You specify the MODEL statement if you want to fit a theoretical semivariogram model to the empirical semivariogram data that are produced in the COMPUTE statement. You must have nonmissing empirical semivariogram estimates at a minimum of three lags to perform model fitting.
Table 109.3 summarizes the options available in the MODEL statement.
Table 109.3: MODEL Statement Options
Option 
Description 

Fitting Options 

Specifies confidence level 

Ranks the fitted models and chooses the optimally fit model 

Constructs a ttype confidence interval 

Specifies a positive upper value tolerance 

Specifies which type of empirical semivariogram to fit 

Specifies the functional form (type) of the semivariogram model 

Specifies the input data set 

Fits a theoretical model to the empirical semivariance 

Adds a minimal nugget effect 

Specifies the nugget effect 

Specifies the range parameter 

Uses consecutive nonmissing empirical semivariance lags to fit model 

Specifies the minimum threshold to compare fit quality 

Specifies the scale parameter in semivariogram models 

Specifies the positive smoothness parameter 

Model Options 

Requests the covariance matrix 

Requests the approximate correlation matrix 

Produces different levels of output 

Displays the gradient of the objective function 

Specifies a threshold value for the smoothness parameter 

Suppresses the model fitting process 

Suppresses the display of the iteration history table 
You can choose to perform a fully automated fitting or to fit one model with specific forms. In the first case you simply specify a list of forms or no forms at all. All suitable combinations are tested, and the result is the model that produces the best fit according to specified criteria. In the second case you specify one theoretical semivariogram model, and you have more control over its parameters for the fitting process.
Furthermore, you can specify a theoretical semivariogram model in two ways:
You explicitly specify the FORM option and any of the options SCALE , RANGE , and NUGGET in the MODEL statement.
You can specify an MDATA= data set. This data set contains variables that correspond to the FORM option and to any of the options SCALE , RANGE , NUGGET , and SMOOTH . You can also use an MDATA= data set to request a fully automated fitting.
The two methods are exclusive; either you specify all parameters explicitly, or they all are read from the MDATA= data set.
The MODEL statement has the following fittingoptions:
You can explicitly specify a theoretical semivariogram model to fit by using any combination of one, two, or three forms. Use the syntax with the single form to specify a nonnested model. Use the syntax with k structures formi, i = 1, …, k, to specify up to three nested structures () in a semivariogram model. Each of the forms can be any of the following:
All of these forms are presented in more detail in the section Theoretical Semivariogram Models. In addition, you can optionally specify a nugget effect for your model with the NUGGET option in the MODEL statement.
For example, the syntax
FORM=GAU
specifies a model with a single Gaussian structure. Also, the syntax
FORM=(EXP,SHE,MAT)
specifies a nested model with an exponential, a sine hole effect, and a Matérn structure. Finally
FORM=(EXP,EXP)
specifies a nested model with two structures both of which are exponential.
Note: In the documentation, models are named either by using their full names or by using the first three letters of their structures. Also, the names of different structures in a nested model are separated by a hyphen (). According to this convention, the previous examples illustrate how to specify a GAU, an EXPSHEMAT, and an EXPEXP model, respectively, with the FORM= option.
When you explicitly specify the types of structures, you can fix parameter values or ask PROC VARIOGRAM to select default initial values for the forms parameters by using the SCALE , RANGE , NUGGET , and SMOOTH options. You can set your own, nondefault initial parameter values by using the PARMS statement in combination with an explicitly specified semivariogram model in the MODEL statement.
Use the FORM=AUTO option to request the highest level of automation in the best fit selection of the parameters. If you specify FORM=AUTO, any of the SCALE , RANGE , or SMOOTH options that are also specified are ignored. When you specify the FORM=AUTO option, you cannot specify the PARMS statement for the corresponding MODEL statement. As a result, when you use the FORM=AUTO option, you cannot fix any of the model parameters and PROC VARIOGRAM sets initial values for them.
The AUTO option has the following autooptions:
You can use the AUTO value for the form in the MDATA= data set, and also in the FORM= option. However, in the former case the automation functionality is limited compared to the latter case and the autooptions of the FORM=AUTO option. In particular, when you specify the form to be AUTO in the MDATA= data set, then PROC VARIOGRAM follows only the default behavior and searches among all available forms for the best fit with up to three nested structures in a model.
In addition to the fittingoptions, you can specify the following modeloptions after a slash (/) in the MODEL statement.