Yoshio Takane , Forrest W. Young & a l s c a l pc alternating least squares scaling Rostyslaw. Lewyckyj. adaptation by b. erichson & a. bischoff psychometric laboratory final change: febr. 1990 the university of north carolina chapel hill, n.c. 27514 Copyright 1977 by f. w. Young, y. Takane & r. j. Lewyckyj job title: TITLE: 12 CARS, 10 ATTRIBUTES (STANDARDIZED), ARBEITSBUCH MAFO S.61 data specifications- nrow - number of row stimuli 10 row stimuli ncol - number of column stimuli 12 column stimuli ns - number of matrices 1 matrix ndtyp- measurement level 2 = interval nsim - data type 5 = rectangular-similarity nps - measurement process 1 = discrete (tie) nwc - measurement conditionality 1 = matrix-conditional cut - data cutoff -10.0000000 analysis specifications- nwe - model type 0 Simple Euclidean model (Default) ndim - number of dimensions (maximum) 2 dimensions (maximum) ndmn - number of dimensions (minimum) 2 dimensions (minimum) nnc - negative weights permitted 0 = negative weights not permitted i/o options- ndt - print data, distances and disparities 1 = do print npt - plot results 1 = do plot nph - punch results 0 = do not punch indata- data input unit number 1 = read data from cards initx - initial stimulus coordinates 0 = compute initxc- initial column stimulus coordinates 0 = compute initw - initial subject weights 0 = compute initws- initial stimulus weights 0 = compute algorithmic options- maxit- maximum number of iterations 99 iterations (maximum) epsi - convergence criterion 0.0003000 = minimum sstress improvement stmin- minimum sstress 0.0050000 = minimum sstress cutoff noulb- initial missing data estimates 0 = ulbounds maximum problem size : 38000 words required problem size: 5528 input data format- (30F6.2) input data matrix 1 1 2 3 4 5 6 7 8 9 10 1 -1.030 1.400 -0.360 -1.050 -1.290 1.750 -0.290 -0.180 1.170 -0.820 2 -0.250 -0.380 -1.490 -0.810 -0.450 1.370 0.750 0.260 0.400 -0.900 3 0.000 -1.390 -1.430 -0.600 0.350 2.020 0.860 0.160 0.860 -0.030 4 -0.910 -0.500 -1.360 -0.470 -1.000 1.110 0.610 1.720 1.030 -0.220 5 -1.280 0.170 -1.100 -0.540 -0.500 1.750 0.060 0.480 1.190 -0.110 6 -1.240 2.090 -1.240 -0.240 -1.240 0.700 -0.240 -0.050 1.440 -0.240 7 -1.270 1.070 -1.730 -0.250 -1.230 1.070 0.700 0.440 1.090 -0.710 8 -1.030 2.080 -1.030 0.270 -1.720 0.270 -0.170 -0.250 1.390 -0.250 9 0.750 -1.580 1.880 -0.860 1.710 -0.040 0.240 0.170 -0.890 -0.480 10 -0.990 -0.320 -1.550 -0.660 -0.320 1.450 0.450 0.790 0.450 -0.100 11 12 1 -0.200 0.920 2 -0.690 2.190 3 -1.300 0.490 4 -1.050 1.030 5 -1.450 1.330 6 -0.240 0.500 7 -0.240 1.060 8 0.610 -0.170 9 -0.790 -0.110 10 -1.100 1.900 TITLE: 12 CARS, 10 ATTRIBUTES (STANDARDIZED), ARBEITSBUCH MAFO S.61 iteration history for the 2 dimensional solution sstress (in squared distances) formula 2 is used. iteration sstress improvement 1 0.25000 2 0.22122 0.02878 3 0.20604 0.01518 4 0.19803 0.00801 5 0.19375 0.00427 6 0.19131 0.00245 7 0.18984 0.00146 8 0.18893 0.00092 9 0.18833 0.00059 10 0.18793 0.00040 11 0.18765 0.00028 alscal message: iterations stopped because sstress improvement less than 0.000300 stress and squared correlation (rsq) in distances rsq values are the proportion of variance of the scaled data (disparities) in the partition (row, matrix, or entire data) which is accounted for by their corresponding distances. kruskal's stress formula 2 is used. stress = 0.266 rsq = 0.934 configuration derived in 2 dimensions stimulus coordinates dimension stimulus plot 1 2 number symbol column 1 a 1.8734 0.1345 2 b -1.4068 1.1814 3 c 1.7810 1.1901 4 d 0.4776 1.4949 5 e 1.8393 -0.7554 6 f -0.3677 -0.6193 7 g 0.6243 -0.4026 8 h 0.4874 -0.4552 9 i -0.8419 0.1013 10 j 0.9557 0.8872 11 k 0.2617 1.8529 12 l -0.2739 -0.6443 row 1 A -1.1937 0.1188 2 B -0.5312 -1.0307 3 C 0.2359 -1.3450 4 D -0.7396 -0.8498 5 E -0.8219 -0.8073 6 F -1.2644 0.4048 7 G -1.2636 -0.1093 8 H -1.1067 1.1042 9 I 1.8812 -0.4550 10 J -0.6060 -0.9964 TITLE: 12 CARS, 10 ATTRIBUTES (STANDARDIZED), ARBEITSBUCH MAFO S.61 derived stimulus configuration dimension 1 (horizontal) vs dimension 2 (vertical) Y +--------------------------------------------------:--------------------------------------------------+ 2.5 | | | | | | | | | | | | | | | 2.0 | | | | | k | | | | | | | | | | 1.5 | | d | | | | | | | | b | c | | H | | 1.0 | | | | | j | | | | | | | | | | 0.5 | | | | F | | | | | | | | | A i | a | 0.0 0--------------------------------------------------0--------------------------------------------------0 | G | | | | | | | | | | g | -0.5 | | h I | | f l | | | | | | ED | e | | | | -1.0 | JB | | | | | | | | | | C | | | | -1.5 | | | | | | | | | | | | | | | -2.0 | | | | | | | | | | | | | | | -2.5 | | | +:---------:---------:---------:---------:---------0---------:---------:---------:---------:---------:+ -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 x TITLE: 12 CARS, 10 ATTRIBUTES (STANDARDIZED), ARBEITSBUCH MAFO S.61 optimally scaled data (disparities) subject 1 1 2 3 4 5 6 7 8 9 10 1 3.067 1.084 3.162 2.165 3.156 1.108 1.891 1.776 0.352 2.283 2 2.672 2.379 3.206 2.720 2.386 0.443 1.315 1.170 1.174 2.427 3 2.207 3.014 2.969 2.850 1.708 0.944 1.019 0.925 1.804 2.345 4 2.792 2.138 3.243 2.642 2.581 0.438 1.435 1.289 0.957 2.427 5 2.855 2.073 3.281 2.644 2.662 0.492 1.502 1.356 0.909 2.456 6 3.149 0.790 3.145 2.055 3.313 1.361 2.054 1.951 0.520 2.272 7 3.146 1.299 3.310 2.368 3.170 1.031 1.911 1.785 0.471 2.433 8 3.134 0.310 2.889 1.632 3.484 1.875 2.295 2.230 1.037 2.074 9 0.590 3.673 1.648 2.402 0.303 2.255 1.258 1.394 2.779 1.630 10 2.725 2.320 3.237 2.717 2.457 0.446 1.366 1.220 1.123 2.447 11 12 1 2.264 1.195 2 2.991 0.464 3 3.198 0.867 4 2.882 0.509 5 2.872 0.572 6 2.104 1.443 7 2.485 1.125 8 1.560 1.937 9 2.819 2.163 10 2.978 0.484 TITLE: 12 CARS, 10 ATTRIBUTES (STANDARDIZED), ARBEITSBUCH MAFO S.61 scattergram (plot of linear fit) distances (vertical) vs disparities (horizontal) Y +--------------------------------------------------:--------------------------------------------------+ 3.7 | x | | | | | | x| | | 3.3 | x x| | x x x | | x x x | | x x 3x | | x | 3.0 | x x xx | | | | x xx x x | | x 2 | | x x x | 2.7 | x xxx | | x | | | | xx xx x x x | | x xx x | 2.3 | x x x | | x x2 x | | x x x | | x x | | x 3 | 2.0 | | | x x x x | | x | | x x x | | x | 1.7 | x x x | | x | | x | | x x | | x 2 x | 1.3 | x x x | | x x | | x x x | | x x x x | | x x x | 1.0 | x x | | x x | | x | | x | | | 0.6 | | | x x | | x x x x | |x x x 2 | | x | 0.3 | x x | +:---------:---------:---------:---------:---------0---------:---------:---------:---------:---------:+ 0.1 0.4 0.8 1.1 1.5 1.8 2.1 2.5 2.8 3.1 3.5 x STEP0 - Note: END card encountered in input file.