Mds Assignment.docx

AMA Assignment Multidimensional Scaling Avijit Banerjee Sec B, 170103048

Dataset – HBAT_MDS Case Processing Summary Cases

180

Sources

18

Objects

10

Proximities

Total Proximities

810a

Missing Proximities

0

Active Proximitiesb

810

a. Sum over sources of all strictly lower-triangular proximities. b. Active proximities include all non-missing proximities.

Interpretation: a) The no. of objects to be considered are 10 b) With respect to the 10 objects, data is read from 18 sources c) The total no. of cases considered for the scaling is 180

Goodness of Fit

Stress and Fit Measures Normalized Raw Stress

.08328

Stress-I

.28858a

Stress-II

.81673a

S-Stress

.21181b

Dispersion Accounted For (D.A.F.) Tucker's Coefficient of Congruence

.91672

.95746

PROXSCAL minimizes Normalized Raw Stress. a. Optimal scaling factor = 1.091. b. Optimal scaling factor = .956.

Interpretation a) The value of stress is 0.083 and is acceptable b) Stress is minimized when the objects are placed in a configuration such that the distances between the objects best match the original distances c) A trade-off must be made between fit of the solution and the number of dimensions d) The stress value varies for different dimensions; hence we have taken the number of dimensions to be 2 for an acceptable stress value

Common Space

Final Coordinates Dimension 1

2

var1

-.488

-.246

var2

-.467

-.435

var3

-.009

-.504

var4

.739

.120

var5

.650

-.285

var6

.222

.405

var7

-.534

.456

var8

.173

.818

var9

.325

-.449

var10

-.611

.121

Interpretation: a) The above table represents the coordinates for the various objects taken in the twodimensional space b) Here the two dimensions form the axes of the plot c) The measures above have been calculated on the basis of Identity scaling model

Interpretation: a) All the objects are plotted and represented graphically here b) The objects closer to each other have the minimum dissimilarity, whereas the ones far apart have maximum dissimilarity