The SPP Procedure
MODEL Statement
MODEL process-name = <trend-name, …> </model-options>;
The MODEL statement enables you to fit an inhomogeneous Poisson process model. You must specify a process-name as the dependent variable. In addition, the MODEL statement enables you to specify multiple trends as covariates. If you do not specify any trends as covariates in the MODEL statement, PROC SPP fits a second-degree polynomial. The process-name must be defined in a preceding PROCESS statement, and each trend-name must be defined in a preceding TREND statement. Table 2 summarizes the model-options that you can specify.
Table 2: MODEL Statement Options
| Option | Description |
|---|---|
| CENSCALE | Displays optimization centering and scaling information |
| CORRB | Requests the approximate correlation matrix |
| COVB | Requests the approximate covariance matrix |
| CL | Constructs a t-type confidence interval |
| GOF | Performs a chi-square-based goodness-of-fit test |
| GRID | Specifies the intensity response GRID size |
| ITHIST | Requests the optimization iteration history |
| MTYPE | Requests a specific type of model to be fit |
| OUTINTENSITY | Specifies an output data set to store the intensity estimates |
| OUTSIM | Specifies an output data set to store the simulations from an intensity model |
| POLYNOMIAL | Requests an additional polynomial component to be included in the model fitting process |
| RESIDUAL | Requests residual computations and specifies the bandwidth for smoothed residuals |
| SOLUTION | Requests display of raw results |
You can specify the following model-options:
- CENSCALE
lists the centering and scaling (standardization) information for each coordinate and covariate in the model.
- CL<(alpha-value)>
requests a t-type confidence interval for the estimated parameters. You can also specify the significance level via the alpha-value. The default alpha-value is 0.05, which corresponds to the default confidence level of 95%.
- CORRB
requests the estimated correlation matrix for the parameter estimates. To request the estimated correlation matrix for the model parameters with respect to the standardized covariates, specify both this model-option and the SOLUTION model-option.
- COVB
requests the estimated covariance matrix for the parameter estimates. To request the estimated covariance matrix for the model parameters with respect to the standardized covariates, specify this model-option and the SOLUTION model-option.
- GOF(num-simulations )
requests a goodness-of-fit test for the fitted intensity model. You can specify the number of Monte Carlo simulation runs as an integer in num-simulations. By default, the SPP procedure performs 100 simulations when you specify this option. It is recommended that you specify a QUADRAT option in the definition of the response/dependent point pattern in the PROCESS statement. If you do not specify such an option, the SPP procedure uses a default
quadrat.
- GRID(value-NX,value-NY )
specifies the grid resolution for model fitting, where value-NX specifies the number of grids in the horizontal direction and value-NY specifies the number of grids in the vertical direction. By default, the SPP procedure fits the model on a
grid.
- ITHIST<(PARM)>
-
requests an iteration history table for the model-fitting optimization. Specify this option to produce additional levels of output detail. You can specify the following value:
- MTYPE=POISSON | NEGBINOMIAL
-
specifies the type of inhomogeneous intensity model to be fit by PROC SPP. You fit a negative binomial model only in order to diagnose overdispersion, so in this case no fitted intensity is produced, and likewise none of the goodness-of-fit tests or residual diagnostics that are based on the intensity are produced. You can specify the following values:
- POISSON
fits a Poisson process model.
- NEGBINOMIAL
fits a negative binomial model.
- OUTINTENSITY=SAS-data-set
specifies a SAS-data-set in which to store the output intensity estimate.
- OUTSIM<(iter-value)>=SAS-data-set
specifies a SAS-data-set in which to store a simulated point pattern from a fitted intensity model. Specify the number of iterations in <iter-value> to generate multiple point pattern data sets. By default, the number of simulation iterations is set to 1.
- POLYNOMIAL|POLY<(degree )>
specifies a polynomial trend in the coordinates. You can also specify the degree of the polynomial component. If you do not specify the degree, PROC SPP procedure uses a second-degree polynomial by default.
- RESIDUAL(B=value)
requests residual diagnostics for the inhomogeneous Poisson process model. If you specify this option, you must also specify the residual bandwidth for computing smoothed residuals via the B= suboption.
- SOLUTION
displays the parameter estimates table in a location- and scale-standardized space. For optimization purposes, any polynomial coordinates and covariates in the model are centered and scaled. The parameters and the approximate covariance and the correlation matrices are displayed by default in the untransformed, unstandardized space. This option causes the output to be displayed on the basis of the actual fitted parameters in the transformed space. If you also specify the COVB or CORRB model-option (or both), then PROC SPP also displays the estimated covariance or correlation matrix, respectively (or both), in the transformed space.
You can specify additional options that are related to the nonlinear optimization aspects of the MODEL fitting process via the NLOPTIONS statement.