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 107.2 summarizes the model-options that you can specify.

Table 107.2: 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:

PARM: includes the fitting parameters in the iteration history table.

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.

By default, MTYPE=POISSON.

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.