| Title: | Multiple Correspondence Analysis Variants |
|---|---|
| Description: | Provides two variants of multiple correspondence analysis (ca): multiple ca and ordered multiple ca via orthogonal polynomials of Emerson. |
| Authors: | Rosaria Lombardo and Eric J Beh |
| Maintainer: | Rosaria Lombardo <[email protected]> |
| License: | GPL (> 2) |
| Version: | 2.6.1 |
| Built: | 2025-03-03 04:33:36 UTC |
| Source: | https://github.com/cran/MCAvariants |
The data set is a three-way contingency table.
It consists of 2 rows (alligators'size), 5 columns (alligators'food)
by 4 tubes (alligators'lake). The table should be converted in reduced code table,
using the function tableconvert for getting alligatormca.
data(alligator.dat)data(alligator.dat)
A data frame with 300 alligators on the following 3 variables.
A numeric vector of categories ranging from 1 to 2 (small and large).
A numeric vector of categories ranging from 1 to 5 (type of food: fish, invertebrate, reptile, bird, other.
a numeric vector of categories ranging from 1 to 4 for the four American lakes: Hancock, Oklawaha, Trafford, George.
Agresti (2007), p. 270
Agresti A and Gottard A 2007 Independence in multiway contingency tables: S.n. roys breakthroughs and later
developments. Journal of Statistical Planning and Inference, 137:3126–3226.
data(alligator.dat) #dim(alligator.dat) #dimnames(alligator.dat)data(alligator.dat) #dim(alligator.dat) #dimnames(alligator.dat)
This function is used in the plot function plot.CAvariants when the logical parameter is
plot3d = TRUE.
It produces a 3-dimensional visualization of the association.
caplot3d(coordR, coordC, inertiaper, firstaxis = 1, lastaxis = 2, thirdaxis = 3)caplot3d(coordR, coordC, inertiaper, firstaxis = 1, lastaxis = 2, thirdaxis = 3)
coordR |
The row principal or standard coordinates. |
coordC |
The column principal or standard coordinates. |
inertiaper |
The percentage of the total inertia explained inertia by each dimension. |
firstaxis |
The first axis number. By default, |
lastaxis |
The second axis number. By default, |
thirdaxis |
The third axis number. By default, |
This function depends on the R library plotly.
Rosaria Lombardo and Eric J. Beh
Beh EJ and Lombardo R 2014 Correspondence Analysis: Theory, Practice and New Strategies. Wiley.
Lombardo R Beh EJ 2016 Variants of Simple Correspondence Analysis. The R Journal, 8 (2), 167–184.
Secondary function to code data in complete disjunctive form
insertval2(x, nmod)insertval2(x, nmod)
x |
Data matrix in reduced coding (primitive coding) |
nmod |
number of categories of each variable |
It helps to return a matrix from reduced coding in complete disjunctive coding
Rosaria Lombardo
Lombardo R and Meulman JJ (2010) Journal of Classification, 27, 191-210.
Beh EJ Lombardo R (2014) Correspondence Analysis, Theory, Practice and New Strategies. Wiley
This function is used in the main function MCAvariants when
the input parameter is catype="mca".
mcabasic(xo, np, nmod, tmod, rows, idr, idc, idcv)mcabasic(xo, np, nmod, tmod, rows, idr, idc, idcv)
xo |
The starting table of variables in reduced code. |
np |
The column number of the starting table (coincident with the variable number). |
nmod |
The number of variable catgories of each variable. |
tmod |
The total number of variable catgories. |
rows |
The row number of the starting table (coincident with the individual number). |
idr |
The row labels of the data table. |
idc |
The column labels of the data table. |
idcv |
The labels of the categories of each variable. |
This function belongs to the R object class called mcabasicresults.
Rosaria Lombardo
Lombardo R and Meulman JJ (2010) Journal of Classification, 27, 191-210.
Beh EJ Lombardo R (2014) Correspondence Analysis, Theory, Practice and New Strategies. Wiley
This function is used in the secondary function mcabasic when
the input parameter of MCAvariants is catype="mca".
It performs the singular value decomposition of the weighted super-indicator matrix and
compute principal axes, coordinates, weights of rows and columns and
total inertia.
mcafun(XO, Burt, np, idr, idc, nmod)mcafun(XO, Burt, np, idr, idc, nmod)
XO |
The super-indicator data table. |
Burt |
The Burt data table. |
np |
The number of categorical variables. |
idr |
The row labels of data table. |
idc |
The column labels of data table. |
nmod |
The category number of each variable. |
Rosaria Lombardo
Lombardo R and Meulman JJ (2010) Journal of Classification, 27, 191-210.
Beh EJ Lombardo R (2014) Correspondence Analysis, Theory, Practice and New Strategies. Wiley
It performs Classic Multiple Correspondence analysis for nominal variables
(setting catype = "mca") and Ordered Multiple Correspondence analysis via orthogonal polynomials (setting catype="omca").
When the categorical variables are nominal and ordinal, you can specify writing FALSE or TRUE in the input parameter vordered.
MCAvariants(Xtable, catype = "omca", np = 5, vordered=c(TRUE,TRUE,TRUE,TRUE,TRUE))MCAvariants(Xtable, catype = "omca", np = 5, vordered=c(TRUE,TRUE,TRUE,TRUE,TRUE))
Xtable |
The two-way contingency table. |
catype |
The input parameter for specifying what variant of multiple correspondence analysis is considered.
By default, |
np |
The input parameter for specifying the number of categorical variables. By default, |
vordered |
The flag parameter for specifying what variable is ordered, the ordered variables should be in column close each other.
By default, all the five variables are ordered: |
Description of the output returned
Xtable |
The starting table of variables in reduced (primitive) code. |
rows |
The row number of the starting table. |
cols |
The column number of the starting table (coincident with the variable number). |
rowlabels |
The label of the row individuals. |
columnlabels |
The label of the column variable categories. |
Rprinccoord |
The coordinates of individuals. |
Cprinccoord |
The category variable coordinates. |
inertiaXsum |
The total inertia when multiple correspondence analysis is performed on the indicator table. |
inertiaBurtsum |
The total inertia when multiple correspondence analysis is performed on the Burt table. |
inertias |
Benzecri's Adjusted Inertia values, percentages and cumulative values. |
inertiasAdjusted |
The adjusted inertia values. |
catype |
The kind of multiple correspondence analysis chosen, classical or ordered, that is |
printdims |
The dimension of a matrix in print. By default it is equal to 3. |
comp |
The polynomial components of inertia when |
componentpvalue1 |
The p-value of the polynomial components of total inertia, when |
degreef |
The degree of freedom of polynomial components of total inertia when, |
This function recalls internally two other functions, depending on the setting of the input parameter catype, it recalls
multiple correspondence analysis or ordered multiple correspondence analysis.
It gives the output object necessary for printing and plotting the results. These two
important functions are print.MCAvariants and plot.MCAvariants.
Rosaria Lombardo and Eric J Beh
Lombardo R and Meulman JJ (2010) Journal of Classification, 27, 191-210.
Beh EJ Lombardo R (2014) Correspondence Analysis, Theory, Practice and New Strategies. Wiley
The function that counts the number of individuals in each clusters automatically generated in ordered multiple correpsondence analysis.
miocount(x)miocount(x)
x |
The coordinates of axes |
This function is used in the function omcabasic when in the main function MCAvariants
the input parameter is catype="omca".
Rosaria Lombardo
Lombardo R and Meulman JJ (2010) Journal of Classification, 27, 191-210.
Beh EJ Lombardo R (2014) Correspondence Analysis, Theory, Practice and New Strategies. Wiley
This function is used in the main function MCAvariants when
the input parameter is catype="omca". It requires that all categorical variables are ordered variables.
It performs the hybrid decomposition of the weighted super-indicator matrix and
compute polynomial axes, coordinates, weights of rows and columns and
total inertia.
omcabasic(xo,np , nmod , tmod , rows, idr, idc, idcv,vordered)omcabasic(xo,np , nmod , tmod , rows, idr, idc, idcv,vordered)
xo |
The starting table of variables in reduced code. |
np |
The column number of the starting table (coincident with the variable number).
By default, |
nmod |
The number of variable catgories of each variable. |
tmod |
The total number of variable catgories. |
rows |
The row number of the starting table (coincident with the individual number). |
idr |
The row labels of the data table. |
idc |
The column labels of the data table. |
idcv |
The labels of the categories of each variable. |
vordered |
The flag parameter for specifying what variable is ordered.
By default, all the five variables are ordered: |
This function belongs to the R object class called mcabasicresults.
Rosaria Lombardo
Lombardo R and Meulman JJ (2010) Journal of Classification, 27, 191-210.
Beh EJ Lombardo R (2014) Correspondence Analysis, Theory, Practice and New Strategies. Wiley
This function is called from the function
omca.
It allows the analyst to compute the orthogonal polynomials of each ordered categorical variable.
The number of the polynomials is equal to the variable category less one.
The function computes the polynomial transformation of the ordered categorical variable.
orthopoly(marginals, scores)orthopoly(marginals, scores)
scores |
The ordered scores of an ordered variable. By default |
marginals |
The marginals, relative frequencies of the ordered variable. |
Describe the value returned
B |
the matrix of the orthogonal polynomials without the trivial polynomial. |
Note that the sum of the marginals of the ordered variables should be one. At the end, the various polynomial matrices will be stored in a super-diagonal matrix.
Rosaria Lombardo and Eric J Beh
Beh EJ and Lombardo R 2014 Correspondence analysis, Theory, Practice and New Strategies. Wiley.
orthopoly(marginals=c(.1,.2,.3,.2,.2), scores=c(1,2,3,4,5))orthopoly(marginals=c(.1,.2,.3,.2,.2), scores=c(1,2,3,4,5))
This function allows the analyst to produce the suitable graphical displays with respect to the classical and ordered multiple
correspondence analysis.
The main plot function called from the main function MCAvariants.
It produces classical graphical displays for catype = "mca" and catype = "omca".
## S3 method for class 'MCAvariants' plot(x, catype = "mca", firstaxis = 1, lastaxis = 2, thirdaxis = 3, cex = 0.8, cex.lab = 0.8, prop = 1, plot3d = FALSE, plotind= FALSE, M=2,...)## S3 method for class 'MCAvariants' plot(x, catype = "mca", firstaxis = 1, lastaxis = 2, thirdaxis = 3, cex = 0.8, cex.lab = 0.8, prop = 1, plot3d = FALSE, plotind= FALSE, M=2,...)
x |
Represents the set of the output parameters of the main function |
catype |
The input parameter specifying what variant of correspondence analysis is requested. |
firstaxis |
The dimension reflected along the horizontal axis. |
lastaxis |
The dimension reflected along the vertical axis. |
thirdaxis |
The third axis number when |
cex |
The parameter that specifies the size of character labels of points in graphical displays. By default, it is equal to 1. |
cex.lab |
The parameter |
prop |
The scaling parameter for specifying the limits of the plotting area. By default, it is equal to 1. |
plot3d |
The logical parameter specifies whether a 3D plot is to be included
in the output or not. By default, |
plotind |
The logical parameter specifies whether a plot of individuals is to be included
in the output or not. By default, |
M |
The number of axes |
... |
Further arguments passed to or from other methods. |
It produces classical graphical displays. Further when catype is equal to "omca",
the individual clusters are portrayed.
Rosaria Lombardo and Eric J Beh
Lombardo R and Meulman JJ (2010) Journal of Classification, 27, 191-210.
Beh EJ Lombardo R (2014) Correspondence Analysis, Theory, Practice and New Strategies. Wiley
data(satisfaction) res1=MCAvariants(satisfaction, catype = "mca", np=5) plot(res1) res2=MCAvariants(satisfaction, catype = "omca", np = 5, vordered=c(TRUE,TRUE,TRUE,TRUE,TRUE)) plot(res2)data(satisfaction) res1=MCAvariants(satisfaction, catype = "mca", np=5) plot(res1) res2=MCAvariants(satisfaction, catype = "omca", np = 5, vordered=c(TRUE,TRUE,TRUE,TRUE,TRUE)) plot(res2)
This function prints results of classical or ordered multiple correspondence analysis.
The input parameter is the name of the output of the main function MCAvariants.
## S3 method for class 'MCAvariants' print(x, printdims = 2,...)## S3 method for class 'MCAvariants' print(x, printdims = 2,...)
x |
The output of the main function |
printdims |
The number of dimensions, |
... |
Further arguments passed to or from other methods. |
This function uses another function (called printwithaxes) for specifying the number of matrix dimensions to print.
The value of output returned depends on the kind of multiple correspondence analysis performed.
DataTable |
The Burt data table. |
Row coordinates |
Rows in principal coordinates: the first 10. |
Column coordinates |
Column in principal coordinates. |
Polynomials |
Polynomial functions of each variable.
When |
Linear Percentage of Clusters |
The percentage of individuals belonging to each cluster. When |
Polynomial Components of Total Inertia |
The decomposition of total inertia via orthogonal polynomials. When |
Degree of Freedom |
Degree of Freedom of Polynomial Component. When |
Inertia values |
Inertia values of super-indicator and Burt table. |
Benzecri's Inertia values |
Adjusted Inertia values, percentages and cumulative. |
Total Degree of Freedom |
The degree of freedom of total inertia. |
Total inertia of X |
Total inertia of Super-Indicator table |
Total inertia of B |
Total inertia of BURT table. |
Chi-square values |
Chi-square values of BURT Inertia. |
Total Chi-square values |
Chi-square values of total Inertia of Burt table. |
Rosaria Lombardo
Lombardo R and Meulman JJ (2010) Journal of Classification, 27, 191-210.
Beh EJ Lombardo R (2014) Correspondence Analysis, Theory, Practice and New Strategies. Wiley
res=MCAvariants(satisfaction, catype = "omca", np = 5, vordered=c(TRUE,TRUE,TRUE,TRUE,TRUE)) print(res)res=MCAvariants(satisfaction, catype = "omca", np = 5, vordered=c(TRUE,TRUE,TRUE,TRUE,TRUE)) print(res)
The function is called from the main print function printmcacorporateris.
It adds the names to objects.
printwithaxes(res, thenames)printwithaxes(res, thenames)
res |
An |
thenames |
A character vector of up to the same length as |
It is called from printmcacorporateris.
Rosaria Lombardo
Lombardo R and Meulman JJ (2010) Journal of Classification, 27, 191-210.
Beh EJ Lombardo R (2014) Correspondence Analysis, Theory, Practice and New Strategies. Wiley
The data set consists of 235 rows and 5 columns. The rows represent the individuals (patients in an hospital) and the columns concern the five variables of satisfaction (Tangibility, Reliability, Capacity of Response, Capacity of Assurance and Empathy
data(satisfaction)data(satisfaction)
A data frame with 235 observations on the following 5 variables.
TANGa numeric vector of ordered categories ranging from 1 to 5.
RELa numeric vector of ordered categories ranging from 1 to 5.
CRESa numeric vector of ordered categories ranging from 1 to 5.
CASSa numeric vector of ordered categories ranging from 1 to 5.
EMPATa numeric vector of ordered categories ranging from 1 to 5.
Della Valle E (2010) Della Valle E 2010 Analisi Multidimensionale dei Dati: la Qualit\'a del Lavoro nelle Cooperative Sociali. Unpublished thesis, Seconda Universit\'a degli Studi di Napoli, Capua Italy.
data(satisfaction) #dim(satisfaction) #dimnames(satisfaction)data(satisfaction) #dim(satisfaction) #dimnames(satisfaction)
This simple piece of R code converts a two-way or three-way contingency table into what is required to analyse MCA (table of reduced code: n by number of variables).
tableconvert(N)tableconvert(N)
N |
A two-way or three-way contingency table to convert in a table n by np, where np is the number of the categorical variables. |
Rosaria Lombardo and Eric J Beh
Beh EJ Lombardo R (2014) Correspondence Analysis, Theory, Practice and New Strategies. Wiley
alligatormca<-tableconvert(alligator.dat) dimnames(alligatormca)<-list(paste("a", 1:300,sep = ""),c("Size","Food","Lake"))alligatormca<-tableconvert(alligator.dat) dimnames(alligatormca)<-list(paste("a", 1:300,sep = ""),c("Size","Food","Lake"))