SimAn

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Simultaneous Analysis

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.

Keywords
multivariate, simultaneous analysis
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)
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.

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

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.

Aliases
  • 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()
Documentation reproduced from package SimultAnR, version 1.1, License: GPL (>= 2)

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