Published

2013-01-01

Correspondence Analysis of Contingency Tables with Subpartitions on Rows and Columns

Análisis de correspondencias de tablas de contingencia con subparticiones en filas y columnas

Keywords:

Multidimensional contingency table, Principal component analysis (en)
Análisis en componentes principales, tabla de contingencias multidimensional. (es)

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Authors

  • Campo Elías Pardo Universidad Nacional de Colombia
  • Mónica Bécue-Bertaut Universidad Politécnica de Cataluña
  • Jorge Eduardo Ortiz Universidad Santo Tomás
We present Intra-Table Correspondence Analysis using two approaches: Correspondence Analysis with respect to a model and Weighted Principal Component Analysis. In addition, we use the relationship between Correspondence Analysis and the Log-Linear Models to provide a deeper insight into the interactions that each Correspondence Analysis describes. We develop in detail the Internal Correspondence Analysis as an Intra-Table Correspondence Analysis in two dimensions and introduce the Intra-blocks Correspondence Analysis. Moreover, we summarize the superimposed representations and give some aids to interpret the graphics associated to the subpartition structures of the table. Finally, the methods presented in this work are illustrated by their application to the standardized public test data collected from Colombian secondary education students in 2008.
Para presentar los análisis de correspondencias intra-tablas, se usan los enfoques del análisis de correspondencias con respecto a un modelo y del análisis en componentes principales ponderado. Adicionalmente, se utiliza la relación de los análisis de correspondencias con los modelos log-lineales para entender mejor las interacciones que cada análisis de correspondencias describe. Se desarrolla de manera detallada el análisis de correspondencias interno como un análisis de correspondencias intra-tablas en dos dimensiones y se introduce el análisis de correspondencias intrabloques. Por otra parte, se resumen las representaciones superpuestas y las ayudas para la interpretación de las gráficas asociadas a la estructura de subparticiones de la tabla. Finalmente, se ilustran los procedimientos con el análisis de una tabla de contingencia construida a partir de los resultados de las pruebas de estado realizadas a los estudiantes de educación media en Colombia en el año 2008.

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Correspondence Analysis of Contingency Tables with Subpartitions on Rows and Columns. (2013). Revista Colombiana De Estadística, 36(1), 115-144. https://revistas.unal.edu.co/index.php/estad/article/view/39612

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