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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82 views

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 ...
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1answer
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 ...
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1answer
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, ...
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1answer
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. ...
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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 ...
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1answer
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 ...
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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, ...
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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 ...
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1answer
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 ...
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2answers
158 views

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

"This week, we examined the simplest theory of spatial criminology – that crimes are distributed at random. When spatial criminologists want to test observed data for randomness, they test that data’s ...
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1answer
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 ...
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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 ...
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1answer
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 ...
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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 ...
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1answer
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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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1answer
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 ...
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1answer
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 ...
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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 ...
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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 ...
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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 ...
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1answer
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 $s$ ...
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1answer
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 $\zeta$ ...
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2answers
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 "...
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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 I´m examining ...
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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 ...
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1answer
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 ...
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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 ...
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1answer
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 ...
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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 ...
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157 views

Spatial Lag Model and Heteroscedasticity

I am using Spatial Lag Models with the form yi = ρWyi + βXi + εi, and am estimating these in R using spdep::lagsarlm. However, Breusch-Pagan-Tests using ...
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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 "...
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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 ...
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1answer
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 ...
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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 ...
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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 ...
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0answers
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 ...
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1answer
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 ...
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30 views

Comparing measures of spatial autocorrelation in residuals

1) In different regressions Say first regression is: $y = \beta_1 x_1 + \beta_2 x_2 + u $ And the second is : $y = \beta_1 x_1 + \beta_2 x_2 + \beta_3 x_3 + v $ Are Moran's I values on residuals $...
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30 views

How do I fit a Generalised Linear Mixed Model to 3D coordinate data, where the outcome is binary?

I'm trying to understand how I might fit a Generalised Linear Mixed Model (GLMM) to a data set comprising 3D coordinates, with a binary outcome. The basic set-up is as follows: Each subject has its ...
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122 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 ...
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66 views

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 ...
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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 ...
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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 ...
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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 ...
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1answer
166 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 ...

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