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GS+ Other Autocorrelation Measures

GS+ Madograms
Madograms are similar to traditional variograms except that the absolute difference between values at different sample locations is used rather than the square of the difference as for traditional semivariance. Different anisotropic directions appear on separate tabs. Parameters for calculating madograms are set in the Autocorrelation Window.

When the program is running, placing the mouse cursor over a madogram point will produce a box showing the number of pairs in that lag class interval, and clicking on the point will produce a Variance Cloud or h-Scattergram graph of all pairs in that interval.

Other measures of autocorrelation provided by GS+ include variograms, correlograms, rodograms, covariograms, drift, Moran’s I, fractal dimension, and standardized, general relative, and pairwise relative variograms.

GS+ Rodograms
Rodograms are similar to traditional variograms except that the square root of the difference between values at different sample locations is used rather than the square of the difference as for traditional semivariance. Different anisotropic directions appear on separate tabs. Parameters for calculating rodograms are set in the Autocorrelation Window.

When the program is running, placing the mouse cursor over a rodogram point will produce a box showing the number of pairs in that lag class interval, and clicking on the point will produce a Variance Cloud or h-Scattergram graph of all pairs in that interval.

Other measures of autocorrelation provided by GS+ include variograms, correlograms, madograms, covariograms, drift, Moran’s I, fractal dimension, and standardized, general relative, and pairwise relative variograms.

GS+ Drift
Drift is calculated as the difference between values at different sample locations within a particular lag class interval (separation distance class). Different anisotropic directions appear on separate tabs. Parameters for calculating drift are set in the Autocorrelation Window.

When the program is running, placing the mouse cursor over a graphed point will produce a box showing the number of pairs in that lag class interval, and clicking on the point will produce a Variance Cloud or h-Scattergram graph of all pairs in that interval.

Other measures of autocorrelation provided by GS+ include variograms, correlograms, madograms, rodograms, covariograms, Moran’s I, fractal dimension, and standardized, general relative, and pairwise relative variograms.

GS+ Correlograms
Correlograms are presented in the Correlogram window. Different anisotropic directions appear on separate tabs. Parameters for calculating correlograms are set in the Autocorrelation Window.

When the program is running, placing the mouse cursor over a correlogram point will produce a box showing the number of pairs in that lag class interval, and clicking on the point will produce a Variance Cloud or h-Scattergram graph of all pairs in that interval.

Other measures of autocorrelation provided by GS+ include variograms, madograms, rodograms, covariograms, drift, Moran’s I, fractal dimension, and standardized, general relative, and pairwise relative variograms.

GS+ Covariograms
Covariograms are presented in the Covariance window. Different anisotropic directions appear on separate tabs. Parameters for calculating covariograms are set in the Autocorrelation Window.

When the program is running, placing the mouse cursor over a covariogram point will produce a box showing the number of pairs in that lag class interval, and clicking on the point will produce a Variance Cloud or h-Scattergram graph of all pairs in that interval.

Other measures of autocorrelation provided by GS+ include variograms, correlograms, madograms, rodograms, drift, Moran’s I, fractal dimension, and standardized, general relative, and pairwise relative variograms.

GS+ Moran’s I Correlograms
The Moran’s I statistic is a measure of autocorrelation similar in interpretation to the Pearson’s Product Moment correlation statistic for independent samples, in that both statistics range between -1.0 and 1.0 depending on the degree and direction of correlation. Different anisotropic directions appear on separate tabs. Parameters for calculating these variograms are set in the Autocorrelation Window.

When the program is running, placing the mouse cursor over an autocorrelogram point will produce a box showing the number of pairs in that lag class interval, and clicking on the point will produce a Variance Cloud or h-Scattergram graph of all pairs in that interval.

Other measures of autocorrelation provided by GS+ include variograms, correlograms, madograms, rodograms, covariograms, drift, fractal dimension, and standardized, general relative, and pairwise relative variograms.

GS+ Fractal Variograms
GS+ uses a log-log plot of the variogram to derive the fractal dimension D0, presented in the Fractal Variograms window. Different anisotropic directions appear on separate tabs. Parameters for calculating fractal variograms are set in the Autocorrelation Window.
When the program is running, placing the mouse cursor over a variogram point will produce a box showing the number of pairs in that lag class interval, and clicking on the point will produce a Variance Cloud or h-Scattergram graph of all pairs in that interval.

Other measures of autocorrelation provided by GS+ include variograms, correlograms, madograms, rodograms, covariograms, drift, Moran’s I, and standardized, general relative, and pairwise relative variograms.

GS+ Standardized Variograms
Standardized variograms are computed on the natural logarithms of the variates. Different anisotropic directions appear on separate tabs. Parameters for calculating these variograms are set in the Autocorrelation Window.

When the program is running, placing the mouse cursor over a variogram point will produce a box showing the number of pairs in that lag class interval, and clicking on the point will produce a Variance Cloud or h-Scattergram graph of all pairs in that interval.

Other measures of autocorrelation provided by GS+ include variograms, correlograms, madograms, rodograms, covariograms, drift, Moran’s I, fractal dimension, and general relative and pairwise relative variograms.

GS+ General Relative Variograms
The general relative variogram is a graph of semivariance standardized by the squared mean of the data used for each distance interval h. Different anisotropic directions appear on separate tabs. Parameters for calculating general relative variograms are set in the Autocorrelation Window.

When the program is running, placing the mouse cursor over a variogram point will produce a box showing the number of pairs in that lag class interval, and clicking on the point will produce a Variance Cloud or h-Scattergram graph of all pairs in that interval.

Other measures of autocorrelation provided by GS+ include variograms, correlograms, madograms, rodograms, covariograms, drift, Moran’s I, fractal dimension, and standardized and pairwise relative variograms.

GS+ Pairwise Relative Variograms
Pairwise relative variograms are graphs of semivariance normalized by the squared average of tail and head values (values of the different members of each sample pair). Different anisotropic directions appear on separate tabs. Parameters for calculating pairwise relative variograms are set in the Autocorrelation Window.

When the program is running, placing the mouse cursor over a variogram point will produce a box showing the number of pairs in that lag class interval, and clicking on the point will produce a Variance Cloud or h-Scattergram graph of all pairs in that interval.

Other measures of autocorrelation provided by GS+ include variograms, correlograms, madograms, rodograms, covariograms, drift, Moran’s I, fractal dimension, and standardized and general relative variograms.