Ir al contenido

Documat

Finding archetypal patterns for binary questionnaires

  • Ismael Cabero [1] ; Irene Epifanio [2]
    1. [1] Universidad Internacional de La Rioja

      Universidad Internacional de La Rioja

      Logroño, España

    2. [2] Universitat Jaume I

      Universitat Jaume I

      Castellón, España

  • Localización: Sort: Statistics and Operations Research Transactions, ISSN 1696-2281, Vol. 44, Nº. 1, 2020, págs. 39-66
  • Idioma: inglés
  • DOI: 10.2436/20.8080.02.94
  • Enlaces
  • Resumen

    • Archetypal analysis is an exploratory tool that explains a set of observations as mixtures of pure (extreme) patterns. If the patterns are actual observations of the sample, we refer to them as archetypoids. For the first time, we propose to use archetypoid analysis for binary observations. This tool can contribute to the understanding of a binary data set, as in the multivariate case. We illustrate the advantages of the proposed methodology in a simulation study and two applications, one exploring objects (rows) and the other exploring items (columns). One is related to determining student skill set profiles and the other to describing item response functions.

  • Referencias bibliográficas
    • Alcacer, A., Epifanio, I., Ibáñez, M. V., Simó, A. and Ballester, A. (2020). A data-driven classification of 3D foot types by archetypal...
    • Cabero, I. and Epifanio, I. (2019). Archetypal analysis: an alternative to clustering for unsupervised texture segmentation. Image Analysis...
    • Canhasi, E. and Kononenko, I. (2013). Multi-document summarization via archetypal analysis of the content-graph joint model. Knowledge and...
    • Canhasi, E. and Kononenko, I. (2014). Weighted archetypal analysis of the multi-element graph for queryfocused multi-document summarization....
    • Chan, B., Mitchell, D. and Cram, L. (2003). Archetypal analysis of galaxy spectra. Monthly Notices of the Royal Astronomical Society, 338,...
    • Chiu, C.-Y., Douglas, J. A. and Li, X. (2009). Cluster analysis for cognitive diagnosis: Theory and applications. Psychometrika, 74, 633.
    • Cutler, A. and Breiman, L. (1994). Archetypal analysis. Technometrics, 36, 338–347.
    • Davis, T. and Love, B. (2010). Memory for category information is idealized through contrast with competing options. Psychological Science,...
    • de Leeuw, J. and Mair, P. (2009). Gifi methods for optimal scaling in R: The package homals. Journal of Statistical Software, 31, 1–20.
    • Dean, N. and Nugent, R. (2013). Clustering student skill set profiles in a unit hypercube using mixtures of multivariate betas. Advances in...
    • D’Esposito, M. R., Palumbo, F. and Ragozini, G. (2012). Interval archetypes: a new tool for interval data analysis. Statistical Analysis and...
    • Epifanio, I. (2013). H-plots for displaying nonmetric dissimilarity matrices. Statistical Analysis and Data Mining, 6, 136–143.
    • Epifanio, I. (2016). Functional archetype and archetypoid analysis. Computational Statistics & Data Analysis, 104, 24–34.
    • Epifanio, I., Ibáñez, M. V. and Simó, A. (2018). Archetypal shapes based on landmarks and extension to handle missing data. Advances...
    • Epifanio, I., Ibáñez, M. V. and Simó, A. (2020). Archetypal analysis with missing data: see all samples by looking at a few based on...
    • Epifanio, I., Vinué, G. and Alemany, S. (2013). Archetypal analysis: contributions for estimating boundary cases in multivariate accommodation...
    • Eugster, M. J. and Leisch, F. (2009). From Spider-Man to Hero Archetypal Analysis in R. Journal of Statistical Software, 30, 1–23.
    • Eugster, M. J. A. (2012). Performance profiles based on archetypal athletes. International Journal of Performance Analysis in Sport, 12, 166–187.
    • Fernandez, M. and Barnard, A. S. (2015). Identification of nanoparticle prototypes and archetypes. ACS Nano, 9, 11980–11992.
    • Fletcher, R. (2000). Practical Methods of Optimization (Second ed.). John Wiley & Sons.
    • Flynt, A. and Dean, N. (2016). A survey of popular R packages for cluster analysis. Journal of Educational and Behavioral Statistics, 41,...
    • Friedman, J. H. and Tukey, J. W. (1974). A projection pursuit algorithm for exploratory data analysis. IEEE Transactions on Computers, C-23,...
    • Gower, J. C. (1971). A general coefficient of similarity and some of its properties. Biometrics, 27, 857–871.
    • Hastie, T., Tibshirani, R. and Friedman, J. (2009). The Elements of Statistical Learning. Data mining, inference and prediction. 2nd ed.,...
    • Henry, D., Dymnicki, A. B., Mohatt, N., Allen, J. and Kelly, J. G. (2015). Clustering methods with qualitative data: a mixed-methods approach...
    • Hinrich, J. L., Bardenfleth, S. E., Roge, R. E., Churchill, N. W., Madsen, K. H. and Mørup, M. (2016). Archetypal analysis for modeling multisubject...
    • IBM Support (2016). Clustering binary data with K-Means (should be avoided). http://www-01.ibm.com/ support/docview.wss?uid=swg21477401....
    • Jones, M. C. and Rice, J. A. (1992). Displaying the important features of large collections of similar curves. The American Statistician,...
    • Kaufman, L. and Rousseeuw, P. J. (1990). Finding Groups in Data: An Introduction to Cluster Analysis. New York: John Wiley.
    • Lawson, C. L. and Hanson, R. J. (1974). Solving Least Squares Problems. Prentice Hall.
    • Li, S., Wang, P., Louviere, J. and Carson, R. (2003). Archetypal Analysis: A NewWay To Segment Markets Based On Extreme Individuals. In ANZMAC...
    • Linzer, D. A. and Lewis, J. B. (2011). poLCA: An R package for polytomous variable latent class analysis. Journal of Statistical Software,...
    • Lloyd, S. P. (1982). Least squares quantization in PCM. IEEE Transactions on Information Theory, 28, 129–137.
    • Maechler, M., Rousseeuw, P., Struyf, A., Hubert, M. and Hornik, K. (2018). Cluster: Cluster Analysis Basics and Extensions. R package version...
    • Makowski, D. (2016). Package ’neuropsychology’: An R Toolbox for Psychologists, Neuropsychologists and Neuroscientists. (0.5.0).
    • Mazza, A., Punzo, A. and McGuire, B. (2014). KernSmoothIRT: An R package for kernel smoothing in item response theory. Journal of Statistical...
    • Midgley, D. and Venaik, S. (2013). Marketing strategy in MNC subsidiaries: pure versus hybrid archetypes. In P. McDougall-Covin and T. Kiyak,...
    • Millán-Roures, L., Epifanio, I. and Martı́nez, V. (2018). Detection of anomalies in water networks by functional data analysis. Mathematical...
    • Moliner, J. and Epifanio, I. (2019). Robust multivariate and functional archetypal analysis with application to financial time series analysis....
    • Mørup, M. and Hansen, L. K. (2012). Archetypal analysis for machine learning and data mining. Neurocomputing, 80, 54–63.
    • Orús, P. and Gregori, P. (2008). Fictitious Pupils and Implicative Analysis: a Case Study, pp. 321–345. Berlin, Heidelberg: Springer.
    • Pawlowsky-Glahn, V., Egozcue, J. J. and Tolosana-Delgado, R. (2015). Modeling and Analysis of Compositional Data. John Wiley & Sons.
    • Porzio, G. C., Ragozini, G. and Vistocco, D. (2008). On the use of archetypes as benchmarks. Applied Stochastic Models in Business and Industry,...
    • R Development Core Team (2019). R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing....
    • Ragozini, G. and D’Esposito, M. R. (2015). Archetypal networks. In Proceedings of the 2015 IEEE/ACM International Conference on Advances in...
    • Ragozini, G., Palumbo, F. and D’Esposito, M. R. (2017). Archetypal analysis for data-driven prototype identification. Statistical Analysis...
    • Ramsay, J. O. and Silverman, B. W. (2002). Applied Functional Data Analysis. Springer. http://www-01.ibm.com/support/docview.wss?uid=swg21477401
    • Ramsay, J. O. and Silverman, B. W. (2005). Functional Data Analysis (2nd ed.). Springer.
    • Ramsay, J. O. and Wiberg, M. (2017). A strategy for replacing sum scoring. Journal of Educational and Behavioral Statistics, 42, 282–307.
    • Rossi, N., Wang, X. and Ramsay, J. O. (2002). Nonparametric item response function estimates with the EM algorithm. Journal of Educational...
    • Seth, S. and Eugster, M. J. A. (2016a). Archetypal analysis for nominal observations. IEEE Transactions on Pattern Analysis and Machine Intelligence,...
    • Seth, S. and Eugster, M. J. A. (2016b). Probabilistic archetypal analysis. Machine Learning, 102, 85–113.
    • Slater, S., Joksimović, S., Kovanovic, V., Baker, R. S. and Gasevic, D. (2017). Tools for educational data mining: A review. Journal of...
    • Steinley, D. (2006). K-means clustering: A half-century synthesis. British Journal of Mathematical and Statistical Psychology, 59, 1–34.
    • Steinschneider, S. and Lall, U. (2015). Daily precipitation and tropical moisture exports across the Eastern United States: An application...
    • Stone, E. and Cutler, A. (1996). Introduction to archetypal analysis of spatio-temporal dynamics. Physica D: Nonlinear Phenomena, 96, 110–131.
    • Su, Z., Hao, Z., Yuan, F., Chen, X. and Cao, Q. (2017). Spatiotemporal variability of extreme summer precipitation over the Yangtze river...
    • Theodosiou, T., Kazanidis, I., Valsamidis, S. and Kontogiannis, S. (2013). Courseware usage archetyping. In Proceedings of the 17th Panhellenic...
    • Thøgersen, J. C., Mørup, M., Damkiær, S., Molin, S. and Jelsbak, L. (2013). Archetypal analysis of diverse pseudomonas aeruginosa transcriptomes...
    • Thurau, C., Kersting, K., Wahabzada, M. and Bauckhage, C. (2012). Descriptive matrix factorization for sustainability: Adopting the principle...
    • Tsanousa, A., Laskaris, N. and Angelis, L. (2015). A novel single-trial methodology for studying brain response variability based on archetypal...
    • Unwin, A. (2010). Exploratory data analysis. In P. Peterson, E. Baker, and B. McGaw (Eds.), International Encyclopedia of Education (Third...
    • Vinué, G. (2017). Anthropometry: An R package for analysis of anthropometric data. Journal of Statistical Software, 77, 1–39.
    • Vinué, G. and Epifanio, I. (2017). Archetypoid analysis for sports analytics. Data Mining and Knowledge Discovery, 31, 1643–1677.
    • Vinue, G. and Epifanio, I. (2019). Adamethods: Archetypoid Algorithms and Anomaly Detection. R package version 1.2.
    • Vinué, G. and Epifanio, I. (2019). Forecasting basketball players’ performance using sparse functional data. Statistical Analysis and Data...
    • Vinué, G., Epifanio, I. and Alemany, S. (2015). Archetypoids: A new approach to define representative archetypal data. Computational Statistics...
    • Wu, C., Kamar, E. and Horvitz, E. (2016). Clustering for set partitioning with a case study in ridesharing. In IEEE 19th International Conference...
Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno