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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4answers
15k views

Why does including latitude and longitude in a GAM account for spatial autocorrelation?

I have produced generalized additive models for deforestation. To account for spatial-autocorrelation, I have included latitude and longitude as a smoothed, interaction term (i.e. s(x,y)). I've based ...
31
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7answers
4k views

Is there an accepted definition for the median of a sample on the plane, or higher ordered spaces?

If so, what? If not, why not? For a sample on the line, the median minimizes the total absolute deviation. It would seem natural to extend the definition to R2, etc., but I've never seen it. But then,...
9
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3answers
687 views

How can I simulate census microdata for small areas using a 1% microdata sample at a large scale and aggregate statistics at the small area scale?

I would like to perform an individual-level multivariate analysis at small levels of geographic aggregation (Australian census collection districts). Clearly, the census isn't available at these ...
17
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5answers
13k views

2D analog of standard deviation?

Consider the following experiment: a group of people is given a list of cities, and asked to mark the corresponding locations on an (otherwise unlabeled) map of the world. For each city, you will get ...
2
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2answers
362 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 "...
5
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1answer
2k views

Volume of the 95% confidence ellipsoid

I'm dealing with 3D data that are the trajectory of a point over time. I would like to have an indication of how much it is "spread" in space and I thought about using the volume of the 95% confidence ...
10
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1answer
4k views

How Does Kriging Interpolation work?

I am working on a problem in which I need to use Kriging to predict the value of some variables based on some surrounding variables. I want to implement its code by myself. So, I've went through too ...
11
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2answers
5k views

Clustering spatial data in R

I have a set of sea surface temperature (SST) monthly data and I want to apply some cluster methodology to detect regions with similar SST patterns. I have a set of monthly data files running from ...
13
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2answers
1k views

Model for population density estimation

A database of (population, area, shape) can be used to map population density by assigning a constant value of population/area to each shape (which is a polygon such as a Census block, tract, county, ...
11
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2answers
895 views

Why is Moran's I not equal to “-1” in perfectly dispersed point pattern

Is wikipedia wrong...or I don't understand it? Wikipedia: The white and black squares ("chess pattern") are perfectly dispersed so Moran's I would be −1. If the white squares were stacked to one ...
5
votes
2answers
833 views

Assessing error of a spatial interpolation algorithm

I have a set of 3D points. The points have three components $x$, $y$, $z$. You can think of these points as the surveyor points that one collects from measuring a terrain for GIS purposes. I have a ...
4
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1answer
288 views

Smoothness of a surface

I am currently working on a model which takes two parameters and produces a measurement statistic. Think of it as Z = f(X,Y). Z is a matrix of my statistics and I am creating a surface plot of it in ...
9
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2answers
231 views

Regression on the unit disk starting from “uniformly spaced” samples

I need to solve a complicated regression problem over the unit disk. The original question attracted some interesting comments, but no answers unfortunately. In meantime, I learned something more on ...
6
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2answers
6k views

What is the interpretation of eps parameter in DBSCAN clustering?

I want to cluster lat-long data such that all clusters formed will have radius<=1000 meters Questions What is the actual meaning of eps parameter? Please given an example. Will setting eps=1000 ...
6
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2answers
240 views

Are there models for “censored” spatial point processes?

This is a problem I'm encountering in the context of analyzing a data set comprised of all crime locations in a city over a fixed time interval, although it could potentially arise in other types of ...
5
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1answer
2k views

Combining multiple similarity measures in hyperspectral images?

I have a hyperspectral image where the pixels are 21 channels. So each pixel $\in \mathbb{R}^{21}$. I want to perform clustering on the pixels with similarity defined by two different measures, one ...
6
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2answers
1k views

Why is Moran's $I$ coming out greater than $1$?

Moran's $I$ statistic is defined to be the quantity $$ \frac{N}{\sum_{i,j} w_{ij}}\frac{\sum_{i,j}w_{ij}(X_i-\bar{X})(X_j-\bar{X})}{\sum_i(X_i-\bar{X})^2} $$ where $w_{ij}$ is some matrix of spatial ...
2
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0answers
132 views

How to bootstrap a (spatial) lag operator?

In relation with this question of mine, which goes beyond what I am asking now. Say one has the following data generating process (DGP) (known as the SAR ou spatial lag model in the literature): $\...
1
vote
1answer
339 views

need derivation of join-count variance (spatial autocorrelation stat), know where it is?

I am using interlibrary loan to get Cliff and Ord's book Spatial Processes, but the semester just ended and it is slow now. On page 18ish of this book, Cliff and Ord show how the variance for the ...
1
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0answers
90 views

How to compute the likelihood's Jacobian of a bootstrapped spatial autoregressive specification?

Say one has the following data generating process (DGP) (known as the SAR ou spatial lag model in the literature): $\boldsymbol{y} = \rho \boldsymbol{W}y + \boldsymbol{X}\boldsymbol{\beta} + \...
35
votes
1answer
9k views

Why is Mantel's test preferred over Moran's I?

Mantel's test is widely used in biological studies to examine the correlation between the spatial distribution of animals (position in space) with, for example, their genetic relatedness, rate of ...
18
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2answers
3k views

What is the rationale of the Matérn covariance function?

The Matérn covariance function is commonly used as kernel function in Gaussian Process. It is defined like this $$ {\displaystyle C_{\nu }(d)=\sigma ^{2}{\frac {2^{1-\nu }}{\Gamma (\nu )}}{\Bigg (}{\...
16
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2answers
5k views

Showing spatial and temporal correlation on maps

I have data for a network of weather stations across the United States. This gives me a data frame that contains date, latitude, longitude, and some measured value. Assume that data are collected once ...
8
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1answer
768 views

Suggested books on spatial statistics

What are some of the best books for studying i) variability of univariate and multivariate variables (real, count data) across a spatial domain. ii) sampling a univariate or multivariate variable ...
23
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2answers
11k views

Spatial statistics models: CAR vs SAR

When would one prefer to use a Conditional Autoregressive model over a Simultaneous Autoregressive model when modelling autocorrelated geo-referenced aerial data?
9
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3answers
7k views

What is the difference between spatial dependence and spatial heterogeneity?

What is the difference between spatial dependence and spatial heterogeneity? My question is motivated by readings in model specification problems in spatial econometrics, in particular Anselin (2010)....
14
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2answers
3k views

Question about logistic regression

I want to run a binary logistic regression to model the presence or absence of conflict (dependent variable) from a set of independent variables over a 10 year period (1997-2006), with each year ...
9
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0answers
4k views

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 <...
17
votes
4answers
15k views

Entropy of an image

What is the most information/physics-theoretical correct way to compute the entropy of an image? I don't care about computational efficiency right now - I want it theoretically as correct as possible. ...
23
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2answers
846 views

What statistical model or algorithm could be used to solve the John Snow Cholera problem?

I'm interested in learning how to develop a geographic approximation of some kind of epicenter based on the data from the John Snow Cholera outbreak. What statistical modeling could be used to solve ...
12
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1answer
5k views

Linear Regression and Spatial-Autocorrelation

I want to predict Tree Heights in a certain area using some variables obtained through remote sensing. Like approximate Biomass, etc. I want to first use a linear regression (I know it's not the best ...
11
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1answer
1k views

What is the proper way of calculating the kernel density estimate from geographical coordinates?

I have to calculate the 2d kernel density estimate (kde) from a list of latitude and longitude coordinates. But one degree in latitude is not the same distance as one degree in longitude, this means ...
10
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3answers
4k views

Measure the uniformity of distribution of points in a 2D square

I have a 2D square, and I have a set of points inside it, say, 1000 points. I need a way to see if the distribution of points inside the square are spread out (or more or less uniformly distributed) ...
3
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1answer
4k views

Spatial autocorrelation — GLM, autocovariate, MEM (Moran's eigenvector mapping)

I am currently working on two marine species distribution modelling and also on their overlap distribution. For this I use a binomial logistic regression model (GLM) with response being, respectively, ...
10
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2answers
3k views

spatial autocorrelation for time series data

I have a 20-yr dataset of an annual count of species abundance for a set of polygons (~200 irregularly shaped, continuous polygons). I have been using regression analysis to infer trends (change in ...
9
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2answers
6k views

Density-based spatial clustering of applications with noise (DBSCAN) clustering in R

this question started as "Clustering spatial data in R" and now has moved to DBSCAN question. As the responses to the first question suggested I searched information about DBSCAN and read some docs ...
9
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1answer
681 views

Intrinsic spatial stationarity: doesn't it only apply for small lags?

From the definition of Intrinsic stationarity: $E[Z(x)-Z(x-h)] = 0$ This assumption is used for example in ordinary kriging, instead of assuming a constant mean over the entire space, we assume the ...
6
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1answer
137 views

How, in practice, are spatial covariances determined?

How, in practice, are spatial covariances determined? If one has a single realisation of some observed field, how can the spatial covariance ever be determined? Unless one has access to the many other ...
3
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1answer
1k views

Discrepancy between lagged lm() and lagsarlm()

If we have a spatial autoregressive process, we can estimate a model to control for the autoregression with a spatial lag, $$y=\rho W y + X\beta + \epsilon$$ Where $\rho$ is the strength of the ...
3
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4answers
3k views

Software for making semi variograms and analyses?

Our lab used to have a program called GS+ that let us make semi variograms on our data and analyse them. Unfortunately, the licence has expired. Is there another piece of software that lets you do ...
2
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1answer
2k views

Ripley's K Function and L Function for Point Patterns

The following is a spatial point pattern: and these are the corresponding Ripley's K function and L function for this data: How are these functions interpreted?
6
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1answer
1k views

Problems estimating anisotropy parameters for a spatial model

I am looking for someone with experience in how to handle the anisotropy-parameters in the likfit() function which is part of the GeoR package in R. I am using <...
5
votes
0answers
271 views

Can you use a spline function of the spatial coordinates to control for spatial autocorrelation? [duplicate]

Possible Duplicate: Why does including latitude and longitude in a GAM account for spatial autocorrelation? I am interested in the effect of a predictor vector $X_i$ on a binary outcome $Y_i$, ...
4
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2answers
1k views

Using Anselin Local Moran's I Values in Regression

I am doing a multiple linear regression of factors related to poverty and would like to include some spatial-statistical data. I have come up with Anselin Local Moran's I values (cluster/outlier) data ...
4
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1answer
2k views

Valid method to analyze spatial correlations in images?

Is there a reasonable way to quantify the amount of local correlations in an image? For example, I want to justify the correlations between a neighbourhood of pixels is much higher than the ...
4
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1answer
1k views

How to compare two spatial points patterns in R?

I have two spatial points data sets (relocations of animal A and distribution of plant B). How can I investigate if animal A is more likely to be where plant B is present? With the animal ...
0
votes
1answer
656 views

Spatial autocorrelation (SAC) while analysing survey data

I am confused about some aspects of spatial autocorrelation usind survey data (survey which is repeated every year). I have data from 1991 to 2012 with sampling region pretty consistent every year. I ...
5
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1answer
862 views

beta-regression accounting for residual spatial auto-correlation in R

I have data on the interval (0,1), that I model using beta regression with the betareg package in R. This works well. However, I ...
5
votes
4answers
1k views

Analyze and generate “clumpy” distributions?

Are there standard ways of analyzing and generating "clumpy" distributions? analyze: how clumpy is a given point cloud (in 1d, 2d, nd), what are its clumpy coefficients? generate or synthesize a ...
5
votes
1answer
424 views

Hypothesis test on data with confounding spatial clustering

This is a bit of an elaboration on a question I posted earlier, since I feel like my approach to the problem as a whole is probably quite flawed. Suppose I have a set of treatment and control cells, ...