# 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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### Inhomogeneous K-function to indicate need for spatial dependence/interaction term in Poisson point process model

I am mapping and modelling a disease of sheep. I have approx 4200 point locations in my dataset, each of which represents the centroid of a given sheep farm. I have created a K-function difference ...
38 views

### Estimating population concentrations in spatially autocorrelated data

I'm stuck on which statistic to use with a spatial data set to resolve population concentrations in a large area, when I have only sampled a small area relative to that large area. Here's an example ...
70 views

### Does standard distance follow the 68-95-99.7 rule?

I'm wanting to do a simple standard distance demonstration for my students in R, but I've come across a conundrum. When I simulate the creation of 10,000 points in a spatial normal distribution, ...
525 views

### How to estimate the leafsize of the kd-tree?

The kd-tree implementation proposed by the scipy python libray asks for the value of the leafsize parameter that is to say the maximum number of points a node can hold. It is by default set to 10. ...
38 views

### Using Markov random field spatial weights to account for spatial autocorrelation

I am looking at the relationship between life expectancy and smoking rate within the London boroughs. I thus created a bayesx spatial regression model including a term which assigns spatial ...
73 views

### Spatio-temporal convolutional networks on irregular grids

I'm contemplating a project where I try to take a time series of maps of polygons (which have values) and predict the next map of polygon values. If it were a regular grid, it'd be a ...
35 views

### How can I find a representative point in 3D matrix (time,lon,lat)

I have temperature in a matrix of time, longitude and latitude. I need to find a way or criterion to find a point or location (lon *, lat *) that is representative of my entire area of interest (time, ...
176 views

### Unexpected behavior in inhomogeneous Cross K Function (Kcross.inhom) [closed]

I am currently analyzing a point pattern in R using the "spatstat" package. I am comparing two different areas, therefore I made two plots for each area (first two plot-left-area1; second ...
184 views

### Performing random forest on spatio-temporal rasters

We are trying to train a random forest model on land-use and meteorological variables to predict daily concentrations of air pollution at a 1km resolution. Our input data consists of 1km raster stacks ...
158 views

### Testing for randomness against Poisson distribution - what is the null hypothesis?

"This week, we examined the simplest theory of spatial criminology ā that crimes are distributed at random. When spatial criminologists want to test observed data for randomness, they test that dataās ...
195 views

### Point Pattern Analysis: Assumptions for Hopkins-Skellam Index

I am currently analyzing a point pattern in R using the "spatstat" package. My analyses are primarily exploratory, as I do not have any strong reason to suspect either clustering or regularity, though ...
74 views

### Spatial Analysis with Repeated Measures

I am doing an agricultural study in which I analyzed parameters of fruit and treated them with different conditions. The fruits were measured once a week for four weeks. Now, I would like to know if ...
131 views

### why does ignoring spatial autocorrelation lead to spurious significance

In spatial statistics one often hears the statements like the following: unaccounted for spatial autocorrelation may lead to spurious significance / understimated uncertainty / too narrow ...
86 views

### Gaussian random fields: matrix and convolution sampling

I should be able to generate a stationary GRF from white noise in two different ways: multiplying the white noise vector by the square root of a covariance matrix with appropriate kernel; taking the ...
52 views

### Standard population for SMR estimation

I have deaths by counties from 1980-2010 by age and sex. I want to calculate the SMR and then map the rates. My question is what standard population should I consider. If the SMR is Yi (# deaths ...
22 views

### Should a nugget ever shift the variogram away from zero at distance zero?

I had frequently seen the definition for a "rigorous" spatial isotropic semivariogram being defined as: $$\gamma(h) = K(0) - K(h)$$ Where $K$ is a positive definite covariance matrix. If the ...
39 views

### Spatial Poisson model correlation structure

I'll preface this by saying I'm VERY new to this spatial epidemiology world. I'm running a spatial poisson model and have set its correlation structure as exponential. However once I arrived at my ...
94 views

### Spatial regression: random and fixed effects [closed]

I'm working with spatial data (two rasters or matrix in the attached Figure), that is distributed in a 2D-space and each grid has a value. The two grids have the same number of cells. Variable "Y" is ...
193 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 ...
1k views

### Point process - intensity function vs probability density function

Suppose we have a point process in $\mathbb{R}$ with intensity $\lambda(x)$. Then, for a given compact set ${ S}$ we have $$\Lambda({ S})=\int_{\rm S} \lambda(x) \, dx,$$ where $\Lambda({ S})$ is ...
29 views

### How to get the density estimate for the whole region based on data from several locations?

I am collecting air pollutant data for every area in a region. The available data I can find only has the data from stations in a few areas. Is it possible to estimate the air pollutant density for ...
25 views

### Is the assumption of indepence only for the sampled values informing the regression, or should it also apply to the cells of a prediction grid?

I have 200 discrete, well-spaced plots with reasonably independent sampled values from which I've derived a regression equation. If I use it to predict values on a similarly sized fishnet grid, how ...
370 views

### Problems fitting a model to a variogram

I am having problems fitting a variogram model. I tried to change some parameters to estimate or fix them but I am still not achieving any improvement. I remove trend of the data and use logarithms ...
19 views

### How to combine two different errors

I have an estimated spatial distribution of gas concentration and its ground truth, and I have compared them on account of two errors: (1) the global error or the error in the concentration values in ...
19 views

### Plant density and spatial relationships

I have an experiment that investigates the affects of small mammal presence (present or absent) and fire (burned or unburned) in a replicated full factorial block design (4 plots--each treatment combo ...
20 views

### Display uncertainty on spatialy distributed proportions (visualisation)

This question is related to Distribution of estimator of multiple (spatially related) proportions. We consider here the /visualisation/ issue. Consider a spatial random process $Z(s)$, where $s$ ...
19 views

### Distribution of estimator of multiple (spatially related) proportions

Consider a spatial random process $Z(s)$, where $s$ denotes the spatial location. Our objective is to delineate the zone $\mathcal{Z}$ where the probability that $Z$ exceed a given threshold $\zeta$ ...
872 views

### Trajectory clustering - preprocessing and algorithms

Context Consider the following problem where we have two time dependent (yearly) measures: Fertility rate Life expectancy And a dimension: country. In other words we have over two hundred "...
89 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 IĀ“m examining ...
41 views

### Linear model from iterative process in R

I would like to test a relationship between to factors such as birds occurrence and temperature for instance, to test if temperature affects birds occurrence from a country (e.g. Germany). I have a ...
389 views

### Are kernel Density estimation and gaussian blur related?

I have a set of points in a 2d space representing location of animals. I am interested in a probability heatmap which give lower values for cells far from these locations. I have seen many ...
101 views

### Subsampling to account for spatial autocorrelation of observations

I'm wondering to what extent (if any) subsampling of observations can be used to account for spatial autocorrelation within data. Is taking a smaller sample (subsample) of observations (without ...
148 views

### How can I understand these variograms?

Using grf function from R package geoR, I simulated 6 replicates (each with 1000 samples) of a Gaussian random field on ...
34 views

### Is it common to decompose many time series in a business?

I am working in a industry. Most of the time I do statistical reports on sales. I'm new to time series analysis, so please be patient: the question might be obvious. I would like to monitor the sales ...
157 views

### Spatial Lag Model and Heteroscedasticity

I am using Spatial Lag Models with the form yi = ĻWyi + Ī²Xi + Īµi, and am estimating these in R using spdep::lagsarlm. However, Breusch-Pagan-Tests using ...
20 views

### Dau Genton test - in grandmothers terms

tl;dr Can you explain the Dau Genton test in terms a median grandmother could understand? Background: So I am looking for an "in.chull" for multivariate, concave hull, and I was going through "...
275 views

### Residuals' spatial autocorrelation in Boosted Regression Trees after correcting for it

I am running boosted regression trees (BRT) in R, with the package dismo and I have included a predictor (residual autocovariate) that, in theory, correct for spatial autocorrelation, following a ...
187 views

### How to measure the spatial dipresion of multiple clustered data

Context: My data are binary maps that represent the spatial distribution of events. Whenever an event occurs at a location, the pixel representing that location is assigned with the value 1. Below are ...
77 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 ...
68 views

### Can you use spatial regression models to analyse survey data with a binary outcome?

I have a survey of about 2700 respondents distributed across 35 municipalities in the Netherlands, and I am modelling a binary outcome (voting for a political party) as a function of detailed ...
49 views

### How to evaluate global and local effects in one model

I want to test the effect of elevation on the intensity of burrowing by gopher tortoises in flatwoods [a type of pine savanna characterized by both low (wet) and high (dry) areas]. However, in several ...
367 views

### Clustering spatial data based on location and values

I'm looking for a way, preferably in R, to create a cluster of point data (specifically, the centroids of UK postcodes), where each cluster comes as close as possible to containing a certain number of ...
30 views

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### test the significance of the marginal effects of a spatial probit model

I'm using the CRAN package spatialprobit to estimate a Spatial Probit. The function sarprobit calculates the marginal effects ...
47 views

### Match a path to a roadmap

I do not know if I'm in the right place but let us go. I got a relative path of an object. Which mean I know the distance and the direction between all the points of the path but do not know their GPS ...
177 views

### 2SLS (IV) with fractional outcome variable and spatially autocorrelated error terms

I face the challenge of estimating a 2SLS (IV) model with a fractional (ranging between 0 and 1) outcome variable and spatially autocorrelated error terms (the data is spatially explicit, i.e. for ...
108 views

### Automatically find breakpoints in vector

I am currently working with vectors of hight-measurments i extracted for multiple spatial polygons from a raster.Those are stored as vectors of doubles. As the polygons are not perfectly fitting the ...