculate if the spatial distribution of a certain variable is correlated to the spatial ...
196 views

### Estimating model error in $k$-nearest neighbours with strongly spatially autocorrelated training data

In the palaeoclimate world, palaeoecologists have used spatial training sets of say sea-surface temperture (SST) and related this to micro-organisms living at the locations where SST was measured. A ...
173 views

### cokriging and generalised linear spatial models

The answer to this question gave me an interesting idea. The part that interested me was a brief description of kriging concluded by The way, kriging as usually practiced is not quite the same as ...
273 views

### Spatial interpolation of vectors in vector fields

Statistical modeling is new to me and I would appreciate some thoughts on my project. I am trying to model the spatial (and possibly temporal as well) relationships within vectors in vector fields. ...
130 views

### What is the posterior kernel lengthscale of a Gaussian process?

If I have access to multiple samples from a Gaussian process with known covariance kernel but unknown parameters (i.e. unknown lengthscale), it is straightforward to estimate the lengthscale using ...
47 views

### Spatial regression with overlapping areas

Is it statistically correct to calculate a regression with overlapping areas? I have market areas as the spatial unit with different sociodemographic and (macro)economic variables and I´m examining ...
48 views

### Find unbiased estimators for $\lambda$ and $\lambda^2$.

For the spatial homogeneous Poisson process, find unbiased estimators for $\lambda$ and $\lambda^2$. Attempt: Since the homogeneous Poisson process is over an area, how i would i go about ...
90 views

### Sampling a test set from global spatial data

The basis of testing the accuracy of any machine learning algorithm is to test the trained algorithm on data that it has never seen before. The usual approach to sample the test set is to just ...
366 views

### How to specify a model with spatial correlation AND crossed random intercepts in R (nlme)

I want to model repeated measurements (let's say yearly) from multiple sites. Let's say after modeling these data with random intercepts for site and year we find there remains spatial correlation in ...
200 views

### Whats the deal with Spatial Durbin Models and non-spattial interactions?

I have really been curious about this, but I have been searching around for studies which utilize Spatial Durbin models and I have yet to find any one model that has incorporated the use of ...
26 views

### Implement an average index of spatial proximity for different groups

I have a longitudinal dataset of (c.a.) 100 observations. Each observation is assigned to a point in space. In each period, each observation is assigned to one out of x groups (i.e. no multiple ...
32 views

### How does the size of my sampling grid affect my required sample size

I would like to know how sample size estimation is affected when the categories are artificial rather than naturally occurring and clearly discrete. In my scenario I'm using a grid of a certain size ...
869 views

### Performing spatial logistic regression in R

I am trying to perform a logistic regression with the following code Y ~ x1+x2+x3,data=data, family=binomial(link="logit"). However on inspection of both the ...
199 views

### Checking spatial autocorrelation by plotting residuals?

For my analysis in biology, I want to study the effects of several factors (climate, cultivated area...) on insect dynamics and phenology. For that, I have data of insect captures from several traps ...
81 views

### Likelihood function for spatial Poisson

The dependent variable in our data is the integer number of trips made in a time period. We can regress on socioeconomic attributes of the individual $X$. The most logical model for this is a Poisson ...
30 views

### Critical scale of variation of tree biomass using variography

I have a combination of a philosophical and a technical question. I am interested in an application where I am trying to find a critical scale of autocorrelation of tree biomass on the landscape. Let’...
719 views

### Gaussian Distribution for Latitude/Longitude Coordinates

I have a bunch of latitude/longitude coordinates and if I plot it on a map, it seems to follow a bivariate distribution. I would like to estimate the distribution of points using a bivariate ...
107 views

### Compare Procrustes values

I have two sets of spatial data which underwent a transformation. I'd like to compare the effect of the transformation on two sets of data to test the hypothesis that the transformation had a larger ...
362 views

### What is the theory behind using eigenvectors for spatial filtering

As a programmer I have used the spdep package successfully for spatial filtering. But would appreciate it if someone could offer a description (preferably with supporting references) of how this ...
301 views

### how to bootstrap data on irregular grid?

I have irregular gridded data and I wish to resample from this data in such a way that the spatial correlation in the data is preserved. I will assume that grids that are within 300Kms of one another ...
349 views

### Universal kriging: which variogram to use?

I am working with the build in dataset meuse, which has 155 measurements of Zinc and the distance to the river "Meuse".(http://rspatial.r-forge.r-project.org/gallery/). Now I am trying to imitate ...
334 views

### Statistical methods to compare spatial maps

I would like to compare 4 radon flux maps (Bq m-2 s-1) generated using different methods. All of the maps use same projection and have same resolution. I am having trouble finding statistical method(s)...
51 views

### Statistical test for spatial difference of incidents

I have an area divided into grids. I'm looking for a method to determine statistically, if the occurence of criminal incidents for two time periods is significant equal. I have two datasets with ...
I am using R's package spatstat to study the locational pattern of conflict events in Africa (around 8.000 points) using point pattern analysis techniques. I was able to obtain the plot of $g(r)$, ...