SimultAnR (version 1.1)

SimAn: Simultaneous Analysis

Description

Simultaneous analysis is a factorial method developed for the joint treatment of a set of several data tables, especially frequency tables whose row margins are different, for example when the tables are from different samples or different time points, without modifying the internal structure of each table. In the data tables rows must refer to the same entities, but columns may be different. With the multiple option tables having the same columns are concatenated column-wise. This way, a MSA allows to perform the analysis of an indicator matrix where the rows represent individuals.

Usage

SimAn(data, G, acg, weight = 2, nameg = NA, sr = NA, sc = NA, 
nd = 2, dp = 2, oar = 1, oac = 1, multiple = 0, arg)

Arguments

data

Data set

G

Number of tables to be jointly analyzed

acg

List of number of the active columns for each table (if multiple = 0)

weight

Weighting on each table

nameg

Prefix for identifying partial rows and tables

sr

Indices of supplementary rows

sc

Indices of supplementary columns

nd

Number of dimensions in results

dp

Number of digits in results

oar

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

oac

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

multiple

Multiple Simultaneous Analysis (1 = yes, 0 = no)

arg

List of number of the active rows for each table (if multiple = 1)

Value

totalin

Total inertia

resin

Results of inertia

resi

Results of active rows

resj

Results of active columns

resig

Results of partial rows (if multiple = 0)

resjg

Results of partial columns (if multiple = 1)

Fsg

Projections of each table

ctrg

Contribution of each table to the axes

riig

Relation between the overall rows and the partial rows (if multiple = 0)

rjjg

Relation between the overall rows and the partial columns (if multiple = 1)

RCACA

Relation between separate CA axes

RCASA

Relation between CA axes and SA axes

Fs

Projections of active rows

Gs

Projections of active columns

Fsig

Projections of partial rows (if multiple = 0)

Gsjg

Projections of partial columns (if multiple = 1)

allFs

Projections of rows and partial rows (if multiple = 0) in an array format

allGs

Projections of columns and partial columns (if multiple = 1) in an array format

I

Number of active rows (if multiple = 0)

J

Number of active columns (if multiple = 1)

maxJg

Maximum number of columns for a table (if multiple = 0)

maxIg

Maximum number of rows for a table (if multiple = 1)

G

Number of tables

namei

Names of active rows (if multiple = 0)

namej

Names of active columns (if multiple = 1)

nameg

Prefix for identifying partial points, tables, etc

resisr

Results of supplementary rows

resjsc

Results of supplementary columns

resigsr

Results of partial supplementary rows (if multiple = 0)

resjgsc

Results of partial supplementary columns (if multiple = 1)

Fssr

Projections of supplementary rows

Gssc

Projections of supplementary columns

Fsigsr

Projections of partial supplementary rows (if multiple = 0)

Gsjgsc

Projections of partial supplementary columns (if multiple = 1)

allFssr

Projections of supplementary rows and partial supplementary rows (if multiple = 0) in an array format

allGssc

Projections of supplementary columns and partial supplementary columns (if multiple = 1) in an array format

Isr

Number of supplementary rows (if multiple = 0)

Jsc

Number of supplementary columns (if multiple = 1)

nameisr

Names of supplementary rows (if multiple = 0)

namejsc

Names of supplementary columns (if multiple = 1)

CAres

Results of CA of each table to be used in Summary and Graph functions

multiple

Value of option multiple

Details

The parameter weight refers to the weighting of each table included in simultaneous analysis in order to balance the influence of each table in the joint analysis, as measured by the inertia, and to prevent the joint analysis from being dominated by a particular table. The choice of this weighting depends on the aims of the analysis and on the initial structure of the information, and different values may be used. Three values are possible, weight = 1 means no weighting , weight = 2 means that the weighting is the inverse of the first eigenvalue (square of first singular value) of each table and is given by default, and weight = 3 means that the weighting is the inverse of the total inertia of each table.

The parameter nameg allows the user to distinguish in the interpretation of the results as well as in the graphical representations which partial rows belong to each table. By default, if this parameter is not indicated, partial rows of the first table will be identified as G1 followed by the name of the row, partial rows of the second table as G2 followed by the name of the row and so on. The nameg argument also allows the different tables in the analysis to be identified.

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.

Zarraga, A. & Goitisolo, B. (2011). Simultaneous Analysis in S-PLUS: The SimultAn Package. Journal of Statistical Software, 70 (11), 1--22.

See Also

summary.SimAn, plot.SimAn.

Examples

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"))

### Multiple SA without output for columns
SimAn.out <- SimAn(data=t(dataSA), G=2, weight= 2, 
   nameg=c("M", "F"), oac=0, multiple=1, arg=list(1:9,10:18))

### Summary
summary(SimAn.out)

### Graphs on screen
plot(SimAn.out)

### Graphs on a pdf file (without columns)
pdf('SAGr.pdf', paper="a4r", width=12, height=9)
plot(SimAn.out, s1=1, s2=2, screen=FALSE, oac=0)
dev.off()