I presents a new method called Hybrid DISTATIS that can be applied to the analysis of sorting task and object characteristics data. Hybrid DISTATIS allows to project the object, the characteristics, and the assessor for each object in a map, which is a combining Principal Component Analysis Biplot (PCA Biplot) and DISTATIS method. In these maps, the proximity between two objects or assessor points reflects their similarities, the proximity between characteristic and axis vector reflects their correlations, and therefore these maps can be read using the same rules as standard metric multidimensional scaling (MDS) and PCA Biplot methods. Technically, Hybrid DISTATIS started by transforming the individual sorting task data into cross-product matrices as in classical MDS and evaluating the similarity between these matrices initially. Computes a compromise matrix which is the best aggregate of the individual cross-product matrices, than analyzes it with PCA. After that computes a column effect matrix as a characteristic coordinates with PCA Biplot. The individual matrices and characteristic coordinates are then projected onto the compromise space. The quality of Hybrid DISTATIS map obtained based on the eigenvalue cumulative percent of the compromise matrix. In this paper, the application using sorting task from the college ranks in 2010 is presented, which is published on a website by Webometrics, 4ICU, and QS, as an assessor and the college that became the objects are ITB, ITS, IPB, Unair, Undip, UGM, UI, and Unpad, with the characteristics variable are the number of students and the accreditation values.

1. ANALYZING OBJECTS, OBJECT CHARACTERISTICS
AND ASSESSOR IN SORTING TASK AND
CHARACTERISTICS DATA USING HYBRID DISTATIS
IRLANDIA GINANJAR
Department of Statistics
Padjadjaran University
The 5th International Conference on Research and
Education in Mathematics (ICREM5)
ITB Bandung - INDONESIA
22-24 October 2011

2. Introduction
Introduction
Methods
General principle
An Example
Concluding
Remarks
Back to Title
Sorting task is done by the assessor on several objects
simultaneously based on a perception of similarity, which is a
simple method for collecting data of similarity.
Sorting task
Similarity between
objects and assessors
Object characteristic
Assessors Two-dimensional
Maps Based on An Overall
Assessment of The Object
Project the object, the
characteristics, and the assessor
for each object in a map

3. Introduction
Comparison of various methods of mapping objects:
Introduction
Objects and
Assessors Map
(Sorting Task)
Methods
MDS
General principle
MCA
BIPLOT
An Example
INDSCAL
PARAFAC
GPA
Concluding
Remarks
Back to Title
DISTATIS
Objects and
Characteristics
Map
(Metrics data)
Objects,
Characteristics,
and Assessors
Map
Non-iterative
Method

4. Methods
Flowcharts analysis of the data
Introduction
a
Sorting Task Data
Methods
Create an Indicator Matrix
Transform an indicators matrix
to a co-occurrence matrix
Normalize a cross-product matrix
Compute a between-assessors
similarity matrix
Transform a co-occurrence
matrix to a distance matrix
Compute eigenvectors and
eigenvalues from a between-assessor
similarity matrix
An Example
Transform a distance matrix to
a cross-product matrix
Compute factor scores from a
between-assessor similarity matrix
Concluding
Remarks
a
b
General principle
Back to Title

5. Methods
b
c
Mapping the assessor from two
dimension of a between-assessor
similarity matrix factor scores
Compute factor scores
from a compromise matrix
Introduction
Methods
General principle
Assessors perceptual
map based on an overall
assessment of objects
Compute correlations
between characteristic
variables and compromise
matrix factor scores
Derive an optimal set of weights
An Example
Concluding
Remarks
Back to Title
Compute a column effect matrix
Compute a compromise matrix
Compute the assessors
cross-product matrices
factor scores
Compute eigenvectors and eigenvalues
from a compromise matrix
c
d

6. Methods
Introduction
Methods
d
Mapping objects, object characteristics and assessors for each object
Objects, object characteristics,
and assessors for each object map
General principle
Identify the percentage of variability explained by the map
An Example
Concluding
Remarks
Back to Title
Identify information of assessors similarity based on an
overall assessment objects, the similarity between objects,
the relationship with the objects characteristics and the
similarities between the assessors for each object

7. General principle
Introduction
Methods
1. If we have T assessors, N objects, and Z characteristics, so each
assessor sorts the objects with the constraint that he or she uses more
than 1 group and less than N groups.
2. Represent the sorts by an indicator matrix (L[t]) for each assessor in
which one row represents an object and one column represents a
group. A value of 1 in this matrix means that the object represented
by the row was put in to the group represented by the column.
3. Transform L[t] to a co-occurrence matrix
General principle
4. Transform R[t] to a distance matrix
An Example
5. Transform D[t] to a cross-product matrix
Concluding
Remarks
~
6. Normalize a cross-product matrix S [ t ]
Back to Title

8. General principle
Introduction
Methods
General principle
An Example
Concluding
Remarks
Back to Title
7. Compute The RV coefficient between two individuals S[t] and S[t*]
(Assessor order to t and t*)
The RV coefficient is an element of inter-assessor similarity matrix
(C)
8. Compute eigenvectors and eigenvalues from C with
eigendecomposition procedure
where is the diagonal matrix of eigenvalues, P is a matrix of
corresponding eigenvectors, and ei is the i th eigenvector of C

9. General principle
9. Compute factor scores from C
Introduction
The first two columns of G are the coordinates point for mapping
the assessor based on the overall assessment of the product.
Methods
General principle
An Example
Concluding
Remarks
Back to Title
10. Derive an optimal set of weights
11. Compute a compromise matrix
12. Compute eigenvectors and eigenvalues from S[+]
where is the diagonal matrix of eigenvalues, V is a matrix of
corresponding eigenvectors of S[+]

10. General principle
13. Compute factor scores from S[+]
Introduction
14. Compute correlations between characteristic variables (Z) and F
Methods
General principle
An Example
Concluding
Remarks
Back to Title
15. Compute a column effect matrix
16. Compute the assessors cross-product matrices factor scores

11. General principle
Introduction
Methods
General principle
An Example
Concluding
Remarks
Back to Title
17. Mapping objects, object characteristics and assessors for each object
in one map
The first two columns of F are the coordinate points for mapping the
object, the first two columns of H' are the coordinate points for
mapping the characteristic vector, and The first two columns of F[t]
are the coordinate points for mapping the tth assessor for each object.

12. An Example
Introduction
Methods
General principle
An Example
Concluding
Remarks
Back to Title

13. An Example
Introduction
Methods
General principle
An Example
Concluding
Remarks
Back to Title

14. An Example
Introduction
Methods
General principle
An Example
Concluding
Remarks
Back to Title
Coordinates

15. An Example
Introduction
Methods
General principle
An Example
Concluding
Remarks
Back to Title

16. An Example
Introduction
Methods
General principle
An Example
Concluding
Remarks
Back to Title

17. An Example
Introduction
Methods
General principle
An Example
Concluding
Remarks
Back to Title

18. An Example
Introduction
Methods
General principle
An Example
Concluding
Remarks
Back to Title
Coordinates

19. Concluding Remarks
Introduction
Methods
General principle
An Example
Concluding
Remarks
Back to Title
1. Hybrid DISTATIS produces map, where objects, object characteristics,
and the assessor for each object in a single map, because the mapping
object on DISTATIS or PCA Biplot are both based on a factors scores
compromise matrix.
2. The mapping quality of Hybrid DISTATIS map obtained by cumulative
percentage of variability from compromise matrix.
3. The closer distance between the objects that more and more like, the
farther distance between the objects that more and more different, it
can also be used to categorize objects visually.
4. The closer assessors of an object so between the assessors are
assessing more similar objects, the farther assessors of an object
between the assessors are assessing more different objects.
5. The angle between the vector of characteristics and the axis on the
map close to 00 or 3600 then the vector has a very close positive
correlation with the axis, if the angle between the axis and the
characteristic vector map near 1800 then the vector have a very close
negative correlation with axis, if the angle between the characteristics
vector and the axis on the map close to 900 or 2700 then the vectors
are not correlated

20. Recommendation
Introduction
Methods
General principle
An Example
Concluding
Remarks
Back to Title
• If the data come from the sample and the desired analysis
results can be presented the population, should use the
probability sampling techniques.
• Develop other Version of Hybrid DISTATIS data types (other
than sorting data), as long as the data can be transformed into
a distance matrix can then be used Hybrid DISTATIS
• Euclidean distance matrix, obtained based on Pythagoras
theorem, uses the number of squares in its calculations. The
number of squares is very sensitive in presence of outliers, it
would require the development of robust versions of Hybrid
DISTATIS using the algorithm robust eigendecomposition to
obtain robust eigenvectors and eigenvalues.

21. Thank You