Application of axes rotation in correspondence analysis as a factor of interpretation optimization

<p style="text-align: justify;">Correspondence analysis gains increasing popularity in modern research practice. The latter is the method of multidimensional data analysis, which studies contingency tables and renders its graphical representation in the form of points in the reduced dimension space. Interpretation of the results is carried out on the basis of the following indicators analysis: the absolute and relative contribution, inertia, mass, the correlation coefficient. There are formal criteria and the boundaries of acceptable values for each of them. However, it is not always possible to interpret the obtained map accurately. The problem of unambiguous interpretation could be solved by the axis rotation option, which is considered in the current graduation thesis.</p><p style="text-align: justify;">Thus, the object of the research is correspondence analysis. The subject of the investigation is the rotation functions application in correspondence analysis. The target of the paper is to study algorithms of axes rotation and their potential applicability in order to optimize solutions in correspondence analysis. Accordingly, the study assumes the implementation of the following tasks:</p><p style="text-align: justify;">1. To consider a simple correspondence analysis as a method of data analysis and, in particular, the mathematical formalism, which is inherent in the method. To illustrate a method with the appropriate correspondence maps in terms of the empirical example.</p><p style="text-align: justify;">2. To study rotation functions typology and the specificity of several of them.</p><p style="text-align: justify;">3. To select an appropriate rotation function using the empirical example.</p><p style="text-align: justify;">4. To discern the specifics of rotations applied to correspondence analysis.</p><p style="text-align: justify;">5. To execute models of correspondence analysis conjugated with the rotation function implementation. To analyse the effectiveness of iterations.</p><p style="text-align: justify;">The graduation thesis consists of four chapters, which illuminate the classical model of a simple correspondence analysis, rotation functions typology, specificity of rotation in correspondence analysis. The last chapter considers the computation of the correspondence analysis with the axes rotation. Such an iterance was carried out using the Matlab programm, and in particular, with the help of special macros CAR. It should be noted that each chapter involves empirical examples (namely, the one cross-cutting example which is considered at different standpoints in accordance with the text subject-matters), illustrating the operation of the described algorithms. In other words, the study includes a simple correspondence analysis example. Furthermore, the factor analysis was also conducted on the same data. The latter helped us to determine the optimal rotation function - varimax. The pivotal outcome of the paper is correspondence analysis involving the varimax rotation. Thus, there is also an empirical research object of the study, which are citizens of 23 European countries, who participated in the values measuring survey. Subject, from an empirical point of view, - is the importance of the self-expression characteristics and life values from the viewpoint of the research participants.</p><p style="text-align: justify;">A unique feature of this work could be found in the consideration of the rotation specifics in correspondence analysis: accounting of profiles masses in the process of axes turning and the structure duality consideration (status of variables coordinates in relation to each other). Following the results of the conducted operations the author was able to prove that it is indeed much easier to conform the process of maps interpretation with the use of rotations, which makes contributions and correlation coefficients more contrast. The calculated Bentler&#39;s simplicity index formally confirms these findings: the after-rotation structure is easier than it was before the axes turn. In other words