The SPP Procedure

Displayed Output

The SPP procedure produces the following output objects.

  • By default, PROC SPP outputs a "Number of Observations" table, which displays the number of observations that are read from the input data set and the number of valid observations that are used. The actual number of observations that are used in the analysis can be equal to or smaller than the number of valid observations, depending on the specification of the study window and the existence and handling of duplicate observations. When you include a covariate variable in your analysis, this table contains more detailed information about the number of observations that are used in the study window for each variable.

  • If you use the PROCESS statement to specify a point pattern, PROC SPP outputs a table is displayed by default that contains exploratory information about the point pattern, any mark variable that is present, and information about the point pattern domain window and grid.

  • If you use the PROCESS statement to specify a point pattern, PROC SPP outputs a default plot of the event observations in the point pattern.

  • If you specify a mark variable for the point pattern, PROC SPP outputs a table that contains information about the mark variable.

  • If you do not specify any options for the PROCESS statement, PROC SPP performs the quadrat test by default and outputs a table that shows the Pearson chi-square test for CSR by default. If you specify the QUADRAT option with the DETAILS suboption, PROC SPP outputs a detailed quadrat counts table, a quadrat information table that contains Pearson residuals, and a table for the Pearson chi-square test for CSR.

  • If you specify a KERNEL option in the PROCESS statement, PROC SPP outputs a kernel intensity information table. In addition, if you request the ADAPTIVE suboption in the KERNEL option, an adaptive kernel information table is displayed. In addition, if you specify the KERNEL option and ODS Graphics is enabled, a map of the kernel intensity estimate is also produced.

  • If you specify one or more of the K, L, G, and F options in the PROCESS statement, PROC SPP outputs an information table for each of the specified distance functions. The information table contains basic information, such as the minimum analysis distance, maximum analysis distance, maximum difference between the empirical distribution function of the summary statistic and the CSR function, and the distance at which the maximum difference is observed. In addition, PROC SPP outputs a panel plot for each distance function that is included as an option in the PROCESS statement. Each panel plot contains four constituent plots: the empirical distribution function (EDF) plot, the EDF$-$CSR difference plot, a probability-probability plot that compares the EDF and CSR, and a confidence interval plot for the summary statistic.

  • If you specify the J and PCF options in the PROCESS statement, PROC SPP outputs a combined plot that shows the EDF, the simulation intervals, and the confidence interval for the summary statistic.

  • If you specify a COVTEST statement that has appropriate trend covariates on the right side, PROC SPP outputs a table for the Kolmogorov-Smirnov EDF test statistic and creates a plot of the empirical and transformed EDF by default for each covariate that you include in the COVTEST statement. The plot illustrates the Kolmogorov-Smirnov test analysis for testing for point pattern dependency on covariates. If you specify the Cramér–von Mises EDF test statistic in the TEST= option in the COVTEST statement, PROC SPP outputs the table for the Cramér–von Mises EDF test statistic.

  • If you specify a MODEL statement to fit a model for the first-order intensity of the point pattern that is defined in a preceding PROCESS statement, PROC SPP produces the following results by default:

    • a "Model Information" table that lists the intercept, covariates, and polynomial terms that are included in the model, along with the initial values for the coefficients

    • an optimization information table that shows the optimization technique, the number of parameters in the optimization, and the number of fixed parameters and starting values

    • a table for the convergence status that shows the convergence criterion

    • a "Parameter Estimates" table that shows the estimate for each parameter, the standard error, the number of degrees of freedom, a t value, and a p-value

    • a "Fit Statistics" table that shows different fit statistics, such as the log likelihood, Akaike’s information criterion, and the Bayesian information criterion

    • a map that shows the fitted intensity estimate based on the model

  • If you specify the MODEL statement and include the ITHIST option, PROC SPP outputs an iteration history table that shows the value of the objective function and the maximum value of the gradient over different iterations of the optimization algorithm.

  • If you specify the MODEL statement and include the CORRB option, PROC SPP outputs the approximate correlation matrix.

  • If you specify the MODEL statement and include the COVB option, PROC SPP outputs the approximate covariance matrix.

  • If you specify the MODEL statement and include the GOF option, PROC SPP outputs a table that shows the Pearson chi-square test for goodness of fit. This table shows a p-value that indicates how likely it is for the data to be generated by the fitted model. In addition, if you also specify a QUADRAT option with the DETAILS suboption for the response process in a preceding PROCESS statement, PROC SPP also displays a quadrat information table that shows Pearson residuals that are based on the expected counts under the fitted model and observed counts from the point pattern data set that is defined for the response process.

The complete listing of the PROC SPP output follows in the sections ODS Table Names and ODS Graph Names.