summary.SimAn: Summary of Simultaneous Analysis

Description

This function summarizes the results of SimAn.

Usage

"summary"(object, oar = 1, oac = 1, ...)

Arguments

object

The output of the simultaneous analysis (class 'SimAn')

oar

Output for active rows (1 = yes, 0 = no)

oac

Output for active columns (1 = yes, 0 = no)

...

Further arguments passed to or from other methods

Value

Total inertia: Total inertia, as a measure of the total variance of the data table
Eigenvalues and percentages of inertia: Eigenvalues or principal inertias and percentages of explained inertia
Output for rows: Masses, chi-squared distances of points to their average, projections of points on each dimension, contributions and squared correlations
Output for columns: Masses, chi-squared distances of points to their average, projections of points on each dimension, contributions and squared correlations
Output for supplementary rows: Masses, chi-squared distances of points to their average, projections of points on each dimension and squared correlations
Output for supplementary columns: Masses, chi-squared distances of points to their average, projections of points on each dimension and squared correlations
Total inertia: Total inertia, as a measure of the total variance of the data table
Eigenvalues and percentages of inertia: Eigenvalues or principal inertias
Output for rows: Masses, chi-squared distances of points to their average, projections of points on each dimension, contributions and squared correlations
Output for columns: Masses, chi-squared distances of points to their average, projections of points on each dimension, contributions and squared correlations
Output for partial rows: Masses, chi-squared distances of points to their average, projections of points on each dimension and squared correlations (if multiple = 0)
Output for partial columns: Masses, chi-squared distances of points to their average, projections of points on each dimension and squared correlations (if multiple = 1)
Projections of tables: Projections of each table on each dimension
Contributions of tables to SA: Contributions of each table to the dimensions
Relation between overall and partial rows: Relation between overall and partial rows (if multiple = 0)
Relation between overall and partial columns: Relation between overall and partial columns (if multiple = 1)
Relation between factors of separate CA: Relation between factors of separate correspondence analysis
Relation between factors of CA and SA: Relation between factors of correspondence analysis and simultaneous analysis
Output for supplementary rows: Masses, chi-squared distances of points to their average, projections of points on each dimension and squared correlations
Output for supplementary columns: Masses, chi-squared distances of points to their average, projections of points on each dimension and squared correlations
Output for supplementary partial rows: Masses, chi-squared distances of points to their average, projections of points on each dimension and squared correlations (if multiple = 0)
Output for supplementary partial columns: Masses, chi-squared distances of points to their average, projections of points on each dimension and squared correlations (if multiple = 1)

Details

The function summary.SimAn gives the detailed numerical results of the SimAn function.

In its first stage simultaneous analysis performs a simple correspondence analysis of each table, so the summary contains the separate correspondence analysis of each table as provided by the CorrAn function.

The joint analysis of all the tables is performed in the second stage of the simultaneous analysis and total inertia, the eigenvalues, percentages of explained inertia and cumulated percentages of explained inertia for all dimensions are listed. The output also contains for the overall rows and for the columns of the tables, the masses, chi-squared distances and, by default restricted to the first two dimensions, projections of points on each dimension or principal coordinates, contributions of the points to the dimensions and squared correlations. For partial rows and for supplementary elements the same results are listed except for contributions of the points to the dimensions.

The output of summary.SimAn also contains the relations between overall rows and partial rows, the relations between the factors of the CA of the different tables, the relations between the factors of the SA and the factors of the separate CA of the different tables, the projections of the tables and the contributions of each table to the principal axes.

References

Goitisolo, B. (2002). El Analisis Simultaneo. Propuesta y aplicacion de un nuevo metodo de analisis factorial de tablas de contingencia. Phd thesis, Basque Country University Press, Bilbao.

Zarraga, A. & Goitisolo, B. (2002). Methode factorielle pour l analyse simultanee de tableaux de contingence. Revue de Statistique Appliquee, L, 47--70

Zarraga, A. & Goitisolo, B. (2003). Etude de la structure inter-tableaux a travers l Analyse Simultanee, Revue de Statistique Appliquee, LI, 39--60.

Zarraga, A. and Goitisolo, B. (2006). Simultaneous analysis: A joint study of several contingency tables with different margins. In: M. Greenacre, J. Blasius (Eds.), Multiple Correspondence Analysis and Related Methods, Chapman & Hall/CRC, Boca Raton, Fl, 327--350.

Zarraga, A. & Goitisolo, B. (2009). Simultaneous analysis and multiple factor analysis for contingency tables: Two methods for the joint study of contingency tables. Computational Statistics and Data Analysis, 53, 3171--3182.

Examples

Run this code

data(shoplifting)
dataSA <- shoplifting

### SA without supplementary elements
SimAn.out <- SimAn(data=dataSA, G=2, acg=list(1:9,10:18), weight= 2,
   nameg=c("M", "F"))

### Summary without output for columns
summary(SimAn.out, oac=0)

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