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Application of Correspondence Analysis in Disciplinary Development

Author: LiZhongTao
Tutor: HanYan
School: Jilin University
Course: Probability Theory and Mathematical Statistics
Keywords: Correspondence Analysis SAS Standardization Factor Analysis Multivariate statistical analysis
CLC: O212.4
Type: Master's thesis
Year: 2010
Downloads: 217
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Abstract

Correspondence analysis is a multivariate statistical analysis method developed on the basis of R-factor analysis and Q-factor analysis. This paper we first began to describe the theoretical background of correspondence analysis, and then give the mathematical model. Departure from the original data matrixReference to[11]、[1 2], with the help of transformation and duality of R-factor analysis and Q-factor analysis we can give the mathematical model and calculation method of correspondence analysis.Next we use the methods of correspondence analysis on the instance of disciplinary development of Jilin University and obtained some very meaningful results.Taking into account the data differences of the original data matrix and the requirements to do correspondence analysis, we select as the data normalization formula, reference to[15]、[1 6]. Then we use the“proc corresp”program of the Statistical software SAS and obtain the correspondence analysis results as follows:(1) The principal inertia and the chi-square value, that is the singular value of the matrix Z, eigenvalues of the matrix S R= Z′Z, the contribution rate and cumulative contribution rate of eigenvalues.(2) Sample point coordinates, that is the equivalent to factor analysis of the common factor loading, which denote the coordinates on the dim1 - d im2 plane. So we can classify the samples according to the coordinates of each sample.(3) Summary statistics of sample points, which can reveal the information contained in the sample points corresponds to the common factor dim1、d im2.(4) Partial contributions to inertia for the sample points, revealing the information contained in the sample points in the corresponding expression level of each common factor.(5) Indices of the coordinates that contribute most to inertia for the sample points, which is the coordinates of the samples contribute to the characteristic values of the number of qualitative said.(6)Squared cosines for each sample point, which denote their respective contribution about two common factors.(7)Summary statistics for the column points, you can visually see that the classification of all the professional disciplines.(8)Comparison results of different sample points, with which we can easy to see the specific expertise among different sample points.About each icon text description are given to explain. Finally, compare the correspondence analysis method and other multivariate statistical analysis methods, such as attribute data analysis, principal component analysis, factor analysis and cluster analysis about the results. Thus we not only verify the rationality of the application of correspondence analysis in disciplinary development, but also show the advantages of the correspondence analysis. Correspondence analysis can not only present the close relationship between different sample points and different variables, but also reflect the relationship between variables and samples. This is can not be achieved with other multivariate statistical analysis.Compare the correspondence analysis method and other multivariate statistical analysis methods, we have come to the following results about correspondence analysis:1. Shows the principal inertia and the equivalent to each factor which impact the development of various subjects.2. Gives the classification results of all the professional disciplines, as well as the distance between the professional disciplines or similar degree.3. Compare the correspondence analysis method and other multivariate statistical analysis methods, which also show the advantages and rationality of corresponding analysis.4. Applying the correspondence analysis in disciplinary development has much significance, such as disciplinary development, university orientation, the formulation of education policy and education system.

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CLC: > Mathematical sciences and chemical > Mathematics > Probability Theory and Mathematical Statistics > Mathematical Statistics > Multivariate analysis
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