INDSCAL is a program designed for the analysis of individual differences for two or more subjects. INDSCAL is generally not used to analyze data for a single subject. INDSCAL requires as input, a separate data matrix for each subject or group of subjects. Broadly defined, a subject may be an actual individual, or more often, a group of individuals aggregated together because of some common characteristic.
INDSCAL performs two types of analysis: an analysis of individual differences and a canonical decomposition analysis. The analysis of individual differences identifies weights that each subject uses to evaluate the stimuli. The stimuli are identified in terms of a set of underlying dimensions that are common to all subjects. In the individual differences analysis, the canonical decomposition analysis is used to identify the perceptual dimensions underlying the stimulus space.
It should be noted that a separate canonical decomposition analysis may be performed. In this case, rectangular data matrices may be analyzed, identifying the underlying dimensions of each of the n dimensional input matrices.
When performing individual differences analysis, INDSCAL input data is generally of some type of similarity or dissimilarity data. The analysis may be conducted on lower half or full symmetric matrices. The lower half matrices may be either similarity, dissimilarity, Euclidean distance, correlation, or covariance measures. The full matrices may be read in as either similarity or dissimilarity measures.
INDSCAL performs an n way analysis. The n=three way analysis is by far the most common. In this situation, n2 and n3 define the n2 by n3 matrix of similarity judgments, and n1 defines the number of slices in this 3 dimensional matrix. Slices are here defined as respondents or respondent groups.
The INDSCAL solution identifies the underlying dimensions common to the stimuli. Importances of these dimensions are reported. Plots of the importance weights used by the individuals in evaluating the stimuli are produced. Also produced are plots of the stimuli in the underlying dimensional space. Plots for the individuals are not produced, but the plot coordinates for the individuals are easy to compute and could be easily graphed in a program such as Lotus 1-2-3 or Harvard Graphics.
INDSCAL is a computer program capable of performing two kinds of analyses, namely,
CANDECOMP analysis and INDIFF analysis.
Before going into a more detailed description, it is essential to clarify the relationship of these two
analyses. CANDECOMP is used for the more general analysis called 'Canonical decomposition of
N-way tables,' while INDIFF performs the analysis of individual differences in multidimensional
scaling described by Carroll and Chang (1968). Nevertheless, CANDECOMP actually forms the
core of INDIFF analysis. By using the appropriate options provided in the program, the user is
able to use INDSCAL to do either CANDECOMP or INDIFF analysis.
In the ensuing paragraphs, there will be no mention of their specific names when the description
applies to both analyses.
CANDECOMP is a method for decomposing arbitrary N-way tables into a kind of product of N
matrices of appropriate dimensions. The N-way tables are assumed to have n1, n2,...nN
components respectively, where N is less than or equal to 7 (as presently programmed). The N
matrices, into which this N-way table is decomposed, will be of the order r x n1, r x n2,..., r x nN,
respectively, where r is the common dimensionality of the several spaces defined by the matrices
CANDECOMP takes as input rectangular data matrices.
INDIFF uses the CANDECOMP method to do individual differences analysis. In this case the
input may be the square matrices of similarities, dissimilarities, Euclidean distances or scalar
product matrices. If any one of the first three serves as input, an early step is to convert the data
to scalar products.
INDIFF treats the first of the N matrices into which the N-way table is decomposed as the subjects' weight matrix and matrices 2 and 3 as stimulus matrices. Matrices 2 and 3 should asymptotically be equal. In practice matrix 2 is set equal to matrix 3 as a last step and the other matrices (1, 4,...N) are recomputed accordingly. The output of INDSCAL consists of the N matrices resulting from the analysis. In addition, plots for each pair of the dimensions in each matrix are generated showing the ni points (where i=1,...N) in r dimensions.
1. In the case of CANDECOMP analysis
Let n1, n2,...nN be respectively the number of components in the N-way tables, where N is less
than or equal to 7. The data can be viewed as many rectangular matrices (slices) each of order n2
(rows) by n3 (columns). A 3-way table would correspond to a stack of n1 such matrices (slices).
A 4-way table would then be composed of n4 such 3-way tables as units. In the same manner we
can construct data for higher way tables.
The n2 by n3 slices described above are read in as follows: The first data line (or lines) has n3
values corresponding to the first row of the first rectangular matrix (slice) in the first n1 unit,. this
is followed by the second row and down to the n2th row. Each matrix is followed by the next
without interruption.
2. In the case of INDIFF analysis
The data structure for INDIFF is basically the same as in CANDECOMP. However, in the
INDIFF case n2 and n3 are ordinarily assumed to be identical, that is every two-way matrix
derived by holding n1 and n4...nN constant is symmetric.
The n2 by n3 matrix may initially be similarity, dissimilarity or Euclidean distance matrix. They can
be entered in the form of a full symmetric matrix or a lower half matrix without diagonal. If so
there are options for converting them to scalar product matrices, by equations given in Torgerson
(1958) as referred to in Carroll and Chang (1968).
In the most common situation, say a 3-way analysis, the n1 matrices (each of n2 rows and n3 columns) will correspond to individuals, and these matrices will be read in one at a time.
Initial Configuration
The analysis starts with (N-1) sets of matrices. That is the program requires that the initial
matrices 2 through N be either supplied by the user or generated in the program. If to be read in,
the Ith matrix must be entered as an r x nI matrix, where r is the common dimensionality specified
by the user and I=2, 3,...N.
Option on Method of Analysis
Instead of solving for several dimensions simultaneously, the user may choose the option of doing
separate one dimensional analyses, then combining them to form a single r dimensional analysis.
While this results in a less general solution than does the more usual solution, it assures certain
orthogonality properties for successive components.
Solution for Weight Matrices for Fixed Stimulus Matrices (in INDIFF analysis)
This option is used when the coordinates of N stimulus points in K dimensions have been
obtained, say from some multidimensional scaling procedure and the user would like to find the
subjects' weights for this fixed stimulus space.
The program reads in the initial matrices, proceeds with the iterative procedure solving for the
remaining matrices while keeping matrices 2 and 3 unchanged throughout the analysis. In the
case of a 3-way analysis, this procedure will 'converge' in one iteration,. in higher way cases more
iterations will be required.
Equating The Stimulus Matrices (in INDIFF analysis)
At the end of the iterative procedure, the program provides the option of equating the 2 stimulus
matrices, matrices 2 and 3. It is essential that in the solution space matrix 2 should be identical
to 3 if the input data is in the form of a lower half or full symmetric matrix.
After equating matrices 2 and 3, the iterative procedure continues, but matrices 2 and 3 are kept
fixed while the remaining tables are estimated by the iterative procedure (this is similar to the
option in 3 for estimating) weight matrices with a fixed stimulus matrix, except that the fixed
matrix is an internally computed one rather than one provided as input by the user).
Separate Solutions in Spaces of Different Dimensions.
On the parameter line (see Section IV) if MAXDIM is set to 4 and MINDIM to 1, the program will compute successively in spaces of dimensions 4, 3, 2 and 1. The initial configuration for each successive dimensions is taken from the solution of the previous computation.
PARAMETERS:
N, MAXDIM, MINDIM, IRDATA, ITMAX, ISET, IOY, IDR, ISAM, IPUNSP, IRN, IVEC, IP,
IA, IS, CRIT
The parameter variables are read as FREE FORMAT .
N - number of ways (N <_ 7)
MAXDIM - Maximum number of dimensions (Max. = 10)
MINDIM - Minimum number of dimensions (Min. = 1)
(MAXDIM must be <_ 10 or (MAXDIM * Max. N1) <_ 4000)
IRDATA -
IRDATA causes scalar products are computed except for options 4 and 5. Additive Constants
are estimated except for options 3, 4 and 5.
ITMAX - Maximum number of iterations. (Max. = 50). Usually from 15 to 20 iterations is
sufficient.
ISET
IOY
IDR
ISAM
IPUNSP
IRN
IVEC
IP
IA
IS
CRIT
Line 2. NWT(1), NWT(2)...NWT(N) are read in FREE format.
NWTN(I) is the name used in the program for ni, i=1,...N ni < = 64000 where n1 must be < = 100, n2 and n3 must be < = 45.
Line 3. The format for reading in data.
Line 4. Data set, in the form specified in option IRDATA.
Line 5. This set of commands is present only if IRN=0.
Required are:
a. The format for reading in the initial matrices.
b. Initial matrices - matrices 2 to N. Each matrix must be entered as a dimension by ni matrix where i=2,3,...N.
Read in matrix 2 first then followed by 3 and up to matrix N. Note that if matrix 2 is identical to matrix 3, read in matrix 2 twice followed by matrix 4...N.
1. Carroll, J.D. and Chang, J.J. "A New Method for Dealing with Individual Difference in Multidimensional Scaling." Unpublished report, Bell Telephone Laboratories, 1968.
1. This paper was modified for the PC-MDS version of INDSCAL by Scott M. Smith
INDSCAL SAMPLE DATA 3 3 2 2 25 1 0 1 0 0 '12345677' 0 0 1 0 .001 10 10 10 (2X,9F2.0) 0116 018147 01563271 0187684471 016035219834 01849498579999 0150877973199245 019925539852179984 01169290837944241898 0209 029070 02876506 0287778383 023379258939 02868699229040 0281305788693997 027420947805819288 02232672940276812005 0349 039696 03979294 0368129093 037744889026 03979394259349 0354769294202493 034748929435189423 03214790926867875515 0423 049951 04992378 0490162249 047455509913 04148877755070 0425954899997999 046036692421539999 04008972817771745171 0562 057716 05981455 0576224047 058416168107 05178036936090 0576938680943619 057420163805180671 05107278929286160299 0685 068215 06972856 0651313643 067927078207 06138438877682 0682997368804020 066924302716122880 06158078907266170595 0710 075375 07999999 0787276599 076066729999 07969990109075 0798999198883499 077315909909569575 07546284999553859149 0814 086147 08799677 0872211273 086612288113 08666475417182 0851673293496686 080720677115567669 08195106882581500883 0911 099069 09722690 0993176924 093934369880 09268277855399 0980747599938713 097308913517179991 09246290768564772465 1069 106358 10768579 1052145181 106139358336 10809093067885 1028878394644490 108020929851238033 10782840993671826213
I N D S C A L |
INDIVIDUAL DIFFERENCES SCALING |3 3 2 2 25 1 0 1 0 0 '12345677' 0 0 1 0 .001
BY DR. J. D. CARROLL AND JIH JIE CHANG | 10 10 10
PC-MDS VERSION |(2X,9F2.0)
|0116
ANALYSIS TITLE: SCHIFFMAN COLA DATA PP. 33-34 |018147
DATA IS READ FROM FILE: SRY.DAT |01563271
OUTPUT FILE IS: TEST2.PRN |0187684471
|016035219834
INDIFF- INDIVIDUAL DIFFERENCES ANALYSIS USING CANONICAL DECOMPOSITION |01849498579999
OF 3 WAY TABLE IN 3 DIMENSIONS |0150877973199245
|019925539852179984
TITLE: SCHIFFMAN COLA DATA PP. 33-34 |01169290837944241898
PARAMETERS |0209
N NO. OF STIMULI 3 |029070
NF DIMENSION OF SOLUTION 3 |02876506
MAXDIM MAXIMUM NO. OF DIMENSIONS 3 |0287778383
MINDIM MINIMUM NO. OF DIMENSIONS 2 |023379258939
IRDATA TYPE OF DATA INPUT 2 |02868699229040
ITMAX MAXIMUM NO. OF ITERATIONS 25 |0281305788693997
ISET OPTION TO SET MATRIX 2 EQUAL TO MATRIX 3 1 |027420947805819288
IOY SELECT SIMULTANEOUS SOLUTION 0 |02232672940276812005
IDR CORRELATIONS FOR EACH SUBJECT 1 |0349
ISAM SOLVE FOR ALL MATRICES 0 |039696
IPUNSP PRINT SCALAR PRODUCT MATRICES 0 |03979294
IRN RANDOM NUMBER GENERATOR START SET 12345677 |0368129093
CRIT CRITERIA FOR QUITTING ITERATION .001 |037744889026
IVEC MATRIX OR VECTOR FORM FOR DATA 0 |03979394259349
IP OUTPUT NORMALIZED A-MATRIX 0 |0354769294202493
IA PRINT ORIGINAL DATA MATRICES 1 |034748929435189423
IS PRINT INTERMEDIATE ITERATIVE MATRICES 0 |03214790926867875515
|0423
MATRIX SIZES 10 10 10 |049951
***********************************************************************|04992378
*****IDENTIFICATION KEY FOR PLOTS WITH IDENTIFIED POINTS***** |0490162249
PT # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 |047455509913
CHAR 1 2 3 4 5 6 7 8 9 A B C D E F |04148877755070
PT # 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 |0425954899997999
CHAR G H I J K L M N O P Q R S T U |046036692421539999
PT # 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 |04008972817771745171
CHAR V W X Y Z + / = * & $ @ [ ? < |0562
PT # 46 47 48 49 50 |057716
CHAR ( ) " ; ] |05981455
POINT NUMBERS ABOVE 50 IDENTIFIED AS > MULTIPLE POINTS IDENTIFIED AS |0576224047
|058416168107
INITIAL A MATRICES |05178036936090
MATRIX 1 |0576938680943619
1 1.0000 1.0000 1.0000 1.0000 1.0000 |057420163805180671
1.0000 1.0000 1.0000 1.0000 1.0000 |05107278929286160299
2 1.0000 1.0000 1.0000 1.0000 1.0000 |0685
1.0000 1.0000 1.0000 1.0000 1.0000 |068215
3 1.0000 1.0000 1.0000 1.0000 1.0000 |06972856
1.0000 1.0000 1.0000 1.0000 1.0000 |0651313643
|067927078207
MATRIX 2 |06138438877682
1 .4257 -.0724 -.1040 .4653 -.1853 |0682997368804020
-.3849 -.0541 .3826 -.0469 -.3351 |066924302716122880
2 .3026 .1942 -.3516 -.2383 .2954 |06158078907266170595
.3221 .3436 -.4229 .1126 -.3603 |0710
3 .4448 .3780 .4900 .0394 -.4308 |075375
-.2456 -.2815 -.4792 -.4867 .2676 |07999999
|0787276599
MATRIX 3 |076066729999
1 -.2278 -.4010 -.2592 -.1818 .3562 |07969990109075
-.1681 .1906 -.4663 -.3248 .2688 |0798999198883499
2 .2047 -.0229 -.2792 -.3818 .3765 |077315909909569575
.4745 -.1201 -.0642 .1184 .3631 |07546284999553859149
3 -.3375 -.3675 -.2500 -.0406 .3499 |0814
-.3976 -.0936 .0471 .3627 .2707 |086147
|08799677
HISTORY OF COMPUTATION |0872211273
ITERATION CORRELATIONS BETWEEN |086612288113
Y(DATA) AND YHAT (R**2) (1-R**2) |08666475417182
0 -.049669 .002467 .997533 |0851673293496686
1 .454765 .206811 .793189 |080720677115567669
2 .568041 .322671 .677329 |08195106882581500883
3 .596882 .356268 .643732 |0911
4 .646604 .418097 .581903 |099069
5 .731775 .535495 .464505 |09722690
6 .775493 .601389 .398611 |0993176924
7 .787444 .620068 .379932 |093934369880
8 .791152 .625921 .374079 |09268277855399
9 .792406 .627908 .372092 |0980747599938713
10 .792987 .628828 .371172 |097308913517179991
11 .793351 .629405 .370595 |09246290768564772465
12 .793609 .629815 .370185 |1069
13 .793797 .630114 .369886 |106358
14 .793933 .630330 .369670 |10768579
15 .794032 .630486 .369514 |1052145181
16 .794102 .630598 .369402 |106139358336
17 .794152 .630678 .369322 |10809093067885
***********************************************************************|1028878394644490
EQUATE MATRIX 2 AND MATRIX 3, ITERATE AGAIN |108020929851238033
INITIAL A MATRICES |10782840993671826213
MATRIX 1 |
1 -.0664 -.1137 -.0796 -.1329 -.0729 |VALUES FOR MATRIX 1: CORRELATION BETWEEN
-.0829 -.1045 -.1228 -.1263 -.0706 |ORIGINAL (Y DATA) AND COMPUTED
2 .0816 .1411 .1785 .0592 .0164 |DISTANCES (Y HAT).
.0192 .1566 .1335 .0483 .1652 |VAF = SQUARE OF THE CORRELATION, OR 1-TRV =
3 -.1752 -.0518 -.0564 -.1774 -.2176 | 1 - TOTAL RESIDUAL VARIANCE
-.2144 -.0534 -.1159 -.1657 -.0566 |
|RESIDUAL VARIANCE =
MATRIX 2 | 1 - CORRELATION BETWEEN Y AND Y-HAT
1 .4911 .5188 -.8744 .5474 .0105 |
-.6039 .1831 -.7128 .4543 -.0141 |
2 .2175 .2887 -.1341 -.7295 .1839 |
.1180 -.6643 .1534 .3295 .2370 |
3 -.5473 .4163 .3463 .2937 .4616 |
.3534 -.4958 -.5589 .4388 -.7081 |
|VALUES FOR MATRIX 2: (SAME AS MATRIX 1)
MATRIX 3 |
1 .4911 .5188 -.8744 .5474 .0105 |
-.6039 .1831 -.7128 .4543 -.0141 |
2 .2175 .2887 -.1341 -.7295 .1839 |
.1180 -.6643 .1534 .3295 .2370 |
3 -.5473 .4163 .3463 .2937 .4616 |
.3534 -.4958 -.5589 .4388 -.7081 |
|
HISTORY OF COMPUTATION |
ITERATION CORRELATIONS BETWEEN |
Y(DATA) AND YHAT (R**2) (1-R**2) |
0 -.420259 .176618 .823382 |
1 .794166 .630700 .369300 |
|
NORMALIZED A MATRICES |
MATRIX 1 |SUBJECT WEIGHTS FOR EACH DIMENSION
1 .64756 .33860 .22328 |(SUBJECT 1 AND 2). IF WEIGHTS ARE
2 .19180 .58402 .37798 |NEGATIVE, THEY ARE TREATED AS 0.
3 .20780 .73905 .26733 |IF WEIGHTS ARE LARGE, DIMENSIONALITY
4 .65787 .24576 .43888 |MAY BE TOO LARGE.
5 .80606 .06846 .24051 |
6 .79444 .07978 .27314 |THE SUM OF SQUARES OF WGTS FOR
7 .19913 .64866 .34416 |DIM 1 + DIM 2 + ...+DIM K
8 .42905 .55362 .40794 |SHOWS HOW WELL THE WEIGHTED STIMULUS
9 .61510 .20031 .41530 |FITS THE DATA FOR EACH SUBJECT.
10 .20900 .68505 .23409 |SUM OF SQUARES ? R2
|MATRIX 2: GIVES THE NORMALIZED STIMULUS
MATRIX 2 |COORDINATES FOR EACH DIMENSION.
1 -.36331 .18661 .29956 |THE SUM OF THE COORDINATES = 0 AND THE
2 .27636 .24774 .31646 |SUM OF THE SQUARED COORDINATES = 1.
3 .22991 -.11510 -.53337 |
4 .19499 -.62599 .33392 |
5 .30641 .15777 .00643 |MATRIX 3: SAME AS MATRIX 2
6 .23464 .10129 -.36838 |
7 -.32917 -.57003 .11166 |
8 -.37103 .13160 -.43481 |
9 .29127 .28272 .27710 |
10 -.47006 .20339 -.00859 |
|
MATRIX 3 |
1 -.36331 .18661 .29956 |
2 .27636 .24774 .31646 |
3 .22991 -.11510 -.53337 |MATRIX 1:
4 .19499 -.62599 .33392 |DIAGONAL = SUM OF SQUARES OF SUBJECT WGTS.
5 .30641 .15777 .00643 |FOR EACH DIM. IF EACH ELEMENT IS DIVIDED
6 .23464 .10129 -.36838 |BY NWT(1), THE NUMBER OF SUBJECTS, THIS
7 -.32917 -.57003 .11166 |SHOWS THE RELATIVE IMPORTANCE OF EACH
8 -.37103 .13160 -.43481 |DIMENSION.
9 .29127 .28272 .27710 |
10 -.47006 .20339 -.00859 |RELATIVE IMPORTANCES DECREASE DOWN THE
|DIAGONAL. OFF DIAGONAL ENTRIES ARE IGNORED.
MATRIX 1 |MATRIX 1:
SUMS OF PRODUCTS |SUMS OF SQUARES: SUM OF MAIN DIAGONAL OF
1 2.85870 1.39817 1.52015 |MATRIX 1: SUM OF SQUARES/NWT(1) =
2 1.39817 2.31003 1.33268 |R-SQUARED (HISTORY OF COMPUTATION).
3 1.52015 1.33268 1.10139 |DIAGONALS SHOW IMPORTANCE OF DIMENSIONS.
SUM OF SQUARES = 6.27013 |MATRIX 2:
|OFF DIAGONALS SHOW CORRELATIONS BETWEEN
MATRIX 2 |DIMENSIONS. IF OFF DIAGONALS ARE CLOSE
SUMS OF PRODUCTS |TO 0, THEN UNCORRELATED.
1 1.00000 .04980 .04597 |IF OFF DIAGONALS ARE LARGE, EITHER THE
2 .04980 1.00000 -.09392 |DIMENSIONS ARE CORRELATED, OR THE
3 .04597 -.09392 1.00000 |SOLUTION HAS NOT PROPERLY CONVERGED.
SUM OF SQUARES = 3.00000 |IF LARGE OFF DIAGONAL VALUES ARE FOUND,
|RERUN ANALYSIS IN A LOWER DIMENSIONALITY.
MATRIX 3 |
SUMS OF PRODUCTS |
1 1.00000 .04980 .04597 |SUM OF SQUARES = # OF DIMENSIONS
2 .04980 1.00000 -.09392 |
3 .04597 -.09392 1.00000 |MATRIX 3: SAME AS MATRIX 2
SUM OF SQUARES = 3.00000 |
THIS IS PLOT OF DIMENSION 1 VS.DIMENSION 2 FOR TABLE NO. 1 |PLOT OF SUBJECT WEIGHTS FOR ALL PAIRS
+....+....+....+....+....+....+....+....+....+....+....+....+ |OF DIMENSIONS OF STIMULUS SPACES
1.20+ | +|FOR ALL PAIRS OF DIMENSIONS.
. | .|
. | .|(TABLE 1 IS PLOT OF SUBJECT WGTS)
.92+ | +|
. | .|
. | 3 .|
.65+ | # +|
. | 2 8 .|
. | .|
.37+ | 1 +|
. | 4 .|
. | 9 .|
.09+ | # +|
.------------------------------0------------------------------.|
. | .|
-.18+ | +|
. | .|
. | .|
-.46+ | +|
. | .|
. | .|
-.74+ | +|
. | .|
. | .|
-1.02+ | +|
. | .|
. | .|
+....+....+....+....+....+....+....+....+....+....+....+....+ |
-1.2 -1.0 -.8 -.6 -.4 -.2 .0 .2 .4 .6 .8 1.0 1.2|
THIS IS PLOT OF DIMENSION 1 VS.DIMENSION 3 FOR TABLE NO. 1 |
+....+....+....+....+....+....+....+....+....+....+....+....+ |
1.20+ | +|
. | .|
. | .|
.92+ | +|
. | .|
. | .|
.65+ | +|
. | .|
. | 4 .|
.37+ | # 8 9 +|
. | # # .|
. | 1 .|
.09+ | +|
.------------------------------0------------------------------.|
. | .|
-.18+ | +|
. | .|
. | .|
-.46+ | +|
. | .|
. | .|
-.74+ | +|
. | .|
. | .|
-1.02+ | +|
. | .|
. | .|
+....+....+....+....+....+....+....+....+....+....+....+....+ |
-1.2 -1.0 -.8 -.6 -.4 -.2 .0 .2 .4 .6 .8 1.0 1.2|
THIS IS PLOT OF DIMENSION 2 VS.DIMENSION 3 FOR TABLE NO. 1 |
+....+....+....+....+....+....+....+....+....+....+....+....+ |
1.20+ | +|
. | .|
. | .|
.92+ | +|
. | .|
. | .|
.65+ | +|
. | .|
. | 4 .|
.37+ | 9 827 +|
. | # A3 .|
. | 1 .|
.09+ | +|
.------------------------------0------------------------------.|
. | .|
-.18+ | +|
. | .|
. | .|
-.46+ | +|
. | .|
. | .|
-.74+ | +|
. | .|
. | .|
-1.02+ | +|
. | .|
. | .|
+....+....+....+....+....+....+....+....+....+....+....+....+ |
-1.2 -1.0 -.8 -.6 -.4 -.2 .0 .2 .4 .6 .8 1.0 1.2|
THIS IS PLOT OF DIMENSION 1 VS.DIMENSION 2 FOR TABLE NO. 2 | TABLE 2 GRAPHS SHOW THE GROUP
+....+....+....+....+....+....+....+....+....+....+....+....+ | STIMULUS SPACE FOR THE RESPECTIVE
1.20+ | +| DIMENSIONS. THE STIMULI (OBJECTS)
. | .| ARE HERE PLOTTED FOR THE AGGREGATE
. | .| OF ALL SUBJECTS.
.92+ | +|
. | .|
. | .|
.65+ | +| INDIVIDUAL PERCEPTUAL SPACES ARE NOT
. | .| PLOTTED. THE COORDINATES CAN, HOWEVER
. | .| BE CALCULATED BY MULTIPLYING THE
.37+ | # +| STIMULUS COORDINATES (MATRIX 2 PLOTTED
. | 5 .| IN TABLE 2) OF EACH DIMENSION BY THE
. | 6 .| SQUARE ROOT OF THE SUBJECT'S WEIGHTS
.09+ | +| FOR THAT DIMENSION. THIS MULTIPLICATION
.------------------------------0------------------------------.| WILL GIVE THE COORDINATE OF THE STIMULUS
. | 3 .| FOR THE INDIVIDUAL ON THE DIMENSION.
-.18+ | +| THESE PERCEPTUAL SPACES ALLOW FOR THE
. | .| COMPARISON OF INDIVIDUAL SUBJECTS
. | .| OR SUBJECT GROUPS IF AGGREGATE
-.46+ | +| SIMILARITIES DATA IS USED.
. 7 | .|
. | 4 .|
-.74+ | +|
. | .|
. | .|
-1.02+ | +|
. | .|
. | .|
+....+....+....+....+....+....+....+....+....+....+....+....+ |
-1.2 -1.0 -.8 -.6 -.4 -.2 .0 .2 .4 .6 .8 1.0 1.2|
THIS IS PLOT OF DIMENSION 1 VS.DIMENSION 3 FOR TABLE NO. 2 |
+....+....+....+....+....+....+....+....+....+....+....+....+ |
1.20+ | +|
. | .|
. | .|
.92+ | +|
. | .|
. | .|
.65+ | +|
. | .|
. | .|
.37+ | 4 +|
. 1 | # .|
. | .|
.09+ 7 | +|
.------------------A-----------0-------5----------------------.|
. | .|
-.18+ | +|
. | .|
. | 6 .|
-.46+ 8 | +|
. | 3 .|
. | .|
-.74+ | +|
. | .|
. | .|
-1.02+ | +|
. | .|
. | .|
+....+....+....+....+....+....+....+....+....+....+....+....+ |
-1.2 -1.0 -.8 -.6 -.4 -.2 .0 .2 .4 .6 .8 1.0 1.2|
THIS IS PLOT OF DIMENSION 2 VS.DIMENSION 3 FOR TABLE NO. 2 |
+....+....+....+....+....+....+....+....+....+....+....+....+ |
1.20+ | +|
. | .|
. | .|
.92+ | +|
. | .|
. | .|
.65+ | +|
. | .|
. | .|
.37+ 4 | +|
. | 129 .|
. | .|
.09+ 7 | +|
.------------------------------0---5A-------------------------.|
. | .|
-.18+ | +|
. | .|
. | 6 .|
-.46+ | 8 +|
. 3 | .|
. | .|
-.74+ | +|
. | .|
. | .|
-1.02+ | +|
. | .|
. | .|
+....+....+....+....+....+....+....+....+....+....+....+....+ |
-1.2 -1.0 -.8 -.6 -.4 -.2 .0 .2 .4 .6 .8 1.0 1.2|
THIS IS PLOT OF DIMENSION 1 VS.DIMENSION 2 FOR TABLE NO. 3 | TABLE 3 IS A REPEAT OF TABLE 2.
+....+....+....+....+....+....+....+....+....+....+....+....+ |
1.20+ | +|
. | .|
. | .|
.92+ | +|
. | .|
. | .|
.65+ | +|
. | .|
. | .|
.37+ | +|
. | # .|
. A 1 | 5 .|
.09+ 8 | 6 +|
.------------------------------0------------------------------.|
. | 3 .|
-.18+ | +|
. | .|
. | .|
-.46+ | +|
. 7 | .|
. | 4 .|
-.74+ | +|
. | .|
. | .|
-1.02+ | +|
. | .|
. | .|
+....+....+....+....+....+....+....+....+....+....+....+....+ |
-1.2 -1.0 -.8 -.6 -.4 -.2 .0 .2 .4 .6 .8 1.0 1.2|
THIS IS PLOT OF DIMENSION 1 VS.DIMENSION 3 FOR TABLE NO. 3 |
+....+....+....+....+....+....+....+....+....+....+....+....+ |
1.20+ | +|
. | .|
. | .|
.92+ | +|
. | .|
. | .|
.65+ | +|
. | .|
. | .|
.37+ | 4 +|
. 1 | # .|
. | .|
.09+ 7 | +|
.------------------A-----------0-------5----------------------.|
. | .|
-.18+ | +|
. | .|
. | 6 .|
-.46+ 8 | +|
. | 3 .|
. | .|
-.74+ | +|
. | .|
. | .|
-1.02+ | +|
. | .|
. | .|
+....+....+....+....+....+....+....+....+....+....+....+....+ |
-1.2 -1.0 -.8 -.6 -.4 -.2 .0 .2 .4 .6 .8 1.0 1.2|
THIS IS PLOT OF DIMENSION 2 VS.DIMENSION 3 FOR TABLE NO. 3 |
+....+....+....+....+....+....+....+....+....+....+....+....+ |
1.20+ | +|
. | .|
. | .|
.92+ | +|
. | .|
. | .|
.65+ | +|
. | .|
. | .|
.37+ 4 | +|
. | 129 .|
. | .|
.09+ 7 | +|
.------------------------------0---5A-------------------------.|
. | .|
-.18+ | +|
. | .|
. | 6 .|
-.46+ | 8 +|
. 3 | .|
. | .|
-.74+ | +|
. | .|
. | .|
-1.02+ | +|
. | .|
. | .|
+....+....+....+....+....+....+....+....+....+....+....+....+ |
-1.2 -1.0 -.8 -.6 -.4 -.2 .0 .2 .4 .6 .8 1.0 1.2|
|
CORRELATION BETWEEN COMPUTED SCORES AND ORIGINAL DATA FOR SUBJECTS |
1 .766075 |
2 .724902 |
3 .815670 |
4 .830497 |
5 .844774 |
6 .844815 |
7 .764019 |
8 .814188 |
9 .770781 |
10 .755986 |
|
AVERAGE SUBJECT CORR. COEFF. = .79317 |
MEAN SQUARE CORR. COEFF. = .63070 |