Approximation methods in PROC SPATIALREG
/*--------------------------------------------------------------
SAS Sample Library
Name: sprex05.sas
Description: Example program from SAS/ETS User's Guide,
The SPATIALREG Procedure
Title: Approximation methods in PROC SPATIALREG
Product: SAS/ETS Software
Keys: Taylor and Chebyshev approximations
PROC: SPATIALREG
Notes:
--------------------------------------------------------------*/
data simdata;
input SID $ x1 x2 x3 y;
datalines;
L50 -1.080192664 -0.391837255 2.6720532843 -1.939942256
L34 -0.401471135 0.3513199155 0.3771476344 0.7230873618
L46 0.1314452577 1.5626892891 -0.273442927 1.9925135176
L13 0.7920110978 0.3900768864 -0.780730106 2.4143089527
L11 -0.496266788 -1.161049655 -0.462676297 0.6529367412
L8 0.4673733309 0.7449099388 -0.557031886 2.0709143796
L1 1.0747268604 0.8179241213 -0.552774504 3.7404686845
L44 -0.969128513 -0.532027463 0.6119455357 0.3207327491
L6 1.4849682178 1.6632191757 -1.682192731 4.7136835044
L31 1.6539456214 0.529697017 1.0312325223 2.2623271467
L49 0.4021394645 -1.200222916 -1.690597188 2.3671651538
L26 -0.49813637 -1.7692711 0.4273909093 -1.193951993
L48 -1.974680775 -1.04760534 -0.702733763 0.2958880072
L29 -0.85707891 -0.330706762 0.1059158623 -0.717334237
L37 0.3464385033 -0.256593889 -0.497110119 1.9438614251
L4 -0.482548243 -0.452974096 0.2738674886 0.4065525795
L3 1.2252590297 -0.148304138 0.2901232752 1.5669797681
L40 0.1026758193 -0.982447991 1.8173650332 -1.157783179
L19 1.3368393023 -0.874235931 -0.081595457 2.3832830417
L17 -1.035661208 -0.028786903 0.2457009705 0.069929007
L45 1.3204304867 -0.863550062 0.9757917861 -0.503511316
L47 0.8799907753 -1.107299467 -1.884480816 1.7385015825
L15 -0.097991569 1.1407931953 -1.178890318 2.7025763571
L39 0.5000595821 -1.801018572 1.0955076204 -0.651873723
L41 -0.085590063 -0.95495114 -1.181589807 1.6048483869
L32 -2.452319337 -0.707313442 -0.945681396 0.8784455245
L22 0.5366215036 0.68496118 -0.702203856 3.6422129211
L18 -1.913065732 0.0561821805 -1.289341948 0.811460829
L36 1.1176441189 0.4849829922 -0.633740565 2.6825944244
L16 -1.010013544 0.1501684675 0.6892721371 0.4285848788
L35 0.7746020606 -2.57257665 0.3777694392 -0.952147054
L9 0.0842232867 -1.313573502 -1.931519517 1.1484312409
L38 -0.610859299 0.1587061823 0.9739440971 0.2886113928
L7 0.629140588 1.4323343516 0.3604963698 2.6856130381
L43 0.1869868108 0.1469053516 0.0298671298 1.5537924279
L23 -1.917034243 2.4034547166 -2.447004851 4.6922590646
L24 0.5057919358 -0.675375524 1.0080312836 -1.385196867
L10 0.8171785858 1.0450583561 -0.997780737 2.8727332473
L12 -1.973530252 -0.431360634 0.0467521192 0.1143714659
L14 1.4026821472 0.7753985164 1.3277971886 1.1660025894
L27 1.4020780432 -0.206033167 0.3428467454 1.7546642589
L20 -1.390736973 0.719254447 0.4442360706 -0.023710168
L5 0.218553009 -0.420015176 0.2463559954 0.8474411587
L2 -1.233821987 -0.141535384 1.0420036424 -1.045870218
L42 0.4346834817 -0.59685783 -0.123448644 0.5801302381
L30 -2.227219374 -0.358401709 -0.055078668 -1.209077026
L21 1.1920958462 0.2146500105 -0.050886065 2.2176859357
L25 0.0197744321 0.298455422 -0.361649662 1.7591096992
L33 0.3388960631 0.81292813 -0.087180185 2.4823505199
L28 0.9464460905 0.5921500617 -0.133987881 2.0493385224
;
data simw;
input SID $ L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17 L18 L19 L20 L21 L22 L23 L24 L25 L26 L27 L28 L29 L30 L31 L32 L33 L34 L35 L36 L37 L38 L39 L40 L41 L42 L43 L44 L45 L46 L47 L48 L49 L50;
datalines;
L1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
L2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
L3 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
L4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0
L5 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0
L6 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0
L7 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
L8 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
L9 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
L10 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
L11 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0
L12 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1
L13 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0
L14 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0
L15 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0
L16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
L17 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0
L18 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0
L19 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
L20 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0
L21 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0
L22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
L23 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1
L24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
L25 0 0 0 0 0 1 1 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
L26 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
L27 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
L28 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0
L29 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
L30 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
L31 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
L32 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0
L33 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
L34 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0
L35 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
L36 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0
L37 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0
L38 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
L39 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
L40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0
L41 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
L42 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0
L43 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0
L44 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0
L45 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1
L46 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0
L47 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
L48 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0
L49 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 1 0 1 0 0 0
L50 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
;
data simw_compact;
input SID $ cSID $ Value;
datalines;
L50 L45 1
L30 L22 1
L42 L46 1
L32 L35 1
L7 L25 1
L33 L25 1
L50 L25 1
L23 L50 1
L9 L7 1
L45 L36 1
L32 L9 1
L27 L13 1
L10 L8 1
L18 L6 1
L50 L23 1
L44 L48 1
L8 L43 1
L28 L6 1
L7 L6 1
L34 L36 1
L44 L17 1
L36 L15 1
L39 L13 1
L16 L38 1
L5 L19 1
L15 L4 1
L19 L2 1
L37 L46 1
L4 L43 1
L45 L7 1
L3 L17 1
L29 L42 1
L12 L35 1
L25 L26 1
L47 L27 1
L31 L8 1
L38 L16 1
L3 L37 1
L1 L2 1
L31 L35 1
L19 L49 1
L36 L45 1
L36 L46 1
L8 L11 1
L47 L6 1
L20 L11 1
L6 L28 1
L18 L10 1
L21 L8 1
L32 L4 1
L27 L47 1
L33 L18 1
L48 L15 1
L11 L41 1
L6 L25 1
L49 L5 1
L3 L35 1
L28 L22 1
L26 L25 1
L42 L31 1
L14 L11 1
L48 L44 1
L2 L28 1
L31 L42 1
L46 L36 1
L5 L41 1
L16 L34 1
L9 L28 1
L1 L29 1
L43 L49 1
L7 L11 1
L49 L42 1
L38 L12 1
L3 L13 1
L10 L46 1
L26 L22 1
L6 L18 1
L22 L24 1
L9 L37 1
L26 L44 1
L16 L25 1
L32 L45 1
L23 L3 1
L10 L18 1
L49 L45 1
L20 L45 1
L46 L12 1
L8 L21 1
L32 L48 1
L21 L2 1
L45 L6 1
L38 L28 1
L21 L43 1
L34 L16 1
L18 L45 1
L25 L7 1
L7 L17 1
L19 L5 1
L12 L50 1
L25 L15 1
L34 L26 1
L50 L12 1
L24 L22 1
L37 L3 1
L22 L30 1
L4 L48 1
L47 L23 1
L13 L46 1
L25 L16 1
L34 L49 1
L20 L44 1
L48 L32 1
L46 L10 1
L20 L49 1
L30 L1 1
L6 L7 1
L11 L36 1
L28 L2 1
L42 L14 1
L12 L27 1
L43 L8 1
L35 L3 1
L9 L32 1
L46 L13 1
L17 L3 1
L14 L42 1
L13 L27 1
L25 L11 1
L26 L34 1
L7 L9 1
L6 L45 1
L46 L37 1
L41 L5 1
L11 L8 1
L28 L9 1
L1 L11 1
L2 L21 1
L12 L46 1
L37 L40 1
L15 L36 1
L48 L14 1
L17 L40 1
L25 L33 1
L11 L14 1
L2 L19 1
L1 L30 1
L5 L44 1
L5 L12 1
L36 L11 1
L6 L47 1
L13 L20 1
L35 L12 1
L27 L12 1
L26 L21 1
L48 L4 1
L18 L2 1
L48 L40 1
L17 L4 1
L40 L17 1
L27 L31 1
L21 L5 1
L5 L21 1
L15 L25 1
L11 L7 1
L49 L19 1
L35 L31 1
L26 L8 1
L49 L47 1
L12 L5 1
L28 L38 1
L4 L32 1
L22 L26 1
L28 L23 1
L3 L23 1
L11 L1 1
L43 L32 1
L49 L34 1
L46 L42 1
L7 L45 1
L32 L43 1
L43 L21 1
L8 L26 1
L5 L23 1
L28 L40 1
L6 L29 1
L40 L28 1
L35 L32 1
L8 L10 1
L29 L1 1
L2 L18 1
L2 L26 1
L13 L25 1
L31 L27 1
L17 L44 1
L22 L28 1
L2 L1 1
L32 L3 1
L12 L38 1
L35 L15 1
L36 L34 1
L42 L49 1
L29 L6 1
L36 L44 1
L31 L13 1
L45 L20 1
L18 L33 1
L41 L11 1
L1 L42 1
L29 L22 1
L3 L32 1
L5 L49 1
L45 L18 1
L14 L48 1
L21 L41 1
L8 L31 1
L45 L49 1
L44 L20 1
L11 L25 1
L21 L26 1
L40 L37 1
L15 L48 1
L4 L15 1
L17 L7 1
L13 L36 1
L40 L48 1
L43 L4 1
L25 L6 1
L26 L2 1
L44 L5 1
L23 L28 1
L18 L41 1
L37 L9 1
L42 L43 1
L15 L35 1
L13 L3 1
L13 L31 1
L23 L47 1
L49 L20 1
L42 L1 1
L4 L17 1
L45 L32 1
L11 L20 1
L49 L43 1
L42 L29 1
L25 L50 1
L25 L13 1
L13 L39 1
L44 L36 1
L45 L50 1
L22 L29 1
L41 L18 1
L20 L13 1
L23 L5 1
L43 L42 1
L44 L26 1
L36 L13 1
L47 L49 1
L41 L21 1
;
/*-- SAR Model : full W --*/
proc spatialreg data=simdata Wmat=simw approximation=(ORDER=10);
model y=x1-x3 / type=SAR;
spatialid SID;
run;
/*-- SAR Model : compact form of W --*/
proc spatialreg data=simdata Wmat=simw_compact approximation=(ORDER=10);
model y=x1-x3 / type=SAR;
spatialid SID;
run;
/*-- SDM : Taylor approximation with full W --*/
proc spatialreg data=simdata Wmat=simw approximation=(Taylor ORDER=50);
model y=x1-x3/ type=SAR;
spatialeffects x1-x3;
spatialid SID;
run;
/*-- SDM : Taylor approximation with compact W --*/
proc spatialreg data=simdata Wmat=simw_compact
approximation=(Taylor ORDER=50);
model y=x1-x3/ type=SAR;
spatialeffects x1-x3;
spatialid SID;
run;
/*-- SDM : Chebyshev approximation with full W --*/
proc spatialreg data=simdata Wmat=simw approximation=(ORDER=10);
model y=x1-x3/ type=SAR;
spatialeffects x1-x3;
spatialid SID;
run;
/*-- SDM : Chebyshev approximation with compact W --*/
proc spatialreg data=simdata Wmat=simw_compact approximation=(ORDER=10);
model y=x1-x3/ type=SAR;
spatialeffects x1-x3;
spatialid SID;
run;
/*-- SEM Model : full W --*/
proc spatialreg data=simdata Wmat=simw approximation=(ORDER=10);
model y=x1-x3 / type=SEM;
spatialid SID;
run;
/*-- SEM Model : compact form of W --*/
proc spatialreg data=simdata Wmat=simw_compact approximation=(ORDER=10);
model y=x1-x3 / type=SEM;
spatialid SID;
run;
/*-- SDEM : Taylor approximation with full W --*/
proc spatialreg data=simdata Wmat=simw approximation=(Taylor ORDER=50);
model y=x1-x3/ type=SEM;
spatialeffects x1-x3;
spatialid SID;
run;
/*-- SDEM : Taylor approximation with compact W --*/
proc spatialreg data=simdata Wmat=simw_compact
approximation=(Taylor ORDER=50);
model y=x1-x3/ type=SEM;
spatialeffects x1-x3;
spatialid SID;
run;
/*-- SDEM : Chebyshev approximation with full W --*/
proc spatialreg data=simdata Wmat=simw approximation=(ORDER=10);
model y=x1-x3/ type=SEM;
spatialeffects x1-x3;
spatialid SID;
run;
/*-- SDEM : Chebyshev approximation with compact W --*/
proc spatialreg data=simdata Wmat=simw_compact approximation=(ORDER=10);
model y=x1-x3/ type=SEM;
spatialeffects x1-x3;
spatialid SID;
run;
