Chapter Contents |
Previous |
Next |
The MDS Procedure |
Jacobowitz (1975) collected conditional rank-order data regarding perceived similarity of parts of the body from children of ages 6, 8, and 10 years and from college sophomores. The following analysis includes data from 15 children (6-year-olds) and 15 sophomores. The method of data collection and some results of an analysis are also described by Young (1987, pp. 4-10). A portion of the data is included below. See "Mds Documentation Examples" in the SAS/STAT Sample Program Library for the complete data set.
data body; title 'Jacobowitz Body Parts Data from 6 Yr Olds and Adults'; title2 'First 15 subjects (obs 1-225) are children'; title3 'Second 15 subjects (obs 226-450) are adults'; input (cheek face mouth head ear body arm elbow hand palm finger leg knee foot toe) (2.); if _n_ <= 225 then subject='C'; else subject='A'; datalines; 0 2 1 3 410 5 9 6 7 811121314 2 012 113 3 81011 9 7 4 5 614 3 2 0 1 4 9 511 6 7 810131214 2 1 3 0 4 9 5 611 7 810121314 10 111 2 0 6 3 4 51213 7 814 9 1412 9 613 0 8 7 51011 1 4 2 3 1214111013 5 0 4 1 3 2 6 9 7 8 5 714 8 6 9 1 0 2 3 410111213 1311121014 9 3 4 0 1 2 6 5 7 8 8 6 7 9 4 5 310 1 0 212111314 14 513 6 912 3 4 1 2 0 7 81011 14121311 9 7 4 6 5 310 0 8 1 2 1211141013 4 5 8 6 7 9 1 0 2 3 1214101311 9 4 5 8 6 7 2 3 0 1 13 8 91114 3 6 5 71012 2 4 1 0 0 4 2 311 91412 1 713 8 6 510 7 011 9 1 2 8 3131410 612 4 5 1011 0 3 7 1 813 212 6 914 5 4 4 811 0 1 2 3 9 71310 51412 6 14 61110 0 1 2 4 9 8 5 713 312 11 61412 3 013 2 1 9 5 410 7 8 1412 8 3 1 7 013 2 6 5 911 410 610 914 3 412 0 813 5 711 1 2 131412 1 4 6 2 7 010 9 311 8 5 6 9 711 3 5 112 2 013 810 414 10 6 9 81113 712 2 1 014 5 3 4 6 9 710 4 21214 1 813 0 3 511 13 2 8 3 1 5 9141211 7 6 010 4 1411 8 413 212 9 5 310 6 7 0 1 14 3 4 713 6 2 8 91110 112 5 0 ... 405 lines omitted ... 0 1 2 4 3141210 6 5 81311 7 9 2 0 3 1 414 810 5 612 911 713 2 1 0 4 31412 9 511 71310 6 8 2 1 4 0 314 810 61112 7 9 513 1 3 2 4 01412 9 8 7 5131011 6 131011 114 0 3 7 512 8 2 6 4 9 13 911101214 0 1 3 6 5 2 4 7 8 1012 813 914 1 0 611 4 3 2 5 7 12 911101314 5 4 0 1 3 8 6 2 7 91211131014 5 4 1 0 2 6 7 3 8 10121113 914 6 5 1 3 0 8 7 4 2 121011 91314 2 5 6 8 7 0 1 3 4 1112 9131014 3 2 7 8 4 1 0 5 6 121011 91314 5 8 1 6 7 3 4 0 2 10121113 914 8 7 4 6 2 3 5 1 0 ;
The data are analyzed as row conditional (CONDITION=ROW) at the ordinal level of measurement (LEVEL=ORDINAL) using the weighted Euclidean model (COEF=DIAGONAL) in three dimensions (DIMENSION=3). The final estimates are displayed (PFINAL). The estimates (OUT=OUT) and fitted values (OUTRES=RES) are saved in output data sets. The following statements produce Output 40.1.1:
options ps=60; proc mds data=body condition=row level=ordinal coef=diagonal dimension=3 pfinal out=out outres=res ; subject subject; title5 'Nonmetric Weighted MDS'; run;
Output 40.1.1: Iteration History and Final Estimates for Body Parts Data
|
|
The following statements produce Output 40.1.2:
title1 'Plot of Over-All Fit'; axis1 label=(angle=90 rotate=0) minor=none order=(0 to 5 by 1); axis2 minor=none order=(0 to 5 by 1); proc gplot data=res; plot fitdata*fitdist/vaxis=axis1 haxis=axis2 frame cframe=ligr; run;Output 40.1.2: Plot of Over-All Fit for Body Parts Data
The dimension coefficients are plotted by selecting observations having _TYPE_=`DIAGCOEF' and by using the Subject variable to distinguish children from adults on the plot. The following statements produce Output 40.1.3:
title1 'Plot of configuration'; %plotit(data=out(where=(_type_='CONFIG')), datatype=mds, labelvar=_name_, vtoh=1.75); %plotit(data=out(where=(_type_='CONFIG')), datatype=mds, plotvars=dim3 dim1, labelvar=_name_, vtoh=1.75); run; title1 'Plot of Dimension Coefficients for Each Subject'; %plotit(data=out(where=(_type_='DIAGCOEF')), symtype=vector, symbols='',datatype=mds, place=0, labelvar=subject, vechead=, ls=100, plotopts=hzero vzero); %plotit(data=out(where=(_type_='DIAGCOEF')), plotvars=dim3 dim1, symtype=vector, symbols='', datatype=mds, place=0, labelvar=subject, ls=100, vechead=, plotopts=hzero vzero); run;
The configuration displayed in Output 40.1.3 has a tripodal shape with Body at the apex. The three legs of the tripod can be distinguished in the plot of dimension 2 by dimension 1, which shows three distinct clusters with Body in the center. Dimension 1 separates head parts from arm and leg parts. Dimension 2 separates arm parts from leg parts. The plot of dimension 3 by dimension 1 shows the tripod from the side. Dimension 3 distinguishes the more inclusive body parts (at the top) from the less inclusive body parts (at the bottom).
Output 40.1.3: Plot of Configuration for Body Parts Data
The plots of dimension coefficients in Output 40.1.4 show that children differ from adults primarily in the emphasis given to dimension 2. Children give about the same weight (approximately 1) to each dimension. Adults are much more variable than children, but all have coefficients less than 1.0 for dimension 2, with an average of
about 0.7. Referring back to the configuration plot, you can see that adults consider arm parts to be more similar to leg parts than do children. Many adults also give a high weight to dimension 1, indicating that they consider head parts to be more dissimilar from arm and leg parts than do children. Dimension 3 shows considerable variability for both children and adults.
Output 40.1.4: Plot of Dimension Coefficients for Body Parts Data
Chapter Contents |
Previous |
Next |
Top |
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.