Imaginary forensic patient's grid 14:10 Saturday, February 10, 1996 9 The following are largely self-explanatory N_COMP is the theoretical maximum no. of principal components which is the lesser of (N_ELEM - 1) or N_CONS N_CONS N_ELEM N_COMP 9 10 9 AV_CONS is the mean rating on the construct VAR_CONS is the total deviation from the construct mean PER_CONS is the percentage of the total variance in the the grid accounted for on that construct MAX_CONS is the highest rating on the construct and MIN_CONS is the lowest rating on the construct AV_CONS VAR_CONS PER_CONS MAX_CONS MIN_CONS 3.9 14.9 9.1805299 6 Dominrg 2.00 3.5 16.5 10.166359 6 Sex attr. 2.00 4.1 18.9 11.645102 6 Easy cont 2.00 4.1 12.9 7.948244 6 Rejecting 2.00 4.4 18.4 11.33703 6 Loving 2.00 3.8 17.6 10.844116 6 Neglectg 2.00 3.5 24.5 15.095502 6 Sex int. 2.00 2.5 30.5 18.79236 5 Protectv 1.00 3.3 8.1 4.9907579 4 Underst 2.00 TOTVAR is the total sum of squares of the deviations from construct means BIAS is Patrick's measure: the mean squared difference between construct means and the mid-rating divided by the absolute half-range (honest!) I think this parametrises the tendency for the ratings on constructs to have means away from the mid-point of the rating scale used. VARI is Patrick's 'variability': the square root of the ratio of the total squared variation from construct means to the product of N_CONS*(N_ELEM - 1), the total square rooted value then divided by the absolute half-range. I think this parametrises the variation from construct means observed against that possible given the rating scale used. TOTVAR BIAS VARI 162.3 0.2239047 0.566209 INTENS Beware, intensity doesn't match that in INGRIDA! 21.305248 My version is 100 times the sum of squared construct intercorrelations divided by the square of N_CONS It may be that they excluded the leading diagonal (which would result in a slightly lower value). Or it may be that they used Spearman correlations or perhaps absolute correlations. *** I need to check this *** Following is full matrix of construct intercorrelations using Pearson correlation coefficients CCORR Dominrg Sex attr. Easy cont Rejecting Loving Neglectg Sex int. Protectv Underst Dominrg 1.00 0.10 0.36 0.51 0.14 0.67 0.13 0.12 -0.52 Sex attr. 0.10 1.00 0.42 0.10 0.06 0.41 0.22 0.33 0.04 Easy cont 0.36 0.42 1.00 -0.39 -0.08 0.23 -0.26 0.31 -0.43 Rejecting 0.51 0.10 -0.39 1.00 0.49 0.61 0.31 0.18 0.26 Loving 0.14 0.06 -0.08 0.49 1.00 -0.01 0.38 0.68 0.39 Neglectg 0.67 0.41 0.23 0.61 -0.01 1.00 -0.14 -0.13 -0.03 Sex int. 0.13 0.22 -0.26 0.31 0.38 -0.14 1.00 0.49 0.04 Protectv 0.12 0.33 0.31 0.18 0.68 -0.13 0.49 1.00 0.16 Underst -0.52 0.04 -0.43 0.26 0.39 -0.03 0.04 0.16 1.00 The following re-expresses those correlations as angular distances, i.e. r=0 -> ang=90 or 270; r=1 -> ang=0; r=-1 -> ang=180 CANG Dominrg Sex attr. Easy cont Rejecting Loving Neglectg Sex int. Protectv Underst Dominrg 0.0 84.5 68.7 59.2 81.7 48.2 82.5 83.3 121.3 Sex attr. 84.5 0.0 64.9 84.1 86.7 65.7 77.1 70.5 87.5 Easy cont 68.7 64.9 0.0 113.0 94.3 76.7 104.8 71.8 115.4 Rejecting 59.2 84.1 113.0 0.0 60.4 52.4 72.0 79.8 74.7 Loving 81.7 86.7 94.3 60.4 0.0 90.6 67.9 47.5 66.8 Neglectg 48.2 65.7 76.7 52.4 90.6 0.0 98.3 97.4 91.9 Sex int. 82.5 77.1 104.8 72.0 67.9 98.3 0.0 60.4 88.0 Protectv 83.3 70.5 71.8 79.8 47.5 97.4 60.4 0.0 80.8 Underst 121.3 87.5 115.4 74.7 66.8 91.9 88.0 80.8 0.0 AV_ELEM is the sum of deviations from the construct means for the element in question (N.B. NOT the mean rating of of the element on all constructs). This follows INGRID MEAN_E _IS_ the mean element rating. This is not provided in INGRID and can be pretty meaningless but is included here partly to underline the distinction! VAR_ELEM is the sum of squared deviations from construct means for the element PER_ELEM expresses the latter as a percentage of the total AV_ELEM MEAN_E VAR_ELEM PER_ELEM -9.1 2.6666667 18.87 U to moth 11.63 0.9 3.7777778 19.07 Moth to U 11.75 -5.1 3.1111111 8.47 U to fath 5.22 -0.1 3.6666667 14.67 Fath to U 9.04 12.9 5.1111111 27.67 U to part 17.05 5.9 4.3333333 11.27 Part to U 6.94 -6.1 3 17.87 U to vict 11.01 -2.1 3.4444444 13.87 Vict to U 8.55 5.9 4.3333333 13.47 U to ther 8.30 -3.1 3.3333333 17.07 Ther to U 10.52 The following is the matrix of Euclidean inter-element distances. A Euclidean distance is the square root of the sum of squared differences between the element ratings on all the constructs EUC U to moth Moth to U U to fath Fath to U U to part Part to U U to vict Vict to U U to ther Ther to U U to moth 0.0 5.3 5.3 5.2 8.7 6.7 5.2 6.4 6.4 6.2 Moth to U 5.3 0.0 6.6 5.4 6.0 4.8 7.5 5.6 6.9 7.6 U to fath 5.3 6.6 0.0 5.2 7.5 5.2 3.9 3.6 5.0 3.5 Fath to U 5.2 5.4 5.2 0.0 6.1 6.6 6.0 6.5 6.0 5.6 U to part 8.7 6.0 7.5 6.1 0.0 5.0 8.3 6.9 5.7 7.7 Part to U 6.7 4.8 5.2 6.6 5.0 0.0 6.0 4.2 4.2 6.2 U to vict 5.2 7.5 3.9 6.0 8.3 6.0 0.0 5.5 6.0 5.9 Vict to U 6.4 5.6 3.6 6.5 6.9 4.2 5.5 0.0 6.3 6.2 U to ther 6.4 6.9 5.0 6.0 5.7 4.2 6.0 6.3 0.0 4.6 Ther to U 6.2 7.6 3.5 5.6 7.7 6.2 5.9 6.2 4.6 0.0 The following is Patrick's 'expected distance' This is the square root of: twice the trace of the element deviation cross-product matrix divided by one less than the number of elements. EXPDIST 6.005553 The following is Patrick's interelement distances It's the Euclidean distances divided by the 'expected' distances. This serves to correct the values to take into account the number of elements and (I think) their deviations from the construct means, i.e. to correct somewhat for the rating scale and how it is being used by the person (I think!) SLATDIST U to moth Moth to U U to fath Fath to U U to part Part to U U to vict Vict to U U to ther Ther to U U to moth 0.00 0.88 0.88 0.87 1.45 1.12 0.87 1.07 1.07 1.03 Moth to U 0.88 0.00 1.10 0.90 1.00 0.80 1.26 0.93 1.14 1.27 U to fath 0.88 1.10 0.00 0.87 1.25 0.87 0.64 0.60 0.83 0.58 Fath to U 0.87 0.90 0.87 0.00 1.01 1.10 1.00 1.08 1.00 0.93 U to part 1.45 1.00 1.25 1.01 0.00 0.83 1.38 1.14 0.96 1.29 Part to U 1.12 0.80 0.87 1.10 0.83 0.00 1.00 0.71 0.71 1.04 U to vict 0.87 1.26 0.64 1.00 1.38 1.00 0.00 0.91 1.00 0.99 Vict to U 1.07 0.93 0.60 1.08 1.14 0.71 0.91 0.00 1.05 1.04 U to ther 1.07 1.14 0.83 1.00 0.96 0.71 1.00 1.05 0.00 0.76 Ther to U 1.03 1.27 0.58 0.93 1.29 1.04 0.99 1.04 0.76 0.00 The following gives the eigenvalues for each component and, usually more comprehensible, the percentage of the total variation in the grid each contains. The rescaling is trivial as the eigenvalues just sum to the total variation in the grid. EIGVAL PERC_VAL 56.117383 PC 1 0.3458 37.472554 PC 2 0.2309 29.637307 PC 3 0.1826 16.980492 PC 4 0.1046 15.311716 PC 5 0.0943 3.6654024 PC 6 0.0226 2.508133 PC 7 0.0155 0.4921727 PC 8 0.0030 0.1148401 PC 9 0.0007 -1.8E-15 -0.0000 The following is the element vectors. These are standardised i.e. don't reflect the variance in the component hence I think the loadings, which are in the next matrix printed, are more useful a reflection of the Principal Component Analysis. EIGVEC PC 1 PC 2 PC 3 PC 4 PC 5 PC 6 PC 7 PC 8 PC 9 Circle radius 8, construct & element loadings plotted Imaginary forensic patient's grid 14:10 Saturday, February 10, 1996 14 U to moth -0.3093 0.5079 -0.1252 0.3923 0.0471 0.2703 0.4162 -0.1062 0.3421 Moth to U 0.3211 0.5485 0.0880 0.1576 -0.2535 -0.2671 -0.1300 0.3074 -0.4653 U to fath -0.2955 -0.1650 0.1408 -0.2447 -0.1954 0.1187 -0.1124 0.7356 0.3159 Fath to U -0.0013 0.2531 -0.5153 -0.4622 0.0765 0.0486 -0.5043 -0.2656 0.1542 U to part 0.6359 -0.1844 -0.1896 -0.2505 0.2353 0.0654 0.5290 0.1269 0.0861 Part to U 0.2686 -0.1567 0.3514 0.3233 0.0389 -0.3968 -0.2893 -0.2214 0.5325 U to vict -0.3899 -0.0382 0.1913 -0.1064 0.7057 -0.3137 0.0585 0.0087 -0.3140 Vict to U -0.0029 -0.0057 0.5909 -0.3288 -0.2473 0.4227 0.0540 -0.4070 -0.1852 U to ther 0.0593 -0.4061 -0.2196 0.5109 0.1048 0.4726 -0.3049 0.0448 -0.3050 Ther to U -0.2860 -0.3535 -0.3128 0.0086 -0.5123 -0.4207 0.2832 -0.2230 -0.1613 E_LOAD PC 1 PC 2 PC 3 PC 4 PC 5 PC 6 PC 7 PC 8 PC 9 U to moth -2.3173 3.1093 -0.6815 1.6164 0.1845 0.5174 0.6591 -0.0745 0.1159 Moth to U 2.4057 3.3574 0.4791 0.6492 -0.9919 -0.5113 -0.2058 0.2156 -0.1577 U to fath -2.2136 -1.0099 0.7667 -1.0085 -0.7645 0.2272 -0.1780 0.5160 0.1071 Fath to U -0.0095 1.5494 -2.8051 -1.9044 0.2995 0.0931 -0.7986 -0.1863 0.0523 U to part 4.7635 -1.1288 -1.0321 -1.0323 0.9206 0.1252 0.8377 0.0890 0.0292 Part to U 2.0119 -0.9595 1.9129 1.3324 0.1523 -0.7597 -0.4582 -0.1554 0.1805 U to vict -2.9209 -0.2337 1.0415 -0.4386 2.7615 -0.6007 0.0926 0.0061 -0.1064 Vict to U -0.0215 -0.0347 3.2169 -1.3549 -0.9678 0.8092 0.0855 -0.2855 -0.0627 U to ther 0.4444 -2.4858 -1.1955 2.1052 0.4102 0.9049 -0.4828 0.0314 -0.1034 Ther to U -2.1428 -2.1638 -1.7029 0.0354 -2.0045 -0.8054 0.4485 -0.1565 -0.0547 The following is th element residuals, i.e. the amount of the squared deviations from the construct means left to be accounted for after extraction of the components up that that PC E_RESI PC 1 PC 2 PC 3 PC 4 PC 5 PC 6 PC 7 PC 8 PC 9 U to moth 13.5002 3.8325 3.3680 0.7552 0.7212 0.4535 0.0190 0.0134 -0.0000 Moth to U 13.2825 2.0101 1.7805 1.3590 0.3752 0.1137 0.0714 0.0249 -0.0000 U to fath 3.5702 2.5504 1.9625 0.9455 0.3611 0.3094 0.2778 0.0115 0.0000 Fath to U 14.6699 12.2693 4.4005 0.7737 0.6839 0.6753 0.0375 0.0027 -0.0000 U to part 4.9789 3.7046 2.6394 1.5738 0.7262 0.7106 0.0088 0.0009 -0.0000 Part to U 7.2221 6.3015 2.6423 0.8670 0.8438 0.2666 0.0567 0.0326 -0.0000 U to vict 9.3385 9.2839 8.1991 8.0067 0.3807 0.0199 0.0114 0.0113 -0.0000 Vict to U 13.8695 13.8683 3.5200 1.6842 0.7476 0.0928 0.0855 0.0039 -0.0000 U to ther 13.2725 7.0931 5.6639 1.2319 1.0636 0.2448 0.0117 0.0107 0.0000 Ther to U 12.4783 7.7964 4.8965 4.8953 0.8772 0.2286 0.0275 0.0030 0.0000 The next three matrices give the construct vectors, loadings and residuals, as for the elements. C_VECT PC 1 PC 2 PC 3 PC 4 PC 5 PC 6 PC 7 PC 8 PC 9 Dominrg 0.1603 -0.4550 -0.2305 -0.1096 -0.4949 0.0265 -0.0183 -0.5512 -0.3903 Sex attr. 0.2306 -0.3105 0.1629 -0.2469 0.6983 0.2532 0.3752 -0.2336 -0.1262 Easy cont 0.0795 -0.4846 0.5508 0.0576 -0.1281 0.1422 -0.3673 -0.0575 0.5265 Rejecting 0.2316 -0.1079 -0.5402 0.1371 0.0317 -0.2188 0.3018 -0.1714 0.6744 Loving 0.4476 0.1408 -0.1151 0.4855 -0.1136 0.7025 0.0174 0.1434 -0.0602 Neglectg 0.0602 -0.5638 -0.3764 0.0820 0.2147 -0.1367 -0.3019 0.5775 -0.2016 Sex int. 0.4631 0.2593 -0.1619 -0.7176 -0.0420 0.1160 -0.3693 0.0960 0.1279 Protectv 0.6616 0.0673 0.3603 0.1880 -0.0784 -0.5620 0.1528 0.1169 -0.1833 Underst 0.0711 0.2014 -0.1191 0.3350 0.4280 -0.1602 -0.6178 -0.4817 -0.0737 C_LOAD PC 1 PC 2 PC 3 PC 4 PC 5 PC 6 PC 7 PC 8 PC 9 Dominrg 1.2005 -2.7854 -1.2550 -0.4517 -1.9367 0.0508 -0.0290 -0.3867 -0.1323 Sex attr. 1.7271 -1.9010 0.8866 -1.0174 2.7323 0.4847 0.5943 -0.1639 -0.0428 Easy cont 0.5953 -2.9664 2.9987 0.2375 -0.5012 0.2723 -0.5818 -0.0403 0.1784 Rejecting 1.7349 -0.6608 -2.9408 0.5651 0.1239 -0.4188 0.4779 -0.1202 0.2285 Loving 3.3533 0.8619 -0.6268 2.0005 -0.4445 1.3449 0.0275 0.1006 -0.0204 Neglectg 0.4506 -3.4515 -2.0490 0.3378 0.8400 -0.2617 -0.4781 0.4052 -0.0683 Sex int. 3.4692 1.5872 -0.8814 -2.9570 -0.1643 0.2221 -0.5848 0.0673 0.0434 Protectv 4.9560 0.4119 1.9614 0.7748 -0.3070 -1.0760 0.2420 0.0820 -0.0621 Underst 0.5329 1.2326 -0.6483 1.3804 1.6747 -0.3068 -0.9785 -0.3379 -0.0250 C_RESI PC 1 PC 2 PC 3 PC 4 PC 5 PC 6 PC 7 PC 8 PC 9 Dominrg 13.4589 5.7003 4.1252 3.9212 0.1704 0.1678 0.1670 0.0175 -0.0000 Sex attr. 13.5171 9.9034 9.1174 8.0823 0.6167 0.3818 0.0287 0.0018 -0.0000 Easy cont 18.5456 9.7459 0.7536 0.6973 0.4460 0.3719 0.0335 0.0318 -0.0000 Rejecting 9.8900 9.4534 0.8052 0.4859 0.4705 0.2951 0.0667 0.0522 -0.0000 Loving 7.1554 6.4124 6.0195 2.0176 1.8200 0.0113 0.0105 0.0004 0.0000 Neglectg 17.3969 5.4841 1.2856 1.1715 0.4659 0.3974 0.1688 0.0047 -0.0000 Sex int. 12.4645 9.9454 9.1686 0.4248 0.3978 0.3484 0.0064 0.0019 -0.0000 Protectv 5.9382 5.7686 1.9214 1.3211 1.2268 0.0691 0.0106 0.0039 -0.0000 Underst 7.8160 6.2966 5.8763 3.9708 1.1663 1.0722 0.1148 0.0006 -0.0000 The following numbering is used in the grid plot ELEMNTS U to moth 1 -2.317276 3.1092995 Moth to U 2 2.4057191 3.3574472 U to fath 3 -2.213552 -1.009851 Fath to U 4 -0.009512 1.5493993 U to part 5 4.7635227 -1.128844 Part to U 6 2.0119316 -0.95947 U to vict 7 -2.920876 -0.233654 Vict to U 8 -0.021537 -0.034729 U to ther 9 0.4444112 -2.485835 Ther to U 10 -2.142832 -2.163764 CONSTRS Dominrg 1 1.200463 -2.785427 Sex attr. 2 1.7271053 -1.900986 Easy cont 3 0.5953028 -2.966426 Rejecting 4 1.7349282 -0.660775 Loving 5 3.3533017 0.8619296 Neglectg 6 0.4506247 -3.451503 Sex int. 7 3.4692262 1.5871621 Protectv 8 4.9559832 0.4118675 Underst 9 0.5329379 1.232631