COMPUTE Statement

The VARIOGRAM Procedure

COMPUTE Statement

COMPUTE computation-options ;

The COMPUTE statement provides a number of options that control the computation of the semivariogram, the robust semivariogram, and the covariance.

ANGLETOLERANCE=angle tolerance

ANGLETOL=angle tolerance

ATOL=angle tolerance

specifies the tolerance, in degrees, around the angles determined by the NDIRECTIONS= specification. The default is [(180^o)/(2×n_d)], where n_d is the NDIRECTIONS= specification.

See the section "Theoretical and Computational Details of the Semivariogram" for more detailed information.

BANDWIDTH=bandwidth distance

BANDW=bandwidth distance

specifies the bandwidth, or perpendicular distance cutoff for determining the angle class for a given pair of points. The distance classes define a series of cylindrically shaped areas, while the angle classes radially cut these cylindrically shaped areas. For a given angle class $(\theta_1 - \delta \theta_1,\theta_1 + \delta \theta_1)$ , as you proceed out radially, the area encompassed by this angle class becomes larger. The BANDWIDTH= option restricts this area by excluding all points with a perpendicular distance from the line $\theta = \theta_1$ that is greater than the BANDWIDTH= value.

If you do not specify the BANDWIDTH= option, no restriction occurs. See Figure 70.15 for more detailed information.

DEPSILON=distance value

DEPS=distance value

specifies the distance value for declaring that two distinct points are zero distance apart. Such pairs, if they occur, cause numeric problems. If you specify DEPSILON= $\varepsilon$ , then pairs of points P₁ and P₂ for which the distance between them $| P_1P_2 | \lt \varepsilon$ are excluded from the continuity measure calculations. The default value of the DEPSILON= option is 100 times machine epsilon; this product is approximately 1E-10 on most computers.

LAGDISTANCE=distance unit

LAGDIST=distance unit

LAGD=distance unit

specifies the basic distance unit defining the lags. For example, a specification of LAGDISTANCE=x results in lag distance classes that are multiples of x. For a given pair of points P₁ and P₂, the distance between them, denoted | P₁P₂ |, is calculated. If | P₁P₂ | = x, then this pair is in the first lag class. If | P₁P₂ | = 2x, then this pair is in the second lag class, and so on.

For irregularly spaced data, the pairwise distances are unlikely to fall exactly on multiples of the LAGDISTANCE= value. A distance tolerance of $\delta x$ is used to accommodate a spread of distances around multiples of x (the LAGTOLERANCE= option specifies the distance tolerance). For example, if | P₁P₂ | is within $x +- \delta x$ , you would place this pair in the first lag class; if | P₁P₂ | is within $2x +- \delta x$ ,you would place this pair in the second lag class, and so on.

You can determine the candidate values for the LAGDISTANCE= option by plotting or displaying the OUTDISTANCE= data set.

A LAGDISTANCE= value is required unless you specify the NOVARIOGRAM option.

See the section "Theoretical and Computational Details of the Semivariogram" for more details.

LAGTOLERANCE=tolerance number

LAGTOL=tolerance number

LAGT=tolerance number

specifies the tolerance around the LAGDISTANCE= value for grouping distance pairs into lag classes. See the preceding description of the LAGDISTANCE= option for information on the use of the LAGTOLERANCE= option, and see the section "Theoretical and Computational Details of the Semivariogram" for more details.

If you do not specify the LAGTOLERANCE= option, a default value of (1/2) times the LAGDISTANCE= value is used.

MAXLAGS=number of lags

MAXLAG=number of lags

MAXL=number of lags

specifies the maximum number of lag classes used in constructing the continuity measures. This option excludes any pair of points P₁ and P₂ for which the distance between them, | P₁P₂ |, exceeds the MAXLAGS= value times the LAGDISTANCE= value.

You can determine candidate values for the MAXLAGS= option by plotting or displaying the OUTDISTANCE= data set.

A MAXLAGS= value is required unless you specify the NOVARIOGRAM option.

NDIRECTIONS=number of directions

NDIR=number of directions

ND=number of directions

specifies the number of angle classes to use in computing the continuity measures. This option is useful when there is potential anisotropy in the spatial continuity measures. Anisotropy occurs when the spatial continuity or dependence between a pair of points depends on the orientation or angle between the pair. Isotropy is the absence of this effect: the spatial continuity or dependence between a pair of points depends only on the distance between the points, not the angle.

The angle classes formed from the NDIRECTIONS= option start from N -S and proceed clockwise. For example, NDIRECTIONS=3 produces three angle classes. In terms of compass points, these classes are centered at 0^o (or its reciprocal 180^o), 60^o (or its reciprocal 240^o), and 120^o (or its reciprocal 300^o). For irregularly spaced data, the angles between pairs are unlikely to fall exactly in these directions, so an angle tolerance of $\delta \theta$ is used (the ANGLETOLERANCE= option specifies the angle tolerance). If NDIRECTIONS=n_d, the base angle is $\theta=\frac{180^o}{n_d}$ , and the angle classes are

$(k\theta - \delta \theta, k\theta + \delta \theta) k=0, ... ,n_{d}-1$

If you do not specify the NDIRECTIONS= option, no angles are formed, and the spatial continuity measures are assumed to be isotropic.

The NDIRECTIONS= option is useful for exploring possible anisotropy. The DIRECTIONS statement, described in the "DIRECTIONS Statement" section, provides greater control over the angle classes. See the section "Theoretical and Computational Details of the Semivariogram" for more detailed information.

NHCLASSES=number of histogram classes

NHCLASS=number of histogram classes

NHC=number of histogram classes

specifies the number of distance or histogram classes to write to the OUTDISTANCE= data set. The actual number of classes is one more than the NHCLASSES= value since a special lag 0 class is also computed. See the OUTDISTANCE= option and the section "OUTDIST=SAS-data-set " for details.

The default value of the NHCLASSES= option is 10. This option is ignored if you do not specify an OUTDISTANCE= data set.

NOVARIOGRAM

prevents the computation of the continuity measures. This option is useful for preliminary analysis when you require only the OUTDISTANCE= or OUTPAIR= data sets.

OUTPDISTANCE=distance limit

OUTPDIST=distance limit

OUTPD=distance limit

specifies the cutoff distance for writing observations to the OUTPAIR= data set. If you specify OUTPDISTANCE=d_max, the distance | P₁P₂ | between each pair of points P₁ and P₂ is checked against d_max. If | P₁P₂ | > d_max, the observation for this pair is not written to the OUTPAIR= data set. If you do not specify the OUTPDISTANCE= option, all distinct pairs are written. This option is ignored if you do not specify an OUTPAIR= data set.

ROBUST

requests that a robust version of the semivariogram be calculated in addition to the regular semivariogram and covariance.

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