Hybrid Distatis
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Hybrid Distatis

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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......

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.

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  • 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