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

