P R E F M A P - 3 *** EXTERNAL UNFOLDING *** JACQUELINE MEULMAN VERSION - 1.0 *** & *** WILLEM HEISER FEBRUARY 1985 *** PROPERTY FITTING *** J. DOUGLAS CARROLL BELL LABORATORIES MURRAY HILL, NJ 1 JOB TITLE: *** TEST PREFMAP 3 *** ECHO OF PARAMETER CARDS: 2 5 5 2 1 3 0 0 3 3 3 2 0 1 1 0 0 500.00000000 4 3 1 1 2 2 1 1 0 0 5 5 5 5 9 8 0 0 0 0 2 DATA SPECIFICATIONS: NUMBER OF ROW POINTS (THESE ARE FITTED) IS 5 NUMBER OF COLUMN POINTS (THESE ARE GIVEN) IS 5 OPTION SET SELECTION: 2 0 = ALL ROWS SAME OPTION SET 1 = ALL ROWS DIFFERENT OPTION SETS 2 = SPECIFIED ROWS SAME OPTION SET OPTION SETS START WITH ROWS 1 3 3 ANALYSIS SPECIFICATIONS: THE NUMBER OF DIMENSIONS IS 3 MAXIMUM NUMBER OF ANALYSES IN ANY OPTION SET 3 PRELIMINARY TRANSFORMATION OF CONFIGURATION 2 0 = REMAINS UNCHANGED 1 = WEIGHTED 2 = ROTATED AND WEIGHTED STANDARDIZE EXTERNAL DATA 0 0 = YES (=1+2) 1 = CENTER ONLY 2 = NORMALIZE ONLY 3 = NONE OF THE ABOVE MODELS: 0 = NOT APPLIED, 1 = APPLIED VECTOR MODEL 1 UNFOLDING MODEL 1 WEIGHTED UNFOLDING MODEL 0 GENERAL UNFOLDING MODEL 0 THE NUMBER OF NON-METRIC ITERATIONS IS 50 THE CONVERGENCE CRITERION IS 0.10E-04 4 PRINT/PLOT OPTIONS: 0 = NONE PRINT INPUT: 3 1 = TARGET CONFIGURATION 2 = EXTERNAL DATA 3 = 1 & 2 PRINT RESULTS ACROSS OPTION SETS 1 1 = COMPLETE RESULTS 2 = FIT 3 = 2 & CRITERION-PREDICTED VALUES SELECTED RESULTS ACROSS ANALYSES 1 SCATTER&TRANSFORMATION PLOT FOR N ROWS, N = 2 PAIRWISE PLOTS IDEAL POINTS/VECTORS, DIM = 2 HISTORY OF NON-METRIC REGRESSION 1 STATISTICS FOR METRIC ANALYSES 1 STORE OUTPUT: 0 1 = COORDINATES 2 = LIKE 1 + WEIGHTS 3 = LIKE 2 + ROTATION MATRICES STORE OUTPUT: 0 1 = PREDICTED VALUES 2 = LIKE 1 + CRITERION 5 UNIT NUMBERS FOR INPUT/OUTPUT THE CONFIGURATION WILL BE READ FROM UNIT 5 THE EXTERNAL DATA WILL BE READ FROM UNIT 5 THE OPTIONS WILL BE READ FROM UNIT 5 UNIT NUMBER FOR SCRATCH FILE 1 9 UNIT NUMBER FOR SCRATCH FILE 2 8 OUTPUT UNIT FOR THE COORDINATES 0 OUTPUT UNIT FOR THE WEIGHTS 0 OUTPUT UNIT FOR THE ROTATION MATRICES 0 OUTPUT UNIT FOR PREDICTED&CRITERION VALUES 0 *** WARNING *** THE PRELIMINARY TRANSFORMATION WILL NOT BE PERFORMED, BECAUSE THE NUMBER OF TARGET POINTS IS NOT SUFFICIENT. THE CONFIGURATION WILL BE READ WITH FORMAT (8X,3F12.7) THE TARGET CONFIGURATION WILL BE CENTERED: MEAN ORIGINAL DIMENSION 1 0.000 THE TARGET CONFIGURATION WILL BE CENTERED: MEAN ORIGINAL DIMENSION 2 0.000 THE TARGET CONFIGURATION WILL BE CENTERED: MEAN ORIGINAL DIMENSION 3 0.000 TARGET CONFIGURATION (CENTERED) ------------------------------- 1 2 3 1 0.286 0.139 -0.400 2 0.246 -0.071 -0.200 3 0.050 0.109 0.000 4 -0.129 -0.184 0.200 5 -0.453 0.007 0.400 THE EXTERNAL DATA WILL BE READ WITH FORMAT (5F7.3) 5 ROWS OF THE EXTERNAL DATA ------------------------------- 1 2 3 4 5 1 1.500 3.500 1.500 1.500 3.000 2 6.500 6.000 4.895 5.273 1.000 3 -9.000 -7.677 -8.115 -7.625 -5.182 4 3.000 3.000 3.000 3.000 3.000 ROW 4 WILL BE OMITTED FROM THE ANALYSIS SINCE IT HAS ZERO VARIANCE 5 9.000 8.667 8.077 8.375 8.000 MODEL: V = VECTOR U = UNFOLDING W = WEIGHTED UNFOLDING G = GENERAL UNFOLDING REGRESSION: M = METRIC P = NON-METRIC, PRIMARY APPROACH TO TIES S = NON-METRIC, SECONDARY APPROACH TO TIES ANALYSIS OPTION SET: 1 2 3 1 VM VP 2 VS UP WM *** WARNING *** OPTION 3 WILL NOT BE APPLIED. EITHER THE MODEL HAS NOT BEEN REFERRED TO ON CARD 3 OR THE NUMBER OF TARGET POINTS IS NOT SUFFICIENT TO FIT THIS MODEL. METRIC REGRESSION ================================================================= METRIC FIT 0.306 VARIANCE 1.000 V.A.F. 0.094 COORDINATES ----------- 1 2 3 1 0.108 0.112 0.100 CRITERION VALUES (EXTERNAL DATA, POSSIBLY TRANSFORMED BY MONOTONE FUNCTION) ---------------- 1 2 3 4 5 1 -0.803 1.491 -0.803 -0.803 0.918 PREDICTED VALUES ---------------- 1 2 3 4 5 1 -0.176 0.040 -0.480 0.397 0.219 SLOPE 27.33365 INTERCEPT 0.00000 VECTOR MODEL .--+------+------+------+------+------+------+------+------+------+------+---. 1.491 I * I 1.450 I I 1.408 I I 1.367 I I 1.325 I I 1.283 I I 1.242 I I 1.200 I I 1.159 I I 1.117 I I 1.076 I I 1.034 I I 0.993 I I 0.951 I I 0.909 I * I 0.868 I I 0.826 I I 0.785 I I 0.743 I I 0.702 I I 0.660 I I 0.619 I I 0.577 I I 0.535 I I 0.494 I I 0.452 I I 0.411 I D I 0.369 I I 0.328 I I 0.286 I I 0.245 I I 0.203 I D I 0.162 I I 0.120 I I 0.078 I I 0.037 I D I -0.005 I I -0.046 I I -0.088 I I -0.129 I I -0.171 I D I -0.212 I I -0.254 I I -0.296 I I -0.337 I I -0.379 I I -0.420 I I -0.462 I D I -0.503 I I -0.545 I I -0.586 I I -0.628 I I -0.670 I I -0.711 I I -0.753 I I -0.794 I M I .--+------+------+------+------+------+------+------+------+------+------+---. -0.803 -0.574 -0.344 -0.115 0.115 0.344 0.574 0.803 1.032 1.262 1.491 PRIMARY APPROACH TO TIES ================================================================================================= METRIC FIT 0.306 VARIANCE 1.000 V.A.F. 0.094 HISTORY OF NON-METRIC REGRESSION -------------------------------- DIFFERENCE WITH ITERATION FIT PRECEDING ITERATION 1 0.92946 0.62341 2 0.94096 0.01150 3 0.94956 0.00860 4 0.95847 0.00891 5 0.96705 0.00858 6 0.97473 0.00769 7 0.98120 0.00646 8 0.98526 0.00406 9 0.98549 0.00023 10 0.98549 0.00000 NON-METRIC FIT 0.985 COORDINATES ----------- 1 2 3 1 0.369 0.258 0.390 CRITERION VALUES (EXTERNAL DATA, POSSIBLY TRANSFORMED BY MONOTONE FUNCTION) ---------------- 1 2 3 4 5 1 0.500 0.500 -2.000 0.500 0.500 PREDICTED VALUES ---------------- 1 2 3 4 5 1 0.612 0.241 -1.942 0.714 0.375 SLOPE 41.88269 INTERCEPT 0.00000 VECTOR MODEL .--+------+------+------+------+------+------+------+------+------+------+---. 0.714 I D I 0.665 I I 0.616 I D I 0.566 I I 0.517 I M * * I 0.468 I I 0.419 I I 0.370 I D I 0.321 I I 0.272 I I 0.222 I D I 0.173 I I 0.124 I I 0.075 I I 0.026 I I -0.023 I I -0.073 I I -0.122 I I -0.171 I I -0.220 I I -0.269 I I -0.318 I I -0.367 I I -0.417 I I -0.466 I I -0.515 I I -0.564 I I -0.613 I I -0.662 I I -0.712 I I -0.761 I I -0.810 I I -0.859 I I -0.908 I I -0.957 I I -1.006 I I -1.056 I I -1.105 I I -1.154 I I -1.203 I I -1.252 I I -1.301 I I -1.351 I I -1.400 I I -1.449 I I -1.498 I I -1.547 I I -1.596 I I -1.646 I I -1.695 I I -1.744 I I -1.793 I I -1.842 I I -1.891 I I -1.940 I D I -1.990 I * I .--+------+------+------+------+------+------+------+------+------+------+---. -1.013 -0.741 -0.470 -0.199 0.073 0.344 0.616 0.887 1.158 1.430 1.701 STATISTICS ACROSS OPTIONS FOR ROW 1 -------------------------------------- THE STATISTICS GIVEN BELOW DEPEND ONLY ON THE METRIC FIT, NOT ON THE NON-METRIC FIT. VECTOR MODEL, P.VAF. = 0.094, F = 0.034 WITH 3 AND 1 DEGREES OF FREEDOM METRIC REGRESSION ================================================================= METRIC FIT 0.961 VARIANCE 1.000 V.A.F. 0.923 COORDINATES ----------- 1 2 3 2 -0.520 0.250 -0.060 CRITERION VALUES (EXTERNAL DATA, POSSIBLY TRANSFORMED BY MONOTONE FUNCTION) ---------------- 1 2 3 4 5 2 0.907 0.650 0.083 0.277 -1.916 PREDICTED VALUES ---------------- 1 2 3 4 5 2 0.724 1.074 -0.012 -0.073 -1.712 SLOPE 8.02532 INTERCEPT 0.00000 VECTOR MODEL .--+------+------+------+------+------+------+------+------+------+------+---. 1.074 I D I 1.020 I I 0.965 I I 0.911 I * I 0.857 I I 0.803 I I 0.749 I D I 0.695 I I 0.640 I * I 0.586 I I 0.532 I I 0.478 I I 0.424 I I 0.370 I I 0.316 I I 0.261 I * I 0.207 I I 0.153 I I 0.099 I * I 0.045 I I -0.009 I D I -0.064 I D I -0.118 I I -0.172 I I -0.226 I I -0.280 I I -0.334 I I -0.388 I I -0.443 I I -0.497 I I -0.551 I I -0.605 I I -0.659 I I -0.713 I I -0.768 I I -0.822 I I -0.876 I I -0.930 I I -0.984 I I -1.038 I I -1.093 I I -1.147 I I -1.201 I I -1.255 I I -1.309 I I -1.363 I I -1.417 I I -1.472 I I -1.526 I I -1.580 I I -1.634 I I -1.688 I D I -1.742 I I -1.797 I I -1.851 I I -1.905 I * I .--+------+------+------+------+------+------+------+------+------+------+---. -2.000 -1.701 -1.402 -1.103 -0.804 -0.505 -0.206 0.093 0.392 0.691 0.990 PRIMARY APPROACH TO TIES ================================================================================================= METRIC FIT 0.961 VARIANCE 1.000 V.A.F. 0.923 HISTORY OF NON-METRIC REGRESSION -------------------------------- DIFFERENCE WITH ITERATION FIT PRECEDING ITERATION 1 0.99313 0.03253 2 0.99790 0.00478 3 0.99934 0.00143 4 0.99979 0.00045 5 0.99993 0.00014 6 0.99998 0.00005 7 0.99999 0.00001 8 1.00000 0.00000 NON-METRIC FIT 1.000 COORDINATES ----------- 1 2 3 2 -0.247 0.405 0.374 CRITERION VALUES (EXTERNAL DATA, POSSIBLY TRANSFORMED BY MONOTONE FUNCTION) ---------------- 1 2 3 4 5 2 1.034 1.034 -0.200 -0.200 -1.667 PREDICTED VALUES ---------------- 1 2 3 4 5 2 1.033 1.037 -0.201 -0.202 -1.666 SLOPE 6.29832 INTERCEPT 0.00000 VECTOR MODEL .--+------+------+------+------+------+------+------+------+------+------+---. 1.096 I I 1.045 I M M I 0.994 I I 0.943 I I 0.891 I I 0.840 I I 0.789 I I 0.738 I I 0.687 I I 0.636 I I 0.585 I I 0.534 I I 0.482 I I 0.431 I I 0.380 I I 0.329 I I 0.278 I I 0.227 I I 0.176 I I 0.125 I I 0.073 I I 0.022 I I -0.029 I I -0.080 I I -0.131 I I -0.182 I M M I -0.233 I I -0.285 I I -0.336 I I -0.387 I I -0.438 I I -0.489 I I -0.540 I I -0.591 I I -0.642 I I -0.694 I I -0.745 I I -0.796 I I -0.847 I I -0.898 I I -0.949 I I -1.000 I I -1.051 I I -1.103 I I -1.154 I I -1.205 I I -1.256 I I -1.307 I I -1.358 I I -1.409 I I -1.460 I I -1.512 I I -1.563 I I -1.614 I I -1.665 I M I -1.716 I I .--+------+------+------+------+------+------+------+------+------+------+---. -1.916 -1.634 -1.352 -1.069 -0.787 -0.505 -0.223 0.060 0.342 0.624 0.907 STATISTICS ACROSS OPTIONS FOR ROW 2 -------------------------------------- THE STATISTICS GIVEN BELOW DEPEND ONLY ON THE METRIC FIT, NOT ON THE NON-METRIC FIT. VECTOR MODEL, P.VAF. = 0.923, F = 3.981 WITH 3 AND 1 DEGREES OF FREEDOM SECONDARY APPROACH TO TIES ================================================================================================= METRIC FIT 0.898 VARIANCE 1.000 V.A.F. 0.807 HISTORY OF NON-METRIC REGRESSION -------------------------------- DIFFERENCE WITH ITERATION FIT PRECEDING ITERATION 1 0.98603 0.08762 2 0.99826 0.01223 3 0.99979 0.00153 4 0.99997 0.00019 5 1.00000 0.00002 6 1.00000 0.00000 NON-METRIC FIT 1.000 COORDINATES ----------- 1 2 3 3 0.488 0.224 0.277 CRITERION VALUES (EXTERNAL DATA, POSSIBLY TRANSFORMED BY MONOTONE FUNCTION) ---------------- 1 2 3 4 5 3 -0.898 -0.724 -0.724 0.728 1.617 PREDICTED VALUES ---------------- 1 2 3 4 5 3 -0.897 -0.725 -0.724 0.729 1.617 SLOPE 14.88136 INTERCEPT 0.00000 PRIMARY APPROACH TO TIES ================================================================================================= METRIC FIT 1.000 VARIANCE 1.000 V.A.F. 1.000 HISTORY OF NON-METRIC REGRESSION -------------------------------- DIFFERENCE WITH ITERATION FIT PRECEDING ITERATION 1 1.00000 0.00000 NON-METRIC FIT 1.000 IDEAL POINT ----------------------- 1 2 3 3 -0.891 -0.162 -0.903 CRITERION VALUES (EXTERNAL DATA, POSSIBLY TRANSFORMED BY MONOTONE FUNCTION) ---------------- 1 2 3 4 5 3 -1.167 -0.124 -0.469 -0.083 1.843 PREDICTED VALUES ---------------- 1 2 3 4 5 3 -1.167 -0.124 -0.469 -0.083 1.843 SLOPE 15.93741 INTERCEPT -28.74561 STATISTICS ACROSS OPTIONS FOR ROW 3 -------------------------------------- THE STATISTICS GIVEN BELOW DEPEND ONLY ON THE METRIC FIT, NOT ON THE NON-METRIC FIT. PERFECT FIT FOR OPTION 2. NO STATISTICS. VECTOR MODEL, P.VAF. = 0.807, F = 1.395 WITH 3 AND 1 DEGREES OF FREEDOM SECONDARY APPROACH TO TIES ================================================================================================= METRIC FIT 0.997 VARIANCE 1.000 V.A.F. 0.994 HISTORY OF NON-METRIC REGRESSION -------------------------------- DIFFERENCE WITH ITERATION FIT PRECEDING ITERATION 1 1.00000 0.00285 2 1.00000 0.00000 NON-METRIC FIT 1.000 COORDINATES ----------- 1 2 3 5 0.311 0.232 0.463 CRITERION VALUES (EXTERNAL DATA, POSSIBLY TRANSFORMED BY MONOTONE FUNCTION) ---------------- 1 2 3 4 5 5 1.502 0.770 -0.960 -0.227 -1.086 PREDICTED VALUES ---------------- 1 2 3 4 5 5 1.502 0.770 -0.960 -0.227 -1.086 SLOPE 23.54391 INTERCEPT 0.00000 PRIMARY APPROACH TO TIES ================================================================================================= METRIC FIT 1.000 VARIANCE 1.000 V.A.F. 1.000 HISTORY OF NON-METRIC REGRESSION -------------------------------- DIFFERENCE WITH ITERATION FIT PRECEDING ITERATION 1 1.00000 0.00000 NON-METRIC FIT 1.000 ANTI-IDEAL POINT ---------------------------- 1 2 3 5 -2.369 -1.184 -2.932 CRITERION VALUES (EXTERNAL DATA, POSSIBLY TRANSFORMED BY MONOTONE FUNCTION) ---------------- 1 2 3 4 5 5 1.547 0.653 -0.931 -0.131 -1.138 PREDICTED VALUES ---------------- 1 2 3 4 5 5 1.547 0.653 -0.931 -0.131 -1.138 SLOPE 2.73802 INTERCEPT 43.19809 STATISTICS ACROSS OPTIONS FOR ROW 5 -------------------------------------- THE STATISTICS GIVEN BELOW DEPEND ONLY ON THE METRIC FIT, NOT ON THE NON-METRIC FIT. PERFECT FIT FOR OPTION 2. NO STATISTICS. VECTOR MODEL, P.VAF. = 0.994, F = 58.234 WITH 3 AND 1 DEGREES OF FREEDOM SUMMARY OF RESULTS: (PROPORTION OF TOTAL VARIANCE ACCOUNTED FOR ONLY GIVEN FOR METRIC OPTIONS) MODEL ' VM ' N = 2 AVERAGE FIT = 0.633 ROOT MEAN SQUARED FIT = 0.713 TOTAL VARIANCE = 2.000 TOTAL VARIANCE ACCOUNTED FOR = 1.016 PROPORTION OF TOTAL VARIANCE ACCOUNTED FOR = 0.508 MODEL ' UP ' N = 2 AVERAGE FIT = 1.000 ROOT MEAN SQUARED FIT = 1.000 MODEL ' VP ' N = 2 AVERAGE FIT = 0.993 ROOT MEAN SQUARED FIT = 0.993 MODEL ' VS ' N = 2 AVERAGE FIT = 1.000 ROOT MEAN SQUARED FIT = 1.000 ANALYSIS 1 COORDINATES ---------------------- 1 VM 0.108 0.112 0.100 2 VM -0.520 0.250 -0.060 3 VS 0.488 0.224 0.277 4 VS 0.000 0.000 0.000 5 VS 0.311 0.232 0.463 ANALYSIS 2 COORDINATES ---------------------- 1 VP 0.369 0.258 0.390 2 VP -0.247 0.405 0.374 3 UP -0.891 -0.162 -0.903 4 UP 0.000 0.000 0.000 5 UP -2.369 -1.184 -2.932 ANALYSIS 2 WEIGHTS ------------------ 3 UP 1.000 1.000 1.000 4 UP 0.000 0.000 0.000 5 UP -1.000 -1.000 -1.000 ANALYSIS 3 COORDINATES ---------------------- 1 N.A. 0.000 0.000 0.000 2 N.A. 0.000 0.000 0.000 3 N.A. 0.000 0.000 0.000 4 N.A. 0.000 0.000 0.000 5 N.A. 0.000 0.000 0.000 IDEAL POINTS AND/OR VECTORS (INTEGERS) IN TARGET CONFIGURATION. ANALYSIS 1 DIM 1 (X-AXIS) VS DIM 2 (Y-AXIS) .--+------+------+------+------+------+------+------+------+------+------+---. 0.537 I I 0.519 I I 0.500 I I 0.482 I I 0.464 I I 0.446 I I 0.427 I I 0.409 I I 0.391 I I 0.373 I I 0.354 I I 0.336 I I 0.318 I I 0.300 I I 0.281 I I 0.263 I I 0.245 I 2 I 0.226 I 5 3 I 0.208 I I 0.190 I I 0.172 I I 0.153 I I 0.135 I A I 0.117 I C 1 I 0.099 I I 0.080 I I 0.062 I I 0.044 I I 0.026 I I 0.007 I E M I -0.011 I I -0.029 I I -0.048 I I -0.066 I B I -0.084 I I -0.102 I I -0.121 I I -0.139 I I -0.157 I I -0.175 I D I -0.194 I I -0.212 I I -0.230 I I -0.248 I I -0.267 I I -0.285 I I -0.303 I I -0.322 I I -0.340 I I -0.358 I I -0.376 I I -0.395 I I -0.413 I I -0.431 I I -0.449 I I -0.468 I I .--+------+------+------+------+------+------+------+------+------+------+---. -0.520 -0.420 -0.319 -0.218 -0.117 -0.016 0.085 0.186 0.286 0.387 0.488 IDEAL POINTS AND/OR VECTORS (INTEGERS) IN TARGET CONFIGURATION. ANALYSIS 2 DIM 1 (X-AXIS) VS DIM 2 (Y-AXIS) .--+------+------+------+------+------+------+------+------+------+------+---. 0.740 I I 0.718 I I 0.695 I I 0.672 I I 0.649 I I 0.626 I I 0.603 I I 0.581 I I 0.558 I I 0.535 I I 0.512 I I 0.489 I I 0.467 I I 0.444 I I 0.421 I I 0.398 I 2 I 0.375 I I 0.352 I I 0.330 I I 0.307 I I 0.284 I I 0.261 I 1 I 0.238 I I 0.216 I I 0.193 I I 0.170 I I 0.147 I A I 0.124 I I 0.101 I C I 0.079 I I 0.056 I I 0.033 I I 0.010 I E M I -0.013 I I -0.035 I I -0.058 I I -0.081 I B I -0.104 I I -0.127 I I -0.150 I I -0.172 I 3 I -0.195 I D I -0.218 I I -0.241 I I -0.264 I I -0.287 I I -0.309 I I -0.332 I I -0.355 I I -0.378 I I -0.401 I I -0.423 I I -0.446 I I -0.469 I I -0.492 I I -0.515 I I .--+------+------+------+------+------+------+------+------+------+------+---. -0.891 -0.765 -0.639 -0.513 -0.387 -0.261 -0.135 -0.009 0.117 0.243 0.369 ANALYSIS 2 *** NOT PLOTTED *** 5 UP -2.369 -1.184 *** SEVERELY OUT OF RANGE *** STOP