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Questions tagged [variogram]

A plot or function used in spatial statistics (or in time series analysis) to describe the degree of spatial (or time) dependence of a stochastic process.

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Checking for temporal autocorrelation in experience sampling data - how to interpret the variogram?

I have day-level data from about 100 participants from 11 days (EDIT. a subset of participants responded for 12 days, which is why there's a distance of 11 in the variogram table). I'm interested in ...
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Creating a Variogram-like plot with distances

I have a dataset of points in space, sampled at a specified time. Now i want to obtain a 'spatial correlation plot, only between points close in time'. What i did is creating a dataframe of pairs of ...
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Geostatistics: Covariance vs Semivariance

I am confused by the following page in Geostatistics for Environmental Scientists, Webster & Oliver: My understanding Given locations specified by a vector $\mathbf{x}$, we assume an underlying ...
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How do you express the variogram $\gamma(h)$ in terms of correlation taking into account also the nugget

let's say that I have a spatial random field $z(\textbf{x})$ with $\textbf{x}$ the spatial coordinate. I can define the semi-variogram as: $\gamma(h)=\frac{1}{2}E[(z(\textbf{x+h})-z(\textbf{x}))^2]$ ...
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Declustering spatial data and kriging

I am doing a simple project on a mining dataset and came across some problems: Should I use the declustered values to model the variogram? Do I apply ordinary kriging to the original or to the ...
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Decreasing trend in semivariogram of nlme model residuals?

I am new to spatial statistics and am trying to fit some spatial models using the nlme package in R. I fit three different models, using the same set of predictors ...
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What am I not understanding about semivariogram and Normal Score Transformation?

I have generated this two dimensional random field: This is done following this page. In particular, I have selected t=23 as dataframe and I have changed some parameters. As you can noticed, I have ...
diedro's user avatar
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Generate a syntetic log-normal two dimensional random field

I would like to test some functions that I wrote related to the kriging applied to rain data. In order to do that, I would like to generate a synthetic log-normal 2D random field. The idea is to ...
diedro's user avatar
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Empirical bayes estimation of variograms for multiple variables

I am looking to estimate variograms, or spatial correlation matrices on all columns of a data matrix $\mathbf{X}_{n\times p}$ with $p>n$. The matrix of spatial coordinates $\mathbf{Y}_{n\times 2}$ ...
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Residual autocorrelation in non-stationary (gaulss) model

I'm fitting a non-stationary model using mgcv (family: gaulss()) where the data have been collected at different points in space....
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How do you express the variogram $\gamma(u)$ in terms of correlation for a stationary process?

The Analysis of Longitudinal Data textbook by Diggle et al. (2002) mentioned twice (p48 f. and then on p82) that given the following definition of the variogram, \begin{equation} \gamma(u) = \frac{1}...
ning's user avatar
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No convergence when fitting theoretical semivariogram to empirical?

I'm kind of new to working with semivariograms. But I just wanted to fit a semivariogramm to my data and when fitting the theoretical variogram to my empirical it tells me that: ...
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Interpreting a Distance & Time 3D Variogram for Variogram modeling

I am trying to understand some concepts of variograms. I have made several variogram models in R and am trying to understand exactly what they mean. My data is ...
Coldchain9's user avatar
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Variogram fit in R not converging

I have taken a shapefile from Open NYC Data and performed the following method. My end goal is to predict Taxi trip_duration at various points across the city of ...
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188 views

Variogram of categorial data?

I have a thematic map as raster data with classes assigned as numbers: 1,2,3,4. These are categorial classes and have no linear meaning. I am interested if there is spatial autocorrelation in this ...
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Semivariance: Are these two formulas equivalent?

Mean Semivariance optimization defines semivariance, variance only below the benchmark/required rate of return, as: $$\frac 1 T \sum_{t=1}^T [\min(R_{it}-B,0)]^2$$ where $B$ is the benchmark rate, $...
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Why do you need a variogram for Kriging? goldingn/gpe package?

I am using golingn/gpe (github) package, and it does not provide a variogram and instead look at co-variances. Is it possible to do kriging without providing variograms?
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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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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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Cokriging, zero distance semivariance [gstat]

Trying cokriging with simulated data, I faced a problem that did not seem one in the demo(cokriging) with the meuse dataset: I can't use ...
Yollanda Beetroot's user avatar
1 vote
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227 views

How to interpret semivariogram parameters from two different raster images?

I know the definitions of the components of a semivariogram. However, I would want to know how they could be interpreted when applied to actual scenarios. For instance, I have two EVI (enhanced ...
GISnew's user avatar
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1 answer
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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 ...
Zheyuan Li's user avatar
1 vote
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257 views

Mixed model with serial correlation and random slope?

I'm making a mixed model for some longitudinal data, where the response is measured fro multiple individuals over time. I have made a model with random intercept, random slope and gaussian serial ...
J. Jensen's user avatar
7 votes
2 answers
10k views

What is the nugget effect?

I don't understand exactly what is meant by the term "nugget effect" in geostatistics. When looking at empirical variograms plotting the variogram $\gamma(h)$ vs. the lag $h$, the nugget is defined as ...
MachineEpsilon's user avatar
2 votes
2 answers
2k views

Temporal Variogram

Can we compute temporal variograms just like spatial variograms? I know about spatio-temporal variograms but I am more interested in doing a comparison of separate spatial and temporal variograms and ...
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330 views

How do you interpret this variogram?

Description: 8000 spatial data points spanned over an entire state 200 bins are used My question: Is the variogram telling something about the nature of the data? Why is it fluctuating? Should I do ...
Ali Jamali's user avatar
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812 views

Spherical vs. Exponential Kriging Covariance Functions

A statistical epidemiologist colleague of mine told me that in comparing spherical vs exponential kriging covariance functions, only the latter (i.e., exponential) function is generally a valid model. ...
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289 views

How SHOULD a variogram plot look like?

Say you fit a model m. You then calculate the variogram. In R, this can e.g. be done by using plot.Variogram using the nlme package on an lme object. Say the plot indicates that yes, there is some ...
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Explain Like I'm Five version for Variograms in R's gstat package

Long story short, I asked a question on StackOverflow about Variograms in the gstat package in R. The person who answered gave me some tips on creating the variogram using the package. My dataset is ...
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warning when fitting variogram - gstat

I'm trying to build a variogram model of the semi variance in Zn concentration with distance using gstat package in R. First I plot the variogram based on my data (it clearly seems to mean that the ...
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Variogram to constrain kernel density bandwidth

I have linear structures transformed into points and spatially distributed like this: I want to perform a kernel density so that zones with lots of structures present high density. The problem is ...
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321 views

How much difference in the Akaike Information Criterion is reasonable between a Spatial and a Non spatial Model

I am doing supervised land value modelling (900 observations) and I am comparing two approaches to do a variable selection (51 variables). I am using R. The first one is a backward step-wise ...
Andrés Morales's user avatar
4 votes
1 answer
688 views

Why is positive definiteness necessary for kriging?

I understand from wikipedia that a variogram model must be positive definite to be used for kriging: Note that the experimental variogram is an empirical ...
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Is there a way to find optimal sensor node locations in a domain when all data is known?

I have an x-y domain where I know the snow depth everywhere. (i.e. the granularity of the values is such that I can assume I know it everywhere). I want to use this information to inform where to ...
makansij's user avatar
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I am not sure if my data are spatially autocorrelated or not.

I have been trying to figure out if my data are spatially autocorrelated by generating semivariogram of the residuals. I do not get the shape similar to any variogram (spherical, exponential or ...
PraStha's user avatar
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157 views

What is the computational complexity of the empirical variogram?

If we use the method of moments estimator: $2\hat{\gamma}(h) = \frac{1}{| N(h) |} \sum_{N(h)} (Z(s_i) - Z(s_j))^2$ What is the computational complexity? My initial assumption was that it would be $...
Andrew Haynes's user avatar
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166 views

Is there an approach to combining variograms?

If we compute two seperate variograms for the same type of measurement, but the areas which they cover overlap, is there a logical way (or does it even make sense) to combine the two variograms? ...
Andrew Haynes's user avatar
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310 views

Why is my semivariance so high?

I am using variograms checking for spatial autocorrelation in a resiudal pattern produced by a GLMM-NB. In theory, the semivariance should be bounded between 0 and 1 (that´s what I think at least as I ...
Jens's user avatar
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2 votes
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481 views

What does it mean that a variogram keeps increasing with distance?

I am modeling my 3D dataset with a Gaussian Process with square-exponential covariance. To test whether this is a good model, I subtract the mean from the observed data and then calculate the ...
cgreen's user avatar
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338 views

Kriging: fit.method and dX argument in variogram

I would like to krige residuals (from multiple linear regression) of yearly precipitation totals from a 50 years time series. Every year has been regressed individually. The residuals will be added to ...
noe's user avatar
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2 votes
1 answer
2k views

Interpreting Spatio-Temporal Variograms

I've got spatio-temporal disease data at the county/annual level for 2000-2014. I'm analyzing it to try to pull out temporal variations in disease incidence and was told that I should generate a ...
Ross Wardrup's user avatar
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0 answers
253 views

Variogram with custom distance matrix

I work in marine ecology and as such all of my distance matrices are constructed using the shortest possible marine route - i.e. avoiding any land. Here is a plot of my "marine distances" against "as ...
Nhold's user avatar
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3 votes
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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’...
Andy Lister's user avatar
3 votes
1 answer
563 views

Gstat: Modelled semivariogram values not matching plotted model using the variogramLine function

I am trying to extract the semivariance values associated with a given semivariogram model developed in gstat, the end goal being to compare modelled semivariance with observed semivariance at defined ...
ChrisWills's user avatar
2 votes
1 answer
176 views

Gaussian Mixture Model: bandwidth parameter versus variogram fitting?

I'm estimating a stationary, spatially random variable over a 2-dimensional domain. I have ground-truth measurements in several locations, over time. I need some way of spatially-interpolating ...
makansij's user avatar
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0 votes
1 answer
1k views

Simple Kriging with linear semivariogram

While studying how to develop a simple kriging model with a linear semivariogram, the various tutorials point towards creating a covariogram using $\sigma(h) = \sigma(0) - \gamma(h)$, but the value of ...
Vishal Anand's user avatar
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0 answers
196 views

Non-parametric variogram estimators

I'm working with overdispersed, count spatial data. The goal is to look specifically at spatial dependence patterns. I'm trying to fit variogram models to empirical variograms, however the only ...
smccain's user avatar
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1 vote
1 answer
421 views

Lag lengths are larger than my domain in gstat in R? variogram object

My problem is that the my resulting variograms are of a larger lag length than my domain. I have the following code to compute lags in the vertical direction: ...
makansij's user avatar
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4 votes
1 answer
992 views

Fitting a variogram model with the pairwise distance matrix supplied

I'm trying to fit a variogram to my data, however the spatial points are confined by an irregular polygon. So I'd like to supply a variogram model function with the distance matrix of the points. I'...
smccain's user avatar
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Measurament error from semivariogram

I am looking at a model to determine the measurement error for a set of measurements of a spatially correlated phenomenon (sea surface temperature measurements) using a semivariogram technique. For ...
user3706794's user avatar