The Autocorrelation Window is where various options for variogram calculations and the end results appear; see the Semivariance Analysis summary for a definition of semivariance and formulas for lag class distance intervals.
The Active Lag Distance specifies the range over which autocorrelation will be calculated. The minimum distance for this field is the minimum distance between adjacent points in the data set, while the maximum distance is the maximum distance between any two points. Specifying a value too large or too small will assign either the largest or smallest possible values to this distance.
For example, a 1200 m transect will have a maximum lag of 1200 m; specifying an Active Lag of 300 m will limit the variogram to lag intervals less than or equal to 300 m along the entire 1200 m length of the transect.
The default active lag is 80% of the maximum lag. This is not likely to be the most appropriate active lag for your data but rather will provide a starting point. Variograms typically decompose at large lag intervals because of decreasing numbers of couples per lag class as the maximum lag interval is approached.
GS+ allows 1 million lag classes to be specified with up to 1 billion pairs per class.
Changing the Active Lag on the Semivariance Screen will also change the Active Lag on the Moran's I Analysis window and on the Fractal Analysis window, and vice versa.
The Lag Class Distance Interval defines how pairs of points will be grouped into lag classes. Each point in a variogram represents the average semivariance for a single lag class, which is a group of pairs separated by a certain Lag Class Distance Interval, sometimes called a step size. This interval can either be calculated by GS+, in which case it will be uniformly distributed across the active lag distance, or it can be manually set by the user:
With this option you may use the Define command to bring up a window to Define Lag Class Intervals, i.e. to specify individual break points for the lag intervals.
With this option, the value specified is the size of the interval, applied uniformly across the active lag distance. E.G. an interval of 2 units with an active lag distance of 10 units will create 5 lag classes, each 2 units wide. The minimum interval allowed is the smallest distance separating any two sample point locations in the data set. The maximum interval is the greatest distance separating any two sample point locations. The default value is 10% of the active lag or, if 10% of the active lag is smaller than the minimum allowed, the minimum allowed. This default may not be appropriate for any given data set; you should try different steps for every set.
The number of lag classes (and therefore plotted points) in a variogram is a function of values for the active lag and the active step; a 300 m active lag with a 15 m active step will have ca. 20 lag classes. Note, however, that the lag distance for a given class will be the average distance separating points within the class and not necessarily the midpoint for the class. For a 10-20 m lag class, e.g., the average lag distance may be 12.3 m rather than 15 m if more pairs of points are separated by 10-15 m intervals than by 15-20 m intervals.
Changing the distance interval will clear results on the screen from previous analyses calculated with a different step. Results based on the new step must be re-generated with Calculate command.
Anisotropy refers to a direction-dependent trend in the data. Consider data collected from a two-dimensional grid on a mountain slope: elevation will be autocorrelated differently in the upslope-downslope direction than in a cross-slope direction, and thus an isotropic (all-direction) analysis may hide much of the autocorrelation that in fact is present. Anisotropic analysis allows you to see if your data have a directional component that might arise from a variety of unforeseen factors. Anisotropic analysis is irrelevant for single-dimension data such as a transect or a time series.
GS+ evaluates geometric anisotropy, i.e. anisotropy which is expressed as variograms with different ranges in different directions. The Principal Anisotropic Axis (the Major Axis of the anisotropic model) is the direction with the longest range, i.e. the direction of major spatial continuity.
The best way to evaluate anisotropy is to view the Anisotropic Semivariance Surface (Semivariance Map) , and use the Azimuth function to define and then set the Principal Anisotropic Axis to the direction aligned with the lowest semivariance values (the direction of maximum spatial continuity, or major axis of the anisotropic variogram model). The map is accessed by pressing the Surface command at the bottom of the Semivariance Analysis window.
The Principal Axis is the direction of maximum spatial continuity, or base axis from which the offset angles for anisotropic analyses are calculated. Offset angles are 0°, 45°, 90°, and 135° clockwise from the base axis; points aligned sufficiently close to one or another of these angles (see Offset Tolerance below) are included in the anisotropic analysis for that angle.
The axis orientation should correspond to the axis of maximum spatial continuity, i.e. the major anisotropic axis. The default axis is 0° from the north-south (y) axis. Use the Anisotropic Surface Map (Surface command at the bottom of this window) to help define the appropriate orientation.
Offset Tolerance (degrees)
In anisotropic analyses, the Offset Tolerance determines how closely the alignment between any two points needs to be for those points to be included in the analysis for a given offset angle. Two points will be included in the analysis for a given offset angle if the angle between them is within the offset tolerance from the offset angle.
For example, if the angle between two points is 59.3° and the offset tolerance is 15.0°, the points will be included only in the 45° angle class, which would include all angles between 30° and 60°. The default tolerance is 22.5°.
Check this option to show a model for the variogram points. If the model has already been defined, either automatically or manually, the variograms will be redrawn with the model now graphed. If a model has not yet been defined, or upon executing the Calculate command, a best-fit model will be calculated and graphed.
To see the model parameters and to change the model, use the Model command at the bottom of the variogram image.
Check this option to show the sample variance for the data as a line on the variogram graphs.
The Expand command brings up a separate variograms window, from which variograms can be printed or formatted. All of the autocorrelation measures can be individually expanded: Variograms, Standardized variograms, Madograms, Rodograms, Drift, Correlograms, Covariance, General relative variograms, Pairwise relative variograms, Moran's I, and Fractals.
Also available from the expanded window are Variance Cloud Analysis, the ability to view individual semivariance values, and the number of pairs per variogram class interval are also available from these windows.
The Model command brings up a Model Dialog window within which you may change the variogram model. The Model command is enabled only when the Show Model Variogram Option is selected.
The Surface command brings up the Anisotropic Variogram Surface Map window . The surface map is useful for visualizing anisotropic autocorrelation when present.
The Calculate command causes the semivariogram to be calculated.
The Exit command closes the Semivariance Analysis Window.