The Analysis of Changes over Time in the Number of Students Using Functional Principal Component Analysis in European Countries
DOI:
https://doi.org/10.15678/krem.740Keywords:
functional data, longitudinal data, functional principal component analysis, higher educationAbstract
Principal component analysis (PCA) transforms an original set of variables into a new orthogonal set called principal components. Functional principal component analysis (FPCA) has the same advantages as classical principal component analysis while also enabling the analysis of dynamic data. The main difference between them is that PCA is based on multidimensional data and FPCA is based on functional data. The functional data are curves, surfaces or anything else varying over a continuum. They are not a single observation. The main aim of the paper is to show the usefulness of applying functional principal component analysis in order to analyse longitudinal data. The paper presents an example of how this method has been used based on the analysis of changes in the number of students (over time) in chosen European countries. Visualisation of the results makes it possible to compare countries and detect outliers.
Downloads
References
Daniele M. [2006], Functional Principal Components Analysis to Study Environmental Data, http://www.sis-statistica.it/files/pdf/atti/Spontanee%202006_677-680.pdf (dostęp: 5.12.2013).
Eurostat Statistics [2012], http://epp.eurostat.ec.europa.eu/portal/page/portal/statistics/search_database?_piref458_1209540_458_211810_211810.node_code=educ_enrl8, (dostęp: 30.10.2012).
Hair J.F. et al. [1998], Multivariate Data Analysis with Readings, Prentice-Hall, New York.
Hall P., Müller H.G., Wang J.L. [2006], Properties of Principal Component Methods for Functional and Longitudinal Data Analysis, „The Annals of Statistics", vol. 34, nr 3. DOI: https://doi.org/10.1214/009053606000000272
Harman H. [1975], Modern Factor Analysis, The University of Chicago Press, Chicago.
Ingrassia S., Costanzo G.D. [2005], Functional Principal Component Analysis of Financial Time Series [w:] New Developments in Classification and Data Analysis, red. M. Vichi et al., Springer, Berlin.
Ramsay J.O., Hooker G., Graves S. [2009], Functional Data Analysis with R and MATLAB, Springer, New York.
Ramsay J.O., Silverman B.W. [2005], Functional Data Analysis, Springer, New York.
