CSPATIALREG Procedure

Example 13.6 Comparison of Multiple Models

Data Description and Objective

Example in this section uses the CrimeOH and CrimeWmat data sets that are described in Columbus Crime Data to demonstrate fitting and comparison of multiple models in PROC CSPATIALREG.

Comparison of Multiple Models

The following statements fit multiple models to the CrimeOH and CrimeWmat data sets, which are described in Columbus Crime Data, using the regressors Income and HValue:

/*-- TYPE=AUTO --*/
proc cspatialreg data=mylib.CrimeOH Wmat=mylib.CrimeWmat;
   model crime=income hvalue / type=AUTO;
   spatialid sid;
run;

In this example, the TYPE=AUTO option is specified in the MODEL statement to fit seven models—SAC, SARMA, SAR, SEM, SMA, CAR, and LINEAR. However, the CAR model is not fitted because the input spatial weights matrix bold upper W is not symmetric. The parameter estimates for the six remaining models—SAC, SARMA, SAR, SEM, SMA, and LINEAR—are shown in Output 13.6.1. The comparison of these six models is provided in Output 13.6.2. If AIC is used for model comparison, Output 13.6.2 suggests that the SAR model is the best model among the six candidate models, because its AIC value is the smallest.

Output 13.6.1: Parameter Estimates of Multiple Models

The CSPATIALREG Procedure

Parameter Estimates
Model TypeParameterDFEstimateStandard
Error
t ValueApprox
Pr > |t|
SACIntercept147.7840329.2795445.15<.0001
 income1-1.0258920.334029-3.070.0021
 hvalue1-0.2816530.093369-3.020.0026
 _rho10.3680610.1811912.030.0422
 _lambda10.1666840.2981470.560.5761
 _sigma2195.60353019.4754454.91<.0001
SARMAIntercept148.8025829.5378305.12<.0001
 income1-1.0185610.334811-3.040.0023
 hvalue1-0.2868790.092709-3.090.0020
 _rho10.3415170.2004921.700.0885
 _lambda1-0.2589550.416859-0.620.5345
 _sigma2196.76219520.6186344.69<.0001
SARIntercept145.0794677.8712415.73<.0001
 income1-1.0316160.328416-3.140.0017
 hvalue1-0.2659270.088222-3.010.0026
 _rho10.4310180.1236193.490.0005
 _sigma2195.49460819.5078964.90<.0001
SEMIntercept159.9144365.88121610.19<.0001
 income1-0.9428920.370508-2.540.0109
 hvalue1-0.3022180.090549-3.340.0008
 _lambda10.5603140.1528093.670.0002
 _sigma2195.55413720.0259094.77<.0001
SMAIntercept159.3757525.87272010.11<.0001
 income1-0.9287940.361190-2.570.0101
 hvalue1-0.2880250.086456-3.330.0009
 _lambda1-0.7883720.273593-2.880.0040
 _sigma21115.68599025.3370654.57<.0001
LINEARIntercept168.6188634.58821014.96<.0001
 income1-1.5973040.323739-4.93<.0001
 hvalue1-0.2739310.099989-2.740.0062
 _sigma21122.75169624.7994934.95<.0001


Output 13.6.2: Comparison of Multiple Models

Model Comparison
Model TypeStatusReasonNumber
of Iterations
Max Abs
Gradient
Log
Likelihood
AICSBC
SAC0Convergence criterion (ABSGCONV=0.00001) satisfied.360.0000-182.4376.8950388.2459
SARMA0Convergence criterion (FCONV=1E-8) satisfied.160.0445-182.4376.8184388.1693
SAR0Convergence criterion (ABSGCONV=0.00001) satisfied.160.0000-182.6375.1147*384.5738*
SEM0Convergence criterion (FCONV=1E-8) satisfied.350.0706-183.6377.1833386.6424
SMA0Convergence criterion (FCONV=1E-8) satisfied.160.0255-183.5376.9300386.3891
LINEAR0Convergence criterion (ABSGCONV=0.00001) satisfied.160.0000-187.4382.7542390.3215
Asterisk (*) denotes the best model in the column.


Last updated: July 09, 2026