Package 'MVar'

Title: Multivariate Analysis
Description: Multivariate analysis, having functions that perform simple correspondence analysis (CA) and multiple correspondence analysis (MCA), principal components analysis (PCA), canonical correlation analysis (CCA), factorial analysis (FA), multidimensional scaling (MDS), linear (LDA) and quadratic discriminant analysis (QDA), hierarchical and non-hierarchical cluster analysis, simple and multiple linear regression, multiple factor analysis (MFA) for quantitative, qualitative, frequency (MFACT) and mixed data, biplot, scatter plot, projection pursuit (PP), grant tour method and other useful functions for the multivariate analysis.
Authors: Paulo Cesar Ossani [aut, cre] , Marcelo Angelo Cirillo [aut]
Maintainer: Paulo Cesar Ossani <[email protected]>
License: GPL-3
Version: 2.2.5
Built: 2024-12-23 06:48:50 UTC
Source: CRAN

Help Index

Multivariate Analysis.

Description

Multivariate analysis, having functions that perform simple correspondence analysis (CA) and multiple correspondence analysis (MCA), principal components analysis (PCA), canonical correlation analysis (CCA), factorial analysis (FA), multidimensional scaling (MDS), linear (LDA) and quadratic discriminant analysis (QDA), hierarchical and non-hierarchical cluster analysis, simple and multiple linear regression, multiple factor analysis (MFA) for quantitative, qualitative, frequency (MFACT) and mixed data, biplot, scatter plot, projection pursuit (PP), grant tour method and other useful functions for the multivariate analysis.

Details

Package: MVar
Type: Package
Version: 2.2.5
Date: 2024-11-22
License: GPL(>=2)
LazyLoad: yes

Author(s)

Paulo Cesar Ossani and Marcelo Angelo Cirillo.

Maintainer: Paulo Cesar Ossani <[email protected]>

References

Abdessemed, L.; Escofier, B.; Analyse factorielle multiple de tableaux de frequencies: comparaison avec l'analyse canonique des correspondences. Journal de la Societe de Statistique de Paris, Paris, v. 137, n. 2, p. 3-18, 1996.

Abdi, H. Singular Value Decomposition (SVD) and Generalized Singular Value Decomposition (GSVD). In: SALKIND, N. J. (Ed.). Encyclopedia of measurement and statistics. Thousand Oaks: Sage, 2007. p. 907-912.

Abdi, H.; Valentin, D. Multiple factor analysis (MFA). In: SALKIND, N. J. (Ed.). Encyclopedia of measurement and statistics. Thousand Oaks: Sage, 2007. p. 657-663.

Abdi, H.; Williams, L. Principal component analysis. WIREs Computational Statatistics, New York, v. 2, n. 4, p. 433-459, July/Aug. 2010.

Abdi, H.; Williams, L.; Valentin, D. Multiple factor analysis: principal component analysis for multitable and multiblock data sets. WIREs Computational Statatistics, New York, v. 5, n. 2, p. 149-179, Feb. 2013.

Asimov, D. The Grand Tour: A Tool for Viewing Multidimensional Data. SIAM Journal of Scientific and Statistical Computing, 6(1), 128-143, 1985.

Asimov, D.; Buja, A. The grand tour via geodesic interpolation of 2-frames. in Visual Data Exploration and Analysis. Symposium on Electronic Imaging Science and Technology, IS&T/SPIE. 1994.

Becue-Bertaut, M.; Pages, J. A principal axes method for comparing contingency tables: MFACT. Computational Statistics & Data Analysis, New York, v. 45, n. 3, p. 481-503, Feb. 2004

Becue-Bertaut, M.; Pages, J. Multiple factor analysis and clustering of a mixture of quantitative, categorical and frequency data. Computational Statistics & Data Analysis, New York, v. 52, n. 6, p. 3255-3268, Feb. 2008.

Benzecri, J. Analyse de l'inertie intraclasse par l'analyse d'un tableau de contingence: intra-classinertia analysis through the analysis of a contingency table. Les Cahiers de l'Analyse des Donnees, Paris, v. 8, n. 3, p. 351-358, 1983.

Buja, A.; Asimov, D. Grand tour methods: An outline. Computer Science and Statistics, 17:63-67. 1986.

Buja, A.; Cook, D.; Asimov, D.; Hurley, C. Computational Methods for High-Dimensional Rotations in Data Visualization, in C. R. Rao, E. J. Wegman & J. L. Solka, eds, "Handbook of Statistics: Data Mining and Visualization", Elsevier/North Holland, http://www.elsevier.com, pp. 391-413. 2005.

Charnet, R., at al. Analise de modelos de regressao lienar, 2a ed. Campinas: Editora da Unicamp, 2008. 357 p.

Cook, D.; Lee, E. K.; Buja, A.; WickmamM, H. Grand tours, projection pursuit guided tours and manual controls. In Chen, Chunhouh, Hardle, Wolfgang, Unwin, e Antony (Eds.), Handbook of Data Visualization, Springer Handbooks of Computational Statistics, chapter III.2, p. 295-314. Springer, 2008.

Cook, D.; Buja, A.; Cabrera, J. Projection pursuit indexes based on orthonormal function expansions. Journal of Computational and Graphical Statistics, 2(3):225-250, 1993.

Cook, D.; Buja, A.; Cabrera, J.; Hurley, C. Grand tour and projection pursuit, Journal of Computational and Graphical Statistics, 4(3), 155-172, 1995.

Cook, D.; Swayne, D. F. Interactive and Dynamic Graphics for Data Analysis: With R and GGobi. Springer. 2007.

Escofier, B. Analyse factorielle en reference a un modele: application a l'analyse d'un tableau d'echanges. Revue de Statistique Appliquee, Paris, v. 32, n. 4, p. 25-36, 1984.

Escofier, B.; Drouet, D. Analyse des differences entre plusieurs tableaux de frequence. Les Cahiers de l'Analyse des Donnees, Paris, v. 8, n. 4, p. 491-499, 1983.

Escofier, B.; Pages, J. Analyse factorielles simples et multiples. Paris: Dunod, 1990. 267 p.

Escofier, B.; Pages, J. Analyses factorielles simples et multiples: objectifs, methodes et interpretation. 4th ed. Paris: Dunod, 2008. 318 p.

Escofier, B.; Pages, J. Comparaison de groupes de variables definies sur le meme ensemble d'individus: un exemple d'applications. Le Chesnay: Institut National de Recherche en Informatique et en Automatique, 1982. 121 p.

Escofier, B.; Pages, J. Multiple factor analysis (AFUMULT package). Computational Statistics & Data Analysis, New York, v. 18, n. 1, p. 121-140, Aug. 1994

Espezua, S.; Villanueva, E.; Maciel, C. D.; Carvalho, A. A projection pursuit framework for supervised dimension reduction of high dimensional small sample datasets. Neurocomputing, 149, 767-776, 2015.

Ferreira, D. F. Estatistica multivariada. 2. ed. rev. e ampl. Lavras: UFLA, 2011. 675 p.

Friedman, J. H., Tukey, J. W. A projection pursuit algorithm for exploratory data analysis. IEEE Transaction on Computers, 23(9):881-890, 1974.

Greenacre, M.; Blasius, J. Multiple correspondence analysis and related methods. New York: Taylor and Francis, 2006. 607 p.

Hastie, T.; Buja, A.; Tibshirani, R. Penalized discriminant analysis. The Annals of Statistics. 23(1), 73-102 . 1995.

Hotelling, H. Analysis of a complex of statistical variables into principal components. Journal of Educational Psychology, Arlington, v. 24, p. 417-441, Sept. 1933.

Huber, P. J. Projection pursuit. Annals of Statistics, 13(2):435-475, 1985.

Hurley, C.; Buja, A. Analyzing high-dimensional data with motion graphics, SIAM Journal of Scientific and Statistical Computing, 11 (6), 1193-1211. 1990.

Johnson, R. A.; Wichern, D. W. Applied multivariate statistical analysis. 6th ed. New Jersey: Prentice Hall, 2007. 794 p.

Jones, M. C.; Sibson, R. What is projection pursuit, (with discussion), Journal of the Royal Statistical Society, Series A 150, 1-36, 1987.

Lee, E.; Cook, D.; Klinke, S.; Lumley, T. Projection pursuit for exploratory supervised classification. Journal of Computational and Graphical Statistics, 14(4):831-846, 2005.

Lee, E. K., Cook, D. A projection pursuit index for large p small n data. Statistics and Computing, 20(3):381-392, 2010.

Martinez, W. L.; Martinez, A. R. Computational Statistics Handbook with MATLAB, 2th. ed. New York: Chapman & Hall/CRC, 2007. 794 p.

Martinez, W. L.; Martinez, A. R.; Solka, J. Exploratory Data Analysis with MATLAB, 2th. ed. New York: Chapman & Hall/CRC, 2010. 499 p.

Mingoti, S. A. Analise de dados atraves de metodos de estatistica multivariada: uma abordagem aplicada. Belo Horizonte: UFMG, 2005. 297 p.

Ossani, P. C.; Cirillo, M. A.; Borem, F. M.; Ribeiro, D. E.; Cortez, R. M. Quality of specialty coffees: a sensory evaluation by consumers using the MFACT technique. Revista Ciencia Agronomica (UFC. Online), v. 48, p. 92-100, 2017.

Ossani, P. C. Qualidade de cafes especiais e nao especiais por meio da analise de multiplos fatores para tabelas de contingencias. 2015. 107 p. Dissertacao (Mestrado em Estatistica e Experimentacao Agropecuaria) - Universidade Federal de Lavras, Lavras, 2015.

Pages, J. Analyse factorielle multiple appliquee aux variables qualitatives et aux donnees mixtes. Revue de Statistique Appliquee, Paris, v. 50, n. 4, p. 5-37, 2002.

Pages, J. Multiple factor analysis: main features and application to sensory data. Revista Colombiana de Estadistica, Bogota, v. 27, n. 1, p. 1-26, 2004.

Pena, D.; Prieto, F. Cluster identification using projections. Journal of the American Statistical Association, 96(456):1433-1445, 2001.

Posse, C. Projection pursuit exploratory data analysis, Computational Statistics and Data Analysis, 29:669-687, 1995a.

Posse, C. Tools for two-dimensional exploratory projection pursuit, Journal of Computational and Graphical Statistics, 4:83-100, 1995b

Rencher, A.C.; Methods of Multivariate Analysis. 2th. ed. New York: J.Wiley, 2002. 708 p.

Young, F. W.; Rheingans P. Visualizing structure in high-dimensional multivariate data, IBM Journal of Research and Development, 35:97-107, 1991.

Young, F. W.; Faldowski R. A.; McFarlane M. M. Multivariate statistical visualization, in Handbook of Statistics, Vol 9, C. R. Rao (ed.), The Netherlands: Elsevier Science Publishers, 959-998, 1993.

Biplot graph.

Description

Plots the Biplot graph.

Usage

Biplot(data, alpha = 0.5, title = NA, xlabel = NA, ylabel = NA,
       size = 1.1, grid = TRUE, color = TRUE, var = TRUE,
       obs = TRUE, linlab = NA, class = NA, classcolor = NA,
       posleg = 2, boxleg = TRUE, axes = TRUE, savptc = FALSE, 
       width = 3236, height = 2000, res = 300)

Arguments

data

Data for plotting.
alpha

Representativeness of the individuals (alpha), representativeness of the variables (1 - alpha), being 0.5 the default.
title

Titles of the graphics, if not set, assumes the default text.
xlabel

Names the X axis, if not set, assumes the default text.
ylabel

Names the Y axis, if not set, assumes the default text.
size

Size of the points in the graphs.
grid

Put grid on graphs (default = TRUE).
color

Colored graphics (default = TRUE).
var

Adds the variable projections to graph (default = TRUE).
obs

Adds the observations to graph (default = TRUE).
linlab

Vector with the labels for the observations.
class

Vector with names of data classes.
classcolor

Vector with the colors of the classes.
posleg

0 with no caption,
1 for caption in the left upper corner,
2 for caption in the right upper corner (default),
3 for caption in the right lower corner,
4 for caption in the left lower corner.
boxleg

Puts the frame in the caption (default = TRUE).
axes

Plots the X and Y axes (default = TRUE).
savptc

Saves graphics images to files (default = FALSE).
width

Graphics images width when savptc = TRUE (defaul = 3236).
height

Graphics images height when savptc = TRUE (default = 2000).
res

Nominal resolution in ppi of the graphics images when savptc = TRUE (default = 300).

Value

Biplot

Biplot graph.
Md

Matrix eigenvalues.
Mu

Matrix U (eigenvectors).
Mv

Matrix V (eigenvectors).
coorI

Coordinates of the individuals.
coorV

Coordinates of the variables.
pvar

Proportion of the principal components.

Author(s)

Paulo Cesar Ossani

Marcelo Angelo Cirillo

References

Rencher, A. C. Methods of multivariate analysis. 2th. ed. New York: J.Wiley, 2002. 708 p.

Examples

data(iris) # dataset

data <- iris[,1:4]

Biplot(data)


cls <- iris[,5]
res <- Biplot(data, alpha = 0.6, title = "Biplot of data valuing individuals",
              class = cls, classcolor = c("goldenrod3","gray56","red"),
              posleg = 2, boxleg = FALSE, axes = TRUE, savptc = FALSE, 
              width = 3236, height = 2000, res = 300)
print(res$pvar)


res <- Biplot(data, alpha = 0.4, title = "Graph valuing the variables",
              xlabel = "", ylabel = "", color = FALSE, obs = FALSE,
              savptc = FALSE, width = 3236, height = 2000, res = 300) 
print(res$pvar)

Correspondence Analysis (CA).

Description

Performs simple correspondence analysis (CA) and multiple (MCA) in a data set.

Usage

CA(data, typdata = "f", typmatrix = "I")

Arguments

data

Data to be analyzed (contingency table).
typdata

"f" for frequency data (default),
"c" for qualitative data.
typmatrix

Matrix used for calculations when typdata = "c".
"I" for indicator matrix (default),
"B" for Burt's matrix.

Value

depdata

Verify if the rows and columns are dependent, or independent by the chi-square test, at the 5% significance level.
typdata

Data type: "F" frequency or "C" qualitative.
numcood

Number of principal components.
mtxP

Matrix of the relative frequency.
vtrR

Vector with sums of the rows.
vtrC

Vector with sums of the columns.
mtxPR

Matrix with profile of the rows.
mtxPC

Matrix with profile of the columns
mtxZ

Matrix Z.
mtxU

Matrix with the eigenvectors U.
mtxV

Matrix with the eigenvectors V.
mtxL

Matrix with eigenvalues.
mtxX

Matrix with the principal coordinates of the rows.
mtxY

Matrix with the principal coordinates of the columns.
mtxAutvlr

Matrix of the inertias (variances), with the proportions and proportions accumulated.

Author(s)

Paulo Cesar Ossani

Marcelo Angelo Cirillo

References

Mingoti, S. A. Analise de dados atraves de metodos de estatistica multivariada: uma abordagem aplicada. Belo Horizonte: UFMG, 2005. 297 p.

Rencher, A. C. Methods of multivariate analysis. 2th. ed. New York: J.Wiley, 2002. 708 p.

See Also

Plot.CA

Examples

data(DataFreq) # frequency data set

data <- DataFreq[,2:ncol(DataFreq)]

rownames(data) <- as.character(t(DataFreq[1:nrow(DataFreq),1]))

res <- CA(data = data, "f") # performs CA

print("Is there dependency between rows and columns?"); res$depdata

print("Number of principal coordinates:"); res$numcood

print("Principal coordinates of the rows:"); round(res$mtxX,2)

print("Principal coordinates of the columns:"); round(res$mtxY,2)

print("Inertia of the principal components:"); round(res$mtxAutvlr,2)

Canonical Correlation Analysis(CCA).

Description

Perform Canonical Correlation Analysis (CCA) on a data set.

Usage

CCA(X = NULL, Y = NULL, type = 1, test = "Bartlett", sign = 0.05)

Arguments

X

First group of variables of a data set.
Y

Second group of variables of a data set.
type

1 for analysis using the covariance matrix (default),
2 for analysis using the correlation matrix.
test

Test of significance of the relationship between the group X and Y:
"Bartlett" (default) or "Rao".
sign

Test significance level (default 5%).

Value

Cxx

Covariance matrix or correlation Cxx.
Cyy

Covariance matrix or correlation Cyy.
Cxy

Covariance matrix or correlation Cxy.
Cyx

Covariance matrix or correlation Cyx.
var.UV

Matrix with eigenvalues (variances) of the canonical pairs U and V.
corr.UV

Matrix of the correlation of the canonical pairs U and V.
coef.X

Matrix of the canonical coefficients of the group X.
coef.Y

Matrix of the canonical coefficients of the group Y.
corr.X

Matrix of the correlations between canonical variables and the original variables of the group X.
corr.Y

Matrix of the correlations between the canonical variables and the original variables of the group Y.
score.X

Matrix with the scores of the group X.
score.Y

Matrix with the scores of the group Y.
sigtest

Returns the significance test of the relationship between group X and Y: "Bartlett" (default) or "Rao".

Author(s)

Paulo Cesar Ossani

Marcelo Angelo Cirillo

References

Mingoti, S. A. Analise de dados atraves de metodos de estatistica multivariada: uma abordagem aplicada. Belo Horizonte: UFMG, 2005. 297 p.

Ferreira, D. F. Estatistica Multivariada. 2a ed. revisada e ampliada. Lavras: Editora UFLA, 2011. 676 p.

Rencher, A. C. Methods of multivariate analysis. 2th. ed. New York: J.Wiley, 2002. 708 p.

Lattin, J.; Carrol, J. D.; Green, P. E. Analise de dados multivariados. 1th. ed. Sao Paulo: Cengage Learning, 2011. 455 p.

See Also

Plot.CCA

Examples

data(DataMix) # data set

data <- DataMix[,2:ncol(DataMix)]

rownames(data) <- DataMix[,1]

X <- data[,1:2]

Y <- data[,5:6]

res <- CCA(X, Y, type = 2, test = "Bartlett", sign = 0.05)

print("Matrix with eigenvalues (variances) of the canonical pairs U and V:"); round(res$var.UV,3)

print("Matrix of the correlation of the canonical pairs U and V:"); round(res$corr.UV,3)

print("Matrix of the canonical coefficients of the group X:"); round(res$coef.X,3)

print("Matrix of the canonical coefficients of the group Y:"); round(res$coef.Y,3)

print("Matrix of the correlations between the canonical 
       variables and the original variables of the group X:"); round(res$corr.X,3)

print("Matrix of the correlations between the canonical 
       variables and the original variables of the group Y:"); round(res$corr.Y,3)

print("Matrix with the scores of the group X:"); round(res$score.X,3)

print("Matrix with the scores of the group Y:"); round(res$score.Y,3)

print("test of significance of the canonical pairs:"); res$sigtest

Cluster Analysis.

Description

Performs hierarchical and non-hierarchical cluster analysis in a data set.

Usage

Cluster(data, titles = NA, hierarquic = TRUE, analysis = "Obs",  
        cor.abs = FALSE, normalize = FALSE, distance = "euclidean",  
        method = "complete", horizontal = FALSE, num.groups = 0,
        lambda = 2, savptc = FALSE, width = 3236, height = 2000, 
        res = 300, casc = TRUE)

Arguments

data

Data to be analyzed.
titles

Titles of the graphics, if not set, assumes the default text.
hierarquic

Hierarchical groupings (default = TRUE), for non-hierarchical groupings (method K-Means), only for case 'analysis' = "Obs".
analysis

"Obs" for analysis on observations (default), "Var" for analysis on variables.
cor.abs

Matrix of absolute correlation case 'analysis' = "Var" (default = FALSE).
normalize

Normalize the data only for case 'analysis' = "Obs" (default = FALSE).
distance

Metric of the distances in case of hierarchical groupings: "euclidean" (default), "maximum", "manhattan", "canberra", "binary" or "minkowski". Case Analysis = "Var" the metric will be the correlation matrix, according to cor.abs.
method

Method for analyzing hierarchical groupings: "complete" (default), "ward.D", "ward.D2", "single", "average", "mcquitty", "median" or "centroid".
horizontal

Horizontal dendrogram (default = FALSE).
num.groups

Number of groups to be formed.
lambda

Value used in the minkowski distance.
savptc

Saves graphics images to files (default = FALSE).
width

Graphics images width when savptc = TRUE (defaul = 3236).
height

Graphics images height when savptc = TRUE (default = 2000).
res

Nominal resolution in ppi of the graphics images when savptc = TRUE (default = 300).
casc

Cascade effect in the presentation of the graphics (default = TRUE).

Value

Several graphics.

tab.res

Table with similarities and distances of the groups formed.
groups

Original data with groups formed.
res.groups

Results of the groups formed.
R.sqt

Result of the R squared.
sum.sqt

Total sum of squares.
mtx.dist

Matrix of the distances.

Author(s)

Paulo Cesar Ossani

References

Rencher, A. C. Methods of multivariate analysis. 2th. ed. New York: J.Wiley, 2002. 708 p.

Mingoti, S. A. analysis de dados atraves de metodos de estatistica multivariada: uma abordagem aplicada. Belo Horizonte: UFMG, 2005. 297 p.

Ferreira, D. F. Estatistica Multivariada. 2a ed. revisada e ampliada. Lavras: Editora UFLA, 2011. 676 p.

Examples

data(DataQuan) # set of quantitative data

data <- DataQuan[,2:8]

rownames(data) <- DataQuan[1:nrow(DataQuan),1]

res <- Cluster(data, titles = NA, hierarquic = TRUE, analysis = "Obs",
               cor.abs = FALSE, normalize = FALSE, distance = "euclidean", 
               method = "ward.D", horizontal = FALSE, num.groups = 2,
               savptc = FALSE, width = 3236, height = 2000, res = 300, 
               casc = FALSE)

print("R squared:"); res$R.sqt
# print("Total sum of squares:"); res$sum.sqt
print("Groups formed:"); res$groups
# print("Table with similarities and distances:"); res$tab.res
# print("Table with the results of the groups:"); res$res.groups
# print("Distance Matrix:"); res$mtx.dist 
 
write.table(file=file.path(tempdir(),"SimilarityTable.csv"), res$tab.res, sep=";",
            dec=",",row.names = FALSE) 
write.table(file=file.path(tempdir(),"GroupData.csv"), res$groups, sep=";",
            dec=",",row.names = TRUE) 
write.table(file=file.path(tempdir(),"GroupResults.csv"), res$res.groups, sep=";",
            dec=",",row.names = TRUE)

Coefficient of variation of the data.

Description

Find the coefficient of variation of the data, either overall or per column.

Usage

CoefVar(data, type = 1)

Arguments

data

Data to be analyzed.
type

1 Coefficient of overall variation (default),
2 Coefficient of variation per column.

Value

Coefficient of variation, either overall or per column.

Author(s)

Paulo Cesar Ossani

Marcelo Angelo Cirillo

References

Ferreira, D. F.; Estatistica Basica. 2 ed. rev. Lavras: UFLA, 2009. 664 p.

Examples

data(DataQuan) # data set

data <- DataQuan[,2:8]

res <- CoefVar(data, type = 1) # Coefficient of overall variation
round(res,2)

res <- CoefVar(data, type = 2) # Coefficient of variation per column
round(res,2)

Linear (LDA) and quadratic discriminant analysis (QDA).

Description

Perform linear and quadratic discriminant analysis.

Usage

DA(data, class = NA, type = "lda", validation = "learning", 
   method = "moment", prior = NA, testing = NA)

Arguments

data

Data to be classified.
class

Vector with data classes names.
type

"lda": linear discriminant analysis (default), or
"qda": quadratic discriminant analysis.
validation

Type of validation:
"learning" - data training (default), or
"testing" - classifies the data of the vector "testing".
method

Classification method:
"mle" to MLEs,
"mve" to use cov.mv,
"moment" (default) for standard mean and variance estimators, or
"t" for robust estimates based on the t distribution.
prior

Probabilities of occurrence of classes. If not specified, it will take the proportions of the classes. If specified, probabilities must follow the order of factor levels.
testing

Vector with indices that will be used in data as test. For validation = "learning", one has testing = NA.

Value

confusion

Confusion table.
error.rate

Overall error ratio.
prior

Probability of classes.
type

Type of discriminant analysis.
validation

Type of validation.
num.class

Number of classes.
class.names

Class names.
method

Classification method.
num.correct

Number of correct observations.
results

Matrix with comparative classification results.

Author(s)

Paulo Cesar Ossani

Marcelo Angelo Cirillo

References

Ferreira, D. F. Estatistica Multivariada. 2a ed. revisada e ampliada. Lavras: Editora UFLA, 2011. 676 p.

Mingoti, S. A. Analise de dados atraves de metodos de estatistica multivariada: uma abordagem aplicada. Belo Horizonte: UFMG, 2005. 297 p.

Rencher, A. C. Methods of multivariate analysis. 2th. ed. New York: J.Wiley, 2002. 708 p.

Ripley, B. D. Pattern Recognition and Neural Networks. Cambridge University Press, 1996.

Venabless, W. N.; Ripley, B. D. Modern Applied Statistics with S. Fourth edition. Springer, 2002.

Examples

data(iris) # data set

data  = iris[,1:4] # data to be classified
class = iris[,5]   # data class
prior = c(1,1,1)/3 # a priori probability of the classs

res <- DA(data, class, type = "lda", validation = "learning", 
          method = "mle", prior = prior, testing = NA)

print("confusion table:"); res$confusion
print("Overall hit ratio:"); 1 - res$error.rate
print("Probability of classes:"); res$prior
print("classification method:"); res$method
print("type of discriminant analysis:"); res$type
print("class names:"); res$class.names
print("Number of classess:"); res$num.class
print("type of validation:"); res$validation
print("Number of correct observations:"); res$num.correct
print("Matrix with comparative classification results:"); res$results


### cross-validation ###
amostra   = sample(2, nrow(data), replace = TRUE, prob = c(0.7,0.3))
datatrain = data[amostra == 1,] # training data
datatest  = data[amostra == 2,] # test data

dim(datatrain) # training data dimension
dim(datatest)  # test data dimension

testing  = as.integer(rownames(datatest)) # test data index

res <- DA(data, class, type = "qda", validation = "testing", 
          method = "moment", prior = NA, testing = testing)

print("confusion table:"); res$confusion
print("Overall hit ratio:"); 1 - res$error.rate
print("Number of correct observations:"); res$num.correct
print("Matrix with comparative classification results:"); res$results

Frequency data set.

Description

Set of data categorized by coffees, on sensorial abilities in the consumption of special coffees.

Usage

data(DataCoffee)

Format

Data set of a research done with the purpose of evaluating the concordance between the responses of different groups of consumers with different sensorial abilities. The experiment relates the sensorial analysis of special coffees defined by (A) Yellow Bourbon, cultivated at altitudes greater than 1200 m; (D) idem to (A) differing only in the preparation of the samples; (B) Acaia cultivated at an altitude of less than 1,100 m; (C) identical to (B) but differentiating the sample preparation. Here the data are categorized by coffees. The example given demonstrates the results found in OSSANI et al. (2017).

References

Ossani, P. C.; Cirillo, M. A.; Borem, F. M.; Ribeiro, D. E.; Cortez, R. M.. Quality of specialty coffees: a sensory evaluation by consumers using the MFACT technique. Revista Ciencia Agronomica (UFC. Online), v. 48, p. 92-100, 2017.

Ossani, P. C. Qualidade de cafes especiais e nao especiais por meio da analise de multiplos fatores para tabelas de contingencias. 2015. 107 p. Dissertacao (Mestrado em Estatistica e Experimentacao Agropecuaria) - Universidade Federal de Lavras, Lavras, 2015.

Examples

data(DataCoffee) # categorized data set

data <- DataCoffee[,2:ncol(DataCoffee)] 

rownames(data) <- as.character(t(DataCoffee[1:nrow(DataCoffee),1]))

group.names = c("Coffee A", "Coffee B", "Coffee C", "Coffee D")

mf <- MFA(data, c(16,16,16,16), c(rep("f",4)), group.names) 

print("Principal components variances:"); round(mf$mtxA,2)

print("Matrix of the Partial Inertia / Score of the Variables:"); round(mf$mtxEV,2)

tit <- c("Scree-plot","Individuals","Individuals / Types coffees","Inercias Groups")

Plot.MFA(mf, titles = tit, xlabel = NA, ylabel = NA,
         posleg = 2, boxleg = FALSE, color = TRUE, 
         namarr = FALSE, linlab = NA, casc = FALSE) # plotting several graphs on the screen

Frequency data set.

Description

Simulated data set with the weekly frequency of the number of coffee cups consumed weekly in some world capitals.

Usage

data(DataFreq)

Format

Set of data with 6 rows and 9 columns. There are 6 observations described by 9 variables: Group by sex and age, Sao Paulo - Cafe Bourbon, London - Cafe Bourbon, Athens - Cafe Bourbon, London - Cafe Acaia, Athens - Cafe Catuai, Sao Paulo - Cafe Catuai, Athens - Cafe Catuai.

Author(s)

Paulo Cesar Ossani

Marcelo Angelo Cirillo

Examples

data(DataFreq)
DataFreq

Frequency data set.

Description

Set of data categorized by coffees, on sensorial abilities in the consumption of special coffees.

Usage

data(DataInd)

Format

Data set of a research done with the purpose of evaluating the concordance between the responses of different groups of consumers with different sensorial abilities. The experiment relates the sensorial analysis of special coffees defined by (A) Yellow Bourbon, cultivated at altitudes greater than 1200 m; (D) idem to (A) differing only in the preparation of the samples; (B) Acaia cultivated at an altitude of less than 1,100 m; (C) identical to (B) but differentiating the sample preparation. Here the data are categorized by coffees. The example given demonstrates the results found in OSSANI et al. (2017).

References

Ossani, P. C.; Cirillo, M. A.; Borem, F. M.; Ribeiro, D. E.; Cortez, R. M.. Quality of specialty coffees: a sensory evaluation by consumers using the MFACT technique. Revista Ciencia Agronomica (UFC. Online), v. 48, p. 92-100, 2017.

Ossani, P. C. Qualidade de cafes especiais e nao especiais por meio da analise de multiplos fatores para tabelas de contingencias. 2015. 107 p. Dissertacao (Mestrado em Estatistica e Experimentacao Agropecuaria) - Universidade Federal de Lavras, Lavras, 2015.

Examples

data(DataInd) # categorized data set

data <- DataInd[,2:ncol(DataInd)] 

rownames(data) <- as.character(t(DataInd[1:nrow(DataInd),1]))

group.names = c("Group 1", "Group 2", "Group 3", "Group 4")

mf <- MFA(data, c(16,16,16,16), c(rep("f",4)), group.names)

print("Principal components variances:"); round(mf$mtxA,2)

print("Matrix of the Partial Inertia / Score of the Variables:"); round(mf$mtxEV,2)

tit <- c("Scree-plot","Individuals","Individuals / Types coffees","Inercias Groups")

Plot.MFA(mf, titles = tit, xlabel = NA, ylabel = NA,
         posleg = 2, boxleg = FALSE, color = TRUE, 
         namarr = FALSE, linlab = NA, casc = FALSE) # plotting several graphs on the screen

Mixed data set.

Description

Simulated set of mixed data on consumption of coffee.

Usage

data(DataMix)

Format

Data set with 10 rows and 7 columns. Being 10 observations described by 7 variables: Cooperatives/Tasters, Average grades given to analyzed coffees, Years of work as a taster, Taster with technical training, Taster exclusively dedicated, Average frequency of the coffees Classified as special, Average frequency of the coffees as commercial.

Author(s)

Paulo Cesar Ossani

Marcelo Angelo Cirillo

Examples

data(DataMix)
DataMix

Qualitative data set

Description

Set simulated of qualitative data on consumption of coffee.

Usage

data(DataQuali)

Format

Data set simulated with 12 rows and 6 columns. Being 12 observations described by 6 variables: Sex, Age, Smoker, Marital status, Sportsman, Study.

Author(s)

Paulo Cesar Ossani

Marcelo Angelo Cirillo

Examples

data(DataQuali)
DataQuali

Quantitative data set

Description

Set simulated of quantitative data on grades given to some sensory characteristics of coffees.

Usage

data(DataQuan)

Format

Data set with 6 rows and 11 columns. Being 6 observations described by 11 variables: Coffee, Chocolate, Caramelised, Ripe, Sweet, Delicate, Nutty, Caramelised, Chocolate, Spicy, Caramelised.

Author(s)

Paulo Cesar Ossani

Marcelo Angelo Cirillo

Examples

data(DataQuan) 
DataQuan

Factor Analysis (FA).

Description

Performs factorial analysis (FA) in a data set.

Usage

FA(data, method = "PC", type = 2, nfactor = 1, rotation = "None",
   scoresobs = "Bartlett", converg = 1e-5, iteracao = 1000, 
   testfit = TRUE)

Arguments

data

Data to be analyzed.
method

Method of analysis:
"PC" - Principal Components (default),
"PF" - Principal Factor,
"ML" - Maximum Likelihood.
type

1 for analysis using the covariance matrix,
2 for analysis using the correlation matrix (default).
rotation

Type of rotation: "None" (default), "Varimax" and "Promax".
nfactor

Number of factors (default = 1).
scoresobs

Type of scores for the observations: "Bartlett" (default) or "Regression".
converg

Limit value for convergence to sum of the squares of the residuals for Maximum likelihood method (default = 1e-5).
iteracao

Maximum number of iterations for Maximum Likelihood method (default = 1000).
testfit

Tests the model fit to the method of Maximum Likelihood (default = TRUE).

Value

mtxMC

Matrix of correlation / covariance.
mtxAutvlr

Matrix of eigenvalues.
mtxAutvec

Matrix of eigenvectors.
mtxvar

Matrix of variances and proportions.
mtxcarga

Matrix of factor loadings.
mtxvaresp

Matrix of specific variances.
mtxcomuna

Matrix of commonalities.
mtxresidue

Matrix of residues.
vlrsqrs

Upper limit value for sum of squares of the residues.
vlrsqr

Sum of squares of the residues.
mtxresult

Matrix with all associated results.
mtxscores

Matrix with scores of the observations.
coefscores

Matrix with the scores of the coefficients of the factors.

Author(s)

Paulo Cesar Ossani

Marcelo Angelo Cirillo

References

Mingot, S. A. Analise de dados atraves de metodos de estatistica multivariada: uma abordagem aplicada. Belo Horizonte: UFMG, 2005. 297 p.

Kaiser, H. F.The varimax criterion for analytic rotation in factor analysis. Psychometrika 23, 187-200, 1958.

Rencher, A. C. Methods of multivariate analysis. 2th. ed. New York: J.Wiley, 2002. 708 p.

Ferreira, D. F. Estatistica Multivariada. 2a ed. revisada e ampliada. Lavras: Editora UFLA, 2011. 676 p.

See Also

Plot.FA

Examples

data(DataQuan) # data set

data <- DataQuan[,2:ncol(DataQuan)]

rownames(data) <- DataQuan[,1]

res <- FA(data, method = "PC", type = 2, nfactor = 3, rotation = "None",
          scoresobs = "Bartlett", converg = 1e-5, iteracao = 1000, 
          testfit = TRUE) 

print("Matrix with all associated results:"); round(res$mtxresult,3)

print("Sum of squares of the residues:"); round(res$vlrsqr,3)

print("Matrix of the factor loadings.:"); round(res$mtxcarga,3)

print("Matrix with scores of the observations:"); round(res$mtxscores,3)

print("Matrix with the scores of the coefficients of the factors:"); round(res$coefscores,3)

Animation technique Grand Tour.

Description

Performs the exploration of the data through the technique of animation Grand Tour.

Usage

GrandTour(data, method = "Interpolation", title = NA, xlabel = NA, 
          ylabel = NA, size = 1.1, grid = TRUE, color = TRUE, linlab = NA, 
          class = NA, classcolor = NA, posleg = 2, boxleg = TRUE,  
          axesvar = TRUE, axes = TRUE, numrot = 200, choicerot = NA, 
          savptc = FALSE, width = 3236, height = 2000, res = 300)

Arguments

data

Numerical data set.
method

Method used for rotations:
"Interpolation" - Interpolation method (default),
"Torus" - Torus method,
"Pseudo" - Pseudo Grand Tour method.
title

Titles of the graphics, if not set, assumes the default text.
xlabel

Names the X axis, if not set, assumes the default text.
ylabel

Names the Y axis, if not set, assumes the default text.
size

Size of the points in the graphs.
grid

Put grid on graphs (default = TRUE).
color

Colored graphics (default = TRUE).
linlab

Vector with the labels for the observations.
class

Vector with names of data classes.
classcolor

Vector with the colors of the classes.
posleg

0 with no caption,
1 for caption in the left upper corner,
2 for caption in the right upper corner (default),
3 for caption in the right lower corner,
4 for caption in the left lower corner.
boxleg

Puts the frame in the caption (default = TRUE).
axesvar

Puts axes of rotation of the variables (default = TRUE).
axes

Plots the X and Y axes (default = TRUE).
numrot

Number of rotations (default = 200). If method = "Interpolation", numrot represents the angle of rotation.
choicerot

Choose specific rotation and display on the screen, or save the image if savptc = TRUE.
savptc

Saves graphics images to files (default = FALSE).
width

Graphics images width when savptc = TRUE (defaul = 3236).
height

Graphics images height when savptc = TRUE (default = 2000).
res

Nominal resolution in ppi of the graphics images when savptc = TRUE (default = 300).

Value

Graphs with rotations.

proj.data

Projected data.
vector.opt

Vector projection.
method

method used on Grand Tour.

Author(s)

Paulo Cesar Ossani

Marcelo Angelo Cirillo

References

Asimov, D. The Grand Tour: A Tool for Viewing Multidimensional data. SIAM Journal of Scientific and Statistical Computing, 6(1), 128-143, 1985.

Asimov, D.; Buja, A. The grand tour via geodesic interpolation of 2-frames. in Visual data Exploration and Analysis. Symposium on Electronic Imaging Science and Technology, IS&T/SPIE. 1994.

Buja, A.; Asimov, D. Grand tour methods: An outline. Computer Science and Statistics, 17:63-67. 1986.

Buja, A.; Cook, D.; Asimov, D.; Hurley, C. Computational methods for High-Dimensional Rotations in data Visualization, in C. R. Rao, E. J. Wegman & J. L. Solka, eds, "Handbook of Statistics: data Mining and Visualization", Elsevier/North Holland, http://www.elsevier.com, pp. 391-413. 2005.

Hurley, C.; Buja, A. Analyzing high-dimensional data with motion graphics, SIAM Journal of Scientific and Statistical Computing, 11 (6), 1193-1211. 1990.

Martinez, W. L.; Martinez, A. R.; Solka, J.; Exploratory data Analysis with MATLAB, 2th. ed. New York: Chapman & Hall/CRC, 2010. 499 p.

Young, F. W.; Rheingans P. Visualizing structure in high-dimensional multivariate data, IBM Journal of Research and Development, 35:97-107, 1991.

Young, F. W.; Faldowski R. A.; McFarlane M. M. Multivariate statistical visualization, in Handbook of Statistics, Vol 9, C. R. Rao (ed.), The Netherlands: Elsevier Science Publishers, 959-998, 1993.

Examples

data(iris) # database

res <- GrandTour(iris[,1:4], method = "Torus", title = NA, xlabel = NA, ylabel = NA,
                 color = TRUE, linlab = NA, class = NA, posleg = 2, boxleg = TRUE, 
                 axesvar = TRUE, axes = FALSE, numrot = 10, choicerot = NA,
                 savptc = FALSE, width = 3236, height = 2000, res = 300)

print("Projected data:"); res$proj.data
print("Projection vectors:"); res$vector.opt
print("Grand Tour projection method:"); res$method

        
res <- GrandTour(iris[,1:4], method = "Interpolation", title = NA, xlabel = NA, ylabel = NA,
                 color = TRUE, linlab = NA, posleg = 2, boxleg = FALSE, axesvar = FALSE, 
                 axes = FALSE, numrot = 10, choicerot = NA, class = iris[,5],
                 classcolor = c("goldenrod3","gray53","red"),savptc = FALSE, 
                 width = 3236, height = 2000, res = 300)
         
print("Projected data:"); res$proj.data
print("Projection vectors:"); res$vector.opt
print("Grand Tour projection method:"); res$method

Generalized Singular Value Decomposition (GSVD).

Description

Given the matrix AA of order nxmnxm, the generalized singular value decomposition (GSVD) involves the use of two sets of positive square matrices of order nxnnxn and mxmmxm respectively. These two matrices express constraints imposed, respectively, on the lines and columns of AA.

Usage

GSVD(data, plin = NULL, pcol = NULL)

Arguments

data

Matrix used for decomposition.
plin

Weight for rows.
pcol

Weight for columns

Details

If plin or pcol is not used, it will be calculated as the usual singular value decomposition.

Value

d

Eigenvalues, that is, line vector with singular values of the decomposition.
u

Eigenvectors referring rows.
v

Eigenvectors referring columns.

Author(s)

Paulo Cesar Ossani

Marcelo Angelo Cirillo

References

Abdi, H. Singular Value Decomposition (SVD) and Generalized Singular Value Decomposition (GSVD). In: SALKIND, N. J. (Ed.). Encyclopedia of measurement and statistics. Thousand Oaks: Sage, 2007. p. 907-912.

Examples

data <- matrix(c(1,2,3,4,5,6,7,8,9,10,11,12), nrow = 4, ncol = 3)

svd(data)  # Usual Singular Value Decomposition

GSVD(data) # GSVD with the same previous results

# GSVD with weights for rows and columns
GSVD(data, plin = c(0.1,0.5,2,1.5), pcol = c(1.3,2,0.8))

Indicator matrix.

Description

In the indicator matrix the elements are arranged in the form of dummy variables, in other words, 1 for a category chosen as a response variable and 0 for the other categories of the same variable.

Usage

IM(data, names = TRUE)

Arguments

data

Categorical data.
names

Include the names of the variables in the levels of the Indicator Matrix (default = TRUE).

Value

mtxIndc

Returns converted data in the indicator matrix.

Author(s)

Paulo Cesar Ossani

Marcelo Angelo Cirillo

References

Rencher, A. C. Methods of multivariate analysis. 2th. ed. New York: J.Wiley, 2002. 708 p.

Examples

data <- matrix(c("S","S","N","N",1,2,3,4,"N","S","T","N"), nrow = 4, ncol = 3)

IM(data, names = FALSE)

data(DataQuali) # qualitative data set

IM(DataQuali, names = TRUE)

Function for better position of the labels in the graphs.

Description

Function for better position of the labels in the graphs.

Usage

LocLab(x, y = NULL, labels = seq(along = x), cex = 1,
       method = c("SANN", "GA"), allowSmallOverlap = FALSE,
       trace = FALSE, shadotext = FALSE, 
       doPlot = TRUE, ...)

Arguments

x

Coordinate x
y

Coordinate y
labels

The labels
cex

cex
method

Not used
allowSmallOverlap

Boolean
trace

Boolean
shadotext

Boolean
doPlot

Boolean
...

Other arguments passed to or from other methods

Value

See the text of the function.

Multidimensional Scaling (MDS).

Description

Performs Multidimensional Scaling (MDS) on a data set.

Usage

MDS(data, distance = "euclidean", title = NA, xlabel = NA,  
    ylabel = NA, posleg = 2, boxleg = TRUE, axes = TRUE, 
    size = 1.1, grid = TRUE, color = TRUE, linlab = NA, 
    class = NA, classcolor = NA, savptc = FALSE, width = 3236, 
    height = 2000, res = 300)

Arguments

data

Data to be analyzed.
distance

Metric of the distance: "euclidean" (default), "maximum", "manhattan", "canberra", "binary" or "minkowski".
title

Titles of the graphics, if not set, assumes the default text.
xlabel

Names the X axis, if not set, assumes the default text.
ylabel

Names the Y axis, if not set, assumes the default text.
posleg

0 with no caption,
1 for caption in the left upper corner,
2 for caption in the right upper corner (default),
3 for caption in the right lower corner,
4 for caption in the left lower corner.
boxleg

Puts the frame in the caption (default = TRUE).
axes

Plot the X and Y axes (default = TRUE).
size

Size of the points in the graphs.
grid

Put grid on graphs (default = TRUE).
color

Colored graphics (default = TRUE).
linlab

Vector with the labels for the observations.
class

Vector with names of data classes.
classcolor

Vector with the colors of the classes.
savptc

Saves graphics images to files (default = FALSE).
width

Graphics images width when savptc = TRUE (defaul = 3236).
height

Graphics images height when savptc = TRUE (default = 2000).
res

Nominal resolution in ppi of the graphics images when savptc = TRUE (default = 300).

Value

Multidimensional Scaling.

mtxD

Matrix of the distances.

Author(s)

Paulo Cesar Ossani

Marcelo Angelo Cirillo

References

Mingoti, S. A. Analise de dados atraves de metodos de estatistica multivariada: uma abordagem aplicada. Belo Horizonte: UFMG, 2005. 297 p.

Rencher, A. C. Methods of multivariate analysis. 2th. ed. New York: J.Wiley, 2002. 708 p.

Examples

data(iris) # data set

data <- iris[,1:4]

cls <- iris[,5] # data class

md <- MDS(data = data, distance = "euclidean", title = NA, xlabel = NA,  
          ylabel = NA, posleg = 2, boxleg = TRUE, axes = TRUE, color = TRUE,
          linlab = NA, class = cls, classcolor = c("goldenrod3","gray53","red"),
          savptc = FALSE, width = 3236, height = 2000, res = 300)
          
print("Matrix of the distances:"); md$mtxD

Multiple Factor Analysis (MFA).

Description

Perform Multiple Factor Analysis (MFA) on groups of variables. The groups of variables can be quantitative, qualitative, frequency (MFACT) data, or mixed data.

Usage

MFA(data, groups, typegroups = rep("n",length(groups)), namegroups = NULL)

Arguments

data

Data to be analyzed.
groups

Number of columns for each group in order following the order of data in 'data'.
typegroups

Type of group:
"n" for numerical data (default),
"c" for categorical data,
"f" for frequency data.
namegroups

Names for each group.

Value

vtrG

Vector with the sizes of each group.
vtrNG

Vector with the names of each group.
vtrplin

Vector with the values used to balance the lines of the Z matrix.
vtrpcol

Vector with the values used to balance the columns of the Z matrix.
mtxZ

Matrix concatenated and balanced.
mtxA

Matrix of the eigenvalues (variances) with the proportions and proportions accumulated.
mtxU

Matrix U of the singular decomposition of the matrix Z.
mtxV

Matrix V of the singular decomposition of the matrix Z.
mtxF

Matrix global factor scores where the lines are the observations and the columns the components.
mtxEFG

Matrix of the factor scores by group.
mtxCCP

Matrix of the correlation of the principal components with original variables.
mtxEV

Matrix of the partial inertias / scores of the variables

Author(s)

Paulo Cesar Ossani

Marcelo Angelo Cirillo

References

Abdessemed, L.; Escofier, B. Analyse factorielle multiple de tableaux de frequencies: comparaison avec l'analyse canonique des correspondences. Journal de la Societe de Statistique de Paris, Paris, v. 137, n. 2, p. 3-18, 1996..

Abdi, H. Singular Value Decomposition (SVD) and Generalized Singular Value Decomposition (GSVD). In: SALKIND, N. J. (Ed.). Encyclopedia of measurement and statistics. Thousand Oaks: Sage, 2007. p. 907-912.

Abdi, H.; Valentin, D. Multiple factor analysis (MFA). In: SALKIND, N. J. (Ed.). Encyclopedia of measurement and statistics. Thousand Oaks: Sage, 2007. p. 657-663.

Abdi, H.; Williams, L. Principal component analysis. WIREs Computational Statatistics, New York, v. 2, n. 4, p. 433-459, July/Aug. 2010.

Abdi, H.; Williams, L.; Valentin, D. Multiple factor analysis: principal component analysis for multitable and multiblock data sets. WIREs Computational Statatistics, New York, v. 5, n. 2, p. 149-179, Feb. 2013.

Becue-Bertaut, M.; Pages, J. A principal axes method for comparing contingency tables: MFACT. Computational Statistics & data Analysis, New York, v. 45, n. 3, p. 481-503, Feb. 2004

Becue-Bertaut, M.; Pages, J. Multiple factor analysis and clustering of a mixture of quantitative, categorical and frequency data. Computational Statistics & data Analysis, New York, v. 52, n. 6, p. 3255-3268, Feb. 2008.

Bezecri, J. Analyse de l'inertie intraclasse par l'analyse d'un tableau de contingence: intra-classinertia analysis through the analysis of a contingency table. Les Cahiers de l'Analyse des Donnees, Paris, v. 8, n. 3, p. 351-358, 1983.

Escofier, B. Analyse factorielle en reference a un modele: application a l'analyse d'un tableau d'echanges. Revue de Statistique Appliquee, Paris, v. 32, n. 4, p. 25-36, 1984.

Escofier, B.; Drouet, D. Analyse des differences entre plusieurs tableaux de frequence. Les Cahiers de l'Analyse des Donnees, Paris, v. 8, n. 4, p. 491-499, 1983.

Escofier, B.; Pages, J. Analyse factorielles simples et multiples. Paris: Dunod, 1990. 267 p.

Escofier, B.; Pages, J. Analyses factorielles simples et multiples: objectifs, methodes et interpretation. 4th ed. Paris: Dunod, 2008. 318 p.

Escofier, B.; Pages, J. Comparaison de groupes de variables definies sur le meme ensemble d'individus: un exemple d'applications. Le Chesnay: Institut National de Recherche en Informatique et en Automatique, 1982. 121 p.

Escofier, B.; Pages, J. Multiple factor analysis (AFUMULT package). Computational Statistics & data Analysis, New York, v. 18, n. 1, p. 121-140, Aug. 1994

Greenacre, M.; Blasius, J. Multiple correspondence analysis and related methods. New York: Taylor and Francis, 2006. 607 p.

Ossani, P. C.; Cirillo, M. A.; Borem, F. M.; Ribeiro, D. E.; Cortez, R. M. Quality of specialty coffees: a sensory evaluation by consumers using the MFACT technique. Revista Ciencia Agronomica (UFC. Online), v. 48, p. 92-100, 2017.

Pages, J. Analyse factorielle multiple appliquee aux variables qualitatives et aux donnees mixtes. Revue de Statistique Appliquee, Paris, v. 50, n. 4, p. 5-37, 2002.

Pages, J.. Multiple factor analysis: main features and application to sensory data. Revista Colombiana de Estadistica, Bogota, v. 27, n. 1, p. 1-26, 2004.

See Also

Plot.MFA

Examples

data(DataMix) # mixed dataset

data <- DataMix[,2:ncol(DataMix)] 

rownames(data) <- DataMix[1:nrow(DataMix),1]

group.names = c("Grade Cafes/Work", "Formation/Dedication", "Coffees")

mf <- MFA(data = data, c(2,2,2), typegroups = c("n","c","f"), group.names) # performs MFA

print("Principal Component Variances:"); round(mf$mtxA,2)

print("Matrix of the Partial Inertia / Score of the Variables:"); round(mf$mtxEV,2)

Normalizes the data.

Description

Function that normalizes the data globally, or by column.

Usage

NormData(data, type = 1)

Arguments

data

Data to be analyzed.
type

1 normalizes overall (default),
2 normalizes per column.

Value

dataNorm

Normalized data.

Author(s)

Paulo Cesar Ossani

Marcelo Angelo Cirillo

Examples

data(DataQuan) # set of quantitative data

data <- DataQuan[,2:8]

res  <- NormData(data, type = 1) # normalizes the data globally

res # Globally standardized data

sd(res)   # overall standard deviation

mean(res) # overall mean


res <- NormData(data, type = 2) # normalizes the data per column

res # standardized data per column

apply(res, 2, sd) # standard deviation per column

colMeans(res)     # column averages

Test of normality of the data.

Description

Check the normality of the data, based on the asymmetry coefficient test.

Usage

NormTest(data, sign = 0.05)

Arguments

data

Data to be analyzed.
sign

Test significance level (default 5%).

Value

statistic

Observed Chi-square value, that is, the test statistic.
chisquare

Chi-square value calculated.
gl

Degree of freedom.
p.value

p-value.

Author(s)

Paulo Cesar Ossani

Marcelo Angelo Cirillo

References

Mingoti, S. A. Analise de dados atraves de metodos de estatistica multivariada: uma abordagem aplicada. Belo Horizonte: UFMG, 2005. 297 p.

Rencher, A. C. Methods of Multivariate Analysis. 2th. ed. New York: J.Wiley, 2002. 708 p.

Ferreira, D. F. Estatistica Multivariada. 2a ed. revisada e ampliada. Lavras: Editora UFLA, 2011. 676 p.

Examples

data <- cbind(rnorm(100,2,3), rnorm(100,1,2))

NormTest(data)

plot(density(data))


data <- cbind(rexp(200,3), rexp(200,3))

NormTest(data, sign = 0.01)

plot(density(data))

Principal Components Analysis (PCA).

Description

Performs principal component analysis (PCA) in a data set.

Usage

PCA(data, type = 1)

Arguments

data

Data to be analyzed.
type

1 for analysis using the covariance matrix (default),
2 for analysis using the correlation matrix.

Value

mtxC

Matrix of covariance or correlation according to "type".
mtxAutvlr

Matrix of eigenvalues (variances) with the proportions and proportions accumulated.
mtxAutvec

Matrix of eigenvectors - principal components.
mtxVCP

Matrix of covariance of the principal components with the original variables.
mtxCCP

Matrix of correlation of the principal components with the original variables.
mtxscores

Matrix with scores of the principal components.

Author(s)

Paulo Cesar Ossani

Marcelo Angelo Cirillo

References

Hotelling, H. Analysis of a complex of statistical variables into principal components. Journal of Educational Psychology, Arlington, v. 24, p. 417-441, Sept. 1933.

Mingoti, S. A. Analise de dados atraves de metodos de estatistica multivariada: uma abordagem aplicada. Belo Horizonte: UFMG, 2005. 297 p.

Ferreira, D. F. Estatistica Multivariada. 2a ed. revisada e ampliada. Lavras: Editora UFLA, 2011. 676 p.

Rencher, A. C. Methods of multivariate analysis. 2th. ed. New York: J.Wiley, 2002. 708 p.

See Also

Plot.PCA

Examples

data(DataQuan) # set of quantitative data

data <- DataQuan[,2:8]

rownames(data) <- DataQuan[1:nrow(DataQuan),1]

pc <- PCA(data, 2) # performs the PCA

print("Covariance matrix / Correlation:"); round(pc$mtxC,2)

print("Principal Components:"); round(pc$mtxAutvec,2)

print("Principal Component Variances:"); round(pc$mtxAutvlr,2)

print("Covariance of the Principal Components:"); round(pc$mtxVCP,2)

print("Correlation of the Principal Components:"); round(pc$mtxCCP,2)

print("Scores of the Principal Components:"); round(pc$mtxscores,2)

Graphs of the simple (CA) and multiple correspondence analysis (MCA).

Description

Graphs of the simple (CA) and multiple correspondence analysis (MCA).

Usage

Plot.CA(CA, titles = NA, xlabel = NA, ylabel = NA,
        size = 1.1, grid = TRUE, color = TRUE, linlab = NA, 
        savptc = FALSE, width = 3236, height = 2000, 
        res = 300, casc = TRUE)

Arguments

CA

Data of the CA function.
titles

Titles of the graphics, if not set, assumes the default text..
xlabel

Names the X axis, if not set, assumes the default text.
ylabel

Names the Y axis, if not set, assumes the default text.
size

Size of the points in the graphs.
grid

Put grid on graphs (default = TRUE).
color

Colored graphics (default = TRUE).
linlab

Vector with the labels for the observations.
savptc

Saves graphics images to files (default = FALSE).
width

Graphics images width when savptc = TRUE (defaul = 3236).
height

Graphics images height when savptc = TRUE (default = 2000).
res

Nominal resolution in ppi of the graphics images when savptc = TRUE (default = 300).
casc

Cascade effect in the presentation of the graphics (default = TRUE).

Value

Returns several graphs.

Author(s)

Paulo Cesar Ossani

Marcelo Angelo Cirillo

See Also

CA

Examples

data(DataFreq) # frequency data set

data <- DataFreq[,2:ncol(DataFreq)]

rownames(data) <- DataFreq[1:nrow(DataFreq),1]

res <- CA(data, "f") # performs CA

tit <- c("Scree-plot","Observations", "Variables", "Observations / Variables")

Plot.CA(res, titles = tit, xlabel = NA, ylabel = NA,
        color = TRUE, linlab = rownames(data), savptc = FALSE,
        width = 3236, height = 2000, res = 300, casc = FALSE)


data(DataQuali) # qualitative data set

data <- DataQuali[,2:ncol(DataQuali)]

res <- CA(data, "c", "b") # performs CA

tit <- c("","","Graph of the variables")

Plot.CA(res, titles = tit, xlabel = NA, ylabel = NA,
        color = TRUE, linlab = NA, savptc = FALSE, 
        width = 3236, height = 2000, res = 300,
        casc = FALSE)

Graphs of the Canonical Correlation Analysis (CCA).

Description

Graphs of the Canonical Correlation Analysis (CCA).

Usage

Plot.CCA(CCA, titles = NA, xlabel = NA, ylabel = NA,
         size = 1.1, grid = TRUE, color = TRUE, savptc = FALSE, 
         width = 3236, height = 2000, res = 300, casc = TRUE)

Arguments

CCA

Data of the CCA function.
titles

Titles of the graphics, if not set, assumes the default text.
xlabel

Names the X axis, if not set, assumes the default text.
ylabel

Names the Y axis, if not set, assumes the default text.
size

Size of the points in the graphs.
grid

Put grid on graphs (default = TRUE).
color

Colored graphics (default = TRUE).
savptc

Saves graphics images to files (default = FALSE).
width

Graphics images width when savptc = TRUE (defaul = 3236).
height

Graphics images height when savptc = TRUE (default = 2000).
res

Nominal resolution in ppi of the graphics images when savptc = TRUE (default = 300).
casc

Cascade effect in the presentation of the graphics (default = TRUE).

Value

Returns several graphs.

Author(s)

Paulo Cesar Ossani

Marcelo Angelo Cirillo

See Also

CCA

Examples

data(DataMix) # database

data <- DataMix[,2:ncol(DataMix)]

rownames(data) <- DataMix[,1]

X <- data[,1:2]

Y <- data[,5:6]

res <- CCA(X, Y, type = 2, test = "Bartlett", sign = 0.05) # performs CCA

tit <- c("Scree-plot","Correlations","Scores of the group X","Scores of the group Y")

Plot.CCA(res, titles = tit, xlabel = NA, ylabel = NA,
         color = TRUE, savptc = FALSE, width = 3236, 
         height = 2000, res = 300, casc = TRUE)

Plot of correlations between variables.

Description

It performs the correlations between the variables of a database and presents it in graph form.

Usage

Plot.Cor(data, title = NA, grid = TRUE, leg = TRUE, boxleg = FALSE, 
         text = FALSE, arrow = TRUE, color = TRUE, namesvar = NA,
         savptc = FALSE, width = 3236, height = 2000, res = 300)

Arguments

data

Numeric data set.
title

Title for the plot, if not defined it assumes standard text.
grid

Puts grid on plot (default = TRUE).
leg

Put the legend on the plot (default = TRUE)
boxleg

Put frame in the legend (default = FALSE).
text

Puts correlation values in circles (default = FALSE).
arrow

Positive (up) and negative (down) correlation arrows (default = TRUE).
color

Colorful plot (default = TRUE).
namesvar

Vector with the variable names, if omitted it assumes the names in 'date'.
savptc

Saves graphics images to files (default = FALSE).
width

Graphics images width when savptc = TRUE (defaul = 3236).
height

Graphics images height when savptc = TRUE (default = 2000).
res

Nominal resolution in ppi of the graphics images when savptc = TRUE (default = 300).

Value

Plot with the correlations between the variables in 'date'.

Author(s)

Paulo Cesar Ossani

Examples

data(iris) # data set

Plot.Cor(data = iris[,1:4], title = NA, grid = TRUE, leg = TRUE, boxleg = FALSE, 
         text = FALSE, arrow = TRUE, color = TRUE, namesvar = NA, savptc = FALSE, 
         width = 3236, height = 2000, res = 300)
         
Plot.Cor(data = iris[,1:4], title = NA, grid = TRUE, leg = TRUE, boxleg = FALSE, 
         text = TRUE, arrow = TRUE, color = TRUE, namesvar = c("A1","B2","C3","D4"),
         savptc = FALSE, width = 3236, height = 2000, res = 300)

Graphs of the Factorial Analysis (FA).

Description

Graphs of the Factorial Analysis (FA).

Usage

Plot.FA(FA, titles = NA, xlabel = NA, ylabel = NA, size = 1.1, 
        grid = TRUE, color = TRUE, linlab = NA, axes = TRUE, class = NA, 
        classcolor = NA, posleg = 2, boxleg = TRUE, savptc = FALSE,
        width = 3236, height = 2000, res = 300, casc = TRUE)

Arguments

FA

Data of the FA function.
titles

Titles of the graphics, if not set, assumes the default text.
xlabel

Names the X axis, if not set, assumes the default text.
ylabel

Names the Y axis, if not set, assumes the default text.
size

Size of the points in the graphs.
grid

Put grid on graphs (default = TRUE).
color

Colored graphics (default = TRUE).
linlab

Vector with the labels for the observations.
axes

Plots the X and Y axes (default = TRUE).
class

Vector with names of data classes.
classcolor

Vector with the colors of the classes.
posleg

0 with no caption,
1 for caption in the left upper corner,
2 for caption in the right upper corner (default),
3 for caption in the right lower corner,
4 for caption in the left lower corner.
boxleg

Puts the frame in the caption (default = TRUE).
savptc

Saves graphics images to files (default = FALSE).
width

Graphics images width when savptc = TRUE (defaul = 3236).
height

Graphics images height when savptc = TRUE (default = 2000).
res

Nominal resolution in ppi of the graphics images when savptc = TRUE (default = 300).
casc

Cascade effect in the presentation of the graphics (default = TRUE).

Value

Returns several graphs.

Author(s)

Paulo Cesar Ossani

Marcelo Angelo Cirillo

See Also

FA

Examples

data(iris) # conjunto de dados

data <- iris[,1:4]

cls <- iris[,5] # classe dos dados

res <- FA(data, method = "PC", type = 2, nfactor = 3)

tit <- c("Scree-plot","Scores of the Observations","Factorial Loadings","Biplot")

cls <- as.character(iris[,5])

Plot.FA(FA = res, titles = tit, xlabel = NA, ylabel = NA,
        color = TRUE, linlab = NA, savptc = FALSE, size = 1.1,
        posleg = 1, boxleg = FALSE, class = cls, axes = TRUE,
        classcolor = c("blue3","red","goldenrod3"),
        width = 3236, height = 2000, res = 300, casc = FALSE)

Graphics of the Multiple Factor Analysis (MFA).

Description

Graphics of the Multiple Factor Analysis (MFA).

Usage

Plot.MFA(MFA, titles = NA, xlabel = NA, ylabel = NA,
         posleg = 2, boxleg = TRUE, size = 1.1, grid = TRUE, 
         color = TRUE, groupscolor = NA, namarr = FALSE, 
         linlab = NA, savptc = FALSE, width = 3236, 
         height = 2000, res = 300, casc = TRUE)

Arguments

MFA

Data of the MFA function.
titles

Titles of the graphics, if not set, assumes the default text.
xlabel

Names the X axis, if not set, assumes the default text.
ylabel

Names the Y axis, if not set, assumes the default text.
posleg

1 for caption in the left upper corner,
2 for caption in the right upper corner (default),
3 for caption in the right lower corner,
4 for caption in the left lower corner.
boxleg

Puts frame in legend (default = TRUE).
size

Size of the points in the graphs.
grid

Put grid on graphs (default = TRUE).
color

Colored graphics (default = TRUE).
groupscolor

Vector with the colors of the groups.
namarr

Puts the points names in the cloud around the centroid in the graph corresponding to the global analysis of the Individuals and Variables (default = FALSE).
linlab

Vector with the labels for the observations, if not set, assumes the default text.
savptc

Saves graphics images to files (default = FALSE).
width

Graphics images width when savptc = TRUE (defaul = 3236).
height

Graphics images height when savptc = TRUE (default = 2000).
res

Nominal resolution in ppi of the graphics images when savptc = TRUE (default = 300).
casc

Cascade effect in the presentation of the graphics (default = TRUE).

Value

Returns several graphs.

Author(s)

Paulo Cesar Ossani

Marcelo Angelo Cirillo

See Also

MFA

Examples

data(DataMix) # set of mixed data

data <- DataMix[,2:ncol(DataMix)] 

rownames(data) <- DataMix[1:nrow(DataMix),1]

group.names = c("Grade Cafes/Work", "Formation/Dedication", "Coffees")
           
mf <- MFA(data, c(2,2,2), typegroups = c("n","c","f"), group.names) # performs MFA

tit <- c("Scree-Plot","Observations","Observations/Variables",
         "Correlation Circle","Inertia of the Variable Groups")

Plot.MFA(MFA = mf, titles = tit, xlabel = NA, ylabel = NA,
         posleg = 2, boxleg = FALSE, color = TRUE, 
         groupscolor = c("blue3","red","goldenrod3"),
         namarr = FALSE, linlab = NA, savptc = FALSE, 
         width = 3236, height = 2000, res = 300, 
         casc = TRUE) # plotting several graphs on the screen

Plot.MFA(MFA = mf, titles = tit, xlabel = NA, ylabel = NA,
         posleg = 2, boxleg = FALSE, color = TRUE, 
         namarr = FALSE, linlab = rep("A?",10), 
         savptc = FALSE, width = 3236, height = 2000,
         res = 300, casc = TRUE) # plotting several graphs on the screen

Graphs of the Principal Components Analysis (PCA).

Description

Graphs of the Principal Components Analysis (PCA).

Usage

Plot.PCA(PC, titles = NA, xlabel = NA, ylabel = NA, size = 1.1, 
         grid = TRUE, color = TRUE, linlab = NA, axes = TRUE, class = NA, 
         classcolor = NA, posleg = 2, boxleg = TRUE, savptc = FALSE,
         width = 3236, height = 2000, res = 300, casc = TRUE)

Arguments

PC

Data of the PCA function.
titles

Titles of the graphics, if not set, assumes the default text.
xlabel

Names the X axis, if not set, assumes the default text.
ylabel

Names the Y axis, if not set, assumes the default text.
size

Size of the points in the graphs.
grid

Put grid on graphs (default = TRUE).
color

Colored graphics (default = TRUE).
linlab

Vector with the labels for the observations.
axes

Plots the X and Y axes (default = TRUE).
class

Vector with names of data classes.
classcolor

Vector with the colors of the classes.
posleg

0 with no caption,
1 for caption in the left upper corner,
2 for caption in the right upper corner (default),
3 for caption in the right lower corner,
4 for caption in the left lower corner.
boxleg

Puts the frame in the caption (default = TRUE).
savptc

Saves graphics images to files (default = FALSE).
width

Graphics images width when savptc = TRUE (defaul = 3236).
height

Graphics images height when savptc = TRUE (default = 2000).
res

Nominal resolution in ppi of the graphics images when savptc = TRUE (default = 300).
casc

Cascade effect in the presentation of the graphics (default = TRUE).

Value

Returns several graphs.

Author(s)

Paulo Cesar Ossani

Marcelo Angelo Cirillo

See Also

PCA

Examples

data(iris) # data set

data <- iris[,1:4]

cls <- iris[,5] # data class

pc <- PCA(data, 2)

tit <- c("Scree-plot","Observations","Correlations")

cls <- as.character(iris[,5])

Plot.PCA(PC = pc, titles = tit, xlabel = NA, ylabel = NA,
         color = TRUE, linlab = NA, savptc = FALSE, size = 1.1,
         posleg = 2, boxleg = FALSE, class = cls, axes = TRUE,
         classcolor = c("blue3","red","goldenrod3"),
         width = 3236, height = 2000, res = 300, casc = FALSE)

Graphics of the Projection Pursuit (PP).

Description

Graphics of the Projection Pursuit (PP).

Usage

Plot.PP(PP, titles = NA, xlabel = NA, ylabel = NA, posleg = 2, boxleg = TRUE,
        size = 1.1, grid = TRUE, color = TRUE, classcolor = NA, linlab = NA, 
        axesvar = TRUE, axes = TRUE, savptc = FALSE, width = 3236, height = 2000, 
        res = 300, casc = TRUE)

Arguments

PP

Data of the PP_Optimizer function.
titles

Titles of the graphics, if not set, assumes the default text.
xlabel

Names the X axis, if not set, assumes the default text.
ylabel

Names the Y axis, if not set, assumes the default text.
posleg

0 with no caption,
1 for caption in the left upper corner,
2 for caption in the right upper corner (default),
3 for caption in the right lower corner,
4 for caption in the left lower corner.
boxleg

Puts the frame in the caption (default = TRUE).
size

Size of the points in the graphs.
grid

Put grid on graphs (default = TRUE).
color

Colored graphics (default = TRUE).
classcolor

Vector with the colors of the classes.
linlab

Vector with the labels for the observations.
axesvar

Puts axes of rotation of the variables, only when dimproj > 1 (default = TRUE).
axes

Plots the X and Y axes (default = TRUE).
savptc

Saves graphics images to files (default = FALSE).
width

Graphics images width when savptc = TRUE (defaul = 3236).
height

Graphics images height when savptc = TRUE (default = 2000).
res

Nominal resolution in ppi of the graphics images when savptc = TRUE (default = 300).
casc

Cascade effect in the presentation of the graphics (default = TRUE).

Value

Graph of the evolution of the indices, and graphs whose data were reduced in two dimensions.

Author(s)

Paulo Cesar Ossani

Marcelo Angelo Cirillo

See Also

PP_Optimizer and PP_Index

Examples

data(iris) # dataset

# Example 1 - Without the classes in the data
data <- iris[,1:4]

findex <- "kurtosismax" # index function

dim <- 1 # dimension of data projection

sphere <- TRUE # spherical data

res <- PP_Optimizer(data = data, class = NA, findex = findex,
                    optmethod = "GTSA", dimproj = dim, sphere = sphere, 
                    weight = TRUE, lambda = 0.1, r = 1, cooling = 0.9, 
                    eps = 1e-3, maxiter = 500, half = 30)

Plot.PP(res, titles = NA, posleg = 1, boxleg = FALSE, color = TRUE,
        linlab = NA, axesvar = TRUE, axes = TRUE, savptc = FALSE, 
        width = 3236, height = 2000, res = 300, casc = FALSE)


# Example 2 - With the classes in the data
class <- iris[,5] # data class

res <- PP_Optimizer(data = data, class = class, findex = findex,
                    optmethod = "GTSA", dimproj = dim, sphere = sphere, 
                    weight = TRUE, lambda = 0.1, r = 1, cooling = 0.9, 
                    eps = 1e-3, maxiter = 500, half = 30)

tit <- c(NA,"Graph example") # titles for the graphics

Plot.PP(res, titles = tit, posleg = 1, boxleg = FALSE, color = TRUE, 
        classcolor = c("blue3","red","goldenrod3"), linlab = NA, 
        axesvar = TRUE, axes = TRUE, savptc = FALSE, width = 3236,
        height = 2000, res = 300, casc = FALSE)


# Example 3 - Without the classes in the data, but informing 
#             the classes in the plot function
res <- PP_Optimizer(data = data, class = NA, findex = "Moment",
                    optmethod = "GTSA", dimproj = 2, sphere = sphere, 
                    weight = TRUE, lambda = 0.1, r = 1, cooling = 0.9, 
                    eps = 1e-3, maxiter = 500, half = 30)

lin <- c(rep("a",50),rep("b",50),rep("c",50)) # data class

Plot.PP(res, titles = NA, posleg = 1, boxleg = FALSE, color = TRUE,
        linlab = lin, axesvar = TRUE, axes = TRUE, savptc = FALSE, 
        width = 3236, height = 2000, res = 300, casc = FALSE)


# Example 4 - With the classes in the data, but not informed in plot function
class <- iris[,5] # data class

dim <- 2 # dimension of data projection

findex <- "lda" # index function

res <- PP_Optimizer(data = data, class = class, findex = findex,
                    optmethod = "GTSA", dimproj = dim, sphere = sphere, 
                    weight = TRUE, lambda = 0.1, r = 1, cooling = 0.9, 
                    eps = 1e-3, maxiter = 500, half = 30)

tit <- c("",NA) # titles for the graphics

Plot.PP(res, titles = tit, posleg = 1, boxleg = FALSE, color = TRUE,
        linlab = NA, axesvar = TRUE, axes = TRUE, savptc = FALSE, 
        width = 3236, height = 2000, res = 300, casc = FALSE)

Graphs of the linear regression results.

Description

Graphs of the linear regression results.

Usage

Plot.Regr(Reg, typegraf = "Scatterplot", title = NA, xlabel = NA, 
          ylabel = NA, namevary = NA, namevarx = NA, size = 1.1, 
          grid = TRUE, color = TRUE, intconf = TRUE, intprev = TRUE,
          savptc = FALSE, width = 3236, height = 2000, res = 300, 
          casc = TRUE)

Arguments

Reg

Regression function data.
typegraf

Type of graphic:
"Scatterplot" - Scatterplot 2 to 2,
"Regression" - Graph of the linear regression,
"QQPlot" - Graph of the normal probability of the residues,
"Histogram" - Histogram of the residues,
"Fits" - Graph of the adjusted values versus residuals,
"Order" - Graph of the order of the observations versus the residuals.
title

Titles of the graphics, if not set, assumes the default text.
xlabel

Names the X axis, if not set, assumes the default text.
ylabel

Names the Y axis, if not set, assumes the default text.
namevary

Variable name Y, if not set, assumes the default text.
namevarx

Name of the variable X, or variables X, if not set, assumes the default text.
size

Size of the points in the graphs.
grid

Put grid on graphs (default = TRUE).
color

Colored graphics (default = TRUE).
intconf

Case typegraf = "Regression". Graphics with confidence interval (default = TRUE).
intprev

Case typegraf = "Regression". Graphics with predictive interval (default = TRUE).
savptc

Saves graphics images to files (default = FALSE).
width

Graphics images width when savptc = TRUE (defaul = 3236).
height

Graphics images height when savptc = TRUE (default = 2000).
res

Nominal resolution in ppi of the graphics images when savptc = TRUE (default = 300).
casc

Cascade effect in the presentation of the graphics (default = TRUE).

Value

Returns several graphs.

Author(s)

Paulo Cesar Ossani

See Also

Regr

Examples

data(DataMix)

Y <- DataMix[,2]

X <- DataMix[,7]

name.y <- "Medium grade"

name.x <- "Commercial coffees"

res <- Regr(Y, X, namevarx = name.x , intercept = TRUE, sigf = 0.05)

tit <- c("Scatterplot")
Plot.Regr(res, typegraf = "Scatterplot", title = tit,
          namevary = name.y, namevarx = name.x, color = TRUE, 
          savptc = FALSE, width = 3236, height = 2000, res = 300)

tit <- c("Scatterplot with the adjusted line")
Plot.Regr(res, typegraf = "Regression", title = tit, 
          xlabel = name.x, ylabel = name.y, color = TRUE,
          intconf = TRUE, intprev = TRUE, savptc = FALSE, 
          width = 3236, height = 2000, res = 300)

dev.new() # necessary to not overlap the following graphs to the previous graph

par(mfrow = c(2,2)) 

Plot.Regr(res, typegraf = "QQPlot", casc = FALSE)
Plot.Regr(res, typegraf = "Histogram", casc = FALSE)
Plot.Regr(res, typegraf = "Fits", casc = FALSE)
Plot.Regr(res, typegraf = "Order", casc = FALSE)

Function to find the Projection Pursuit indexes (PP).

Description

Function used to find Projection Pursuit indexes (PP).

Usage

PP_Index(data, class = NA, vector.proj = NA, 
         findex = "HOLES", dimproj = 2, weight = TRUE, 
         lambda = 0.1, r = 1, ck = NA)

Arguments

data

Numeric dataset without class information.
class

Vector with names of data classes.
vector.proj

Vector projection.
findex

Projection index function to be used:
"lda" - LDA index,
"pda" - PDA index,
"lr" - Lr index,
"holes" - Holes index (default),
"cm" - Central Mass index,
"pca" - PCA index,
"friedmantukey" - Friedman Tukey index,
"entropy" - Entropy index,
"legendre" - Legendre index,
"laguerrefourier" - Laguerre Fourier index,
"hermite" - Hermite index,
"naturalhermite" - Natural Hermite index,
"kurtosismax" - Maximum kurtosis index,
"kurtosismin" - Minimum kurtosis index,
"moment" - Moment index,
"mf" - MF index,
"chi" - Chi-square index.
dimproj

Dimension of data projection (default = 2).
weight

Used in index LDA, PDA and Lr to weight the calculations for the number of elements in each class (default = TRUE).
lambda

Used in the PDA index (default = 0.1).
r

Used in the Lr index (default = 1).
ck

Internal use of the CHI index function.

Value

num.class

Number of classes.
class.names

Class names.
findex

Projection index function used.
vector.proj

Projection vectors found.
index

Projection index found in the process.

Author(s)

Paulo Cesar Ossani

Marcelo Angelo Cirillo

References

Ossani, P. C.; Figueira, M. R.; Cirillo, M. A. Proposition of a new index for projection pursuit in the multiple factor analysis. Computational and Mathematical Methods, v. 1, p. 1-18, 2020.

Cook, D.; Buja, A.; Cabrera, J. Projection pursuit indexes based on orthonormal function expansions. Journal of Computational and Graphical Statistics, 2(3):225-250, 1993.

Cook, D.; Buja, A.; Cabrera, J.; Hurley, C. Grand tour and projection pursuit, Journal of Computational and Graphical Statistics, 4(3), 155-172, 1995.

Cook, D.; Swayne, D. F. Interactive and Dynamic Graphics for data Analysis: With R and GGobi. Springer. 2007.

Espezua, S.; Villanueva, E.; Maciel, C. D.; Carvalho, A. A projection pursuit framework for supervised dimension reduction of high dimensional small sample datasets. Neurocomputing, 149, 767-776, 2015.

Friedman, J. H., Tukey, J. W. A projection pursuit algorithm for exploratory data analysis. IEEE Transaction on Computers, 23(9):881-890, 1974.

Hastie, T., Buja, A., Tibshirani, R. Penalized discriminant analysis. The Annals of Statistics. 23(1), 73-102 . 1995.

Huber, P. J. Projection pursuit. Annals of Statistics, 13(2):435-475, 1985.

Jones, M. C.; Sibson, R. What is projection pursuit, (with discussion), Journal of the Royal Statistical Society, Series A 150, 1-36, 1987.

Lee, E. K.; Cook, D. A projection pursuit index for large p small n data. Statistics and Computing, 20(3):381-392, 2010.

Lee, E.; Cook, D.; Klinke, S.; Lumley, T. Projection pursuit for exploratory supervised classification. Journal of Computational and Graphical Statistics, 14(4):831-846, 2005.

Martinez, W. L., Martinez, A. R.; Computational Statistics Handbook with MATLAB, 2th. ed. New York: Chapman & Hall/CRC, 2007. 794 p.

Martinez, W. L.; Martinez, A. R.; Solka, J. Exploratory data Analysis with MATLAB, 2th. ed. New York: Chapman & Hall/CRC, 2010. 499 p.

Pena, D.; Prieto, F. Cluster identification using projections. Journal of the American Statistical Association, 96(456):1433-1445, 2001.

Posse, C. Projection pursuit exploratory data analysis, Computational Statistics and data Analysis, 29:669-687, 1995a.

Posse, C. Tools for two-dimensional exploratory projection pursuit, Journal of Computational and Graphical Statistics, 4:83-100, 1995b.

See Also

PP_Optimizer and Plot.PP

Examples

data(iris) # data set

data <- iris[,1:4]

# Example 1 - Without the classes in the data
ind <- PP_Index(data = data, class = NA, vector.proj = NA, 
                findex = "moment", dimproj = 2, weight = TRUE, 
                lambda = 0.1, r = 1)

print("Number of classes:"); ind$num.class
print("class Names:"); ind$class.names
print("Projection index function:"); ind$findex
print("Projection vectors:"); ind$vector.proj  
print("Projection index:"); ind$index


# Example 2 - With the classes in the data
class <- iris[,5] # data class

findex <- "pda" # index function

sphere <- TRUE # spherical data

res <- PP_Optimizer(data = data, class = class, findex = findex,
                    optmethod = "SA", dimproj = 2, sphere = sphere, 
                    weight = TRUE, lambda = 0.1, r = 1, cooling = 0.9, 
                    eps = 1e-3, maxiter = 1000, half = 30)

# Comparing the result obtained
if (match(toupper(findex),c("LDA", "PDA", "LR"), nomatch = 0) > 0) {
  if (sphere) {
     data <- apply(predict(prcomp(data)), 2, scale) # spherical data
  }
} else data <- as.matrix(res$proj.data[,1:Dim])

ind <- PP_Index(data = data, class = class, vector.proj = res$vector.opt, 
                findex = findex, dimproj = 2, weight = TRUE, lambda = 0.1,
                r = 1)

print("Number of classes:"); ind$num.class
print("class Names:"); ind$class.names
print("Projection index function:"); ind$findex
print("Projection vectors:"); ind$vector.proj  
print("Projection index:"); ind$index
print("Optimized Projection index:"); res$index[length(res$index)]

Optimization function of the Projection Pursuit index (PP).

Description

Optimization function of the Projection Pursuit index (PP).

Usage

PP_Optimizer(data, class = NA, findex = "HOLES",   
             dimproj = 2, sphere = TRUE, optmethod = "GTSA",   
             weight = TRUE, lambda = 0.1, r = 1, cooling = 0.9,  
             eps = 1e-3, maxiter = 3000, half = 30)

Arguments

data

Numeric dataset without class information.
class

Vector with names of data classes.
findex

Projection index function to be used:
"lda" - LDA index,
"pda" - PDA index,
"lr" - Lr index,
"holes" - Holes index (default),
"cm" - Central Mass index,
"pca" - PCA index,
"friedmantukey" - Friedman Tukey index,
"entropy" - Entropy index,
"legendre" - Legendre index,
"laguerrefourier" - Laguerre Fourier index,
"hermite" - Hermite index,
"naturalhermite" - Natural Hermite index,
"kurtosismax" - Maximum kurtosis index,
"kurtosismin" - Minimum kurtosis index,
"moment" - Moment index,
"mf" - MF index,
"chi" - Chi-square index.
dimproj

Dimension of the data projection (default = 2).
sphere

Spherical data (default = TRUE).
optmethod

Optimization method GTSA - Grand Tour Simulated Annealing or SA - Simulated Annealing (default = "GTSA").
weight

Used in index LDA, PDA and Lr to weight the calculations for the number of elements in each class (default = TRUE).
lambda

Used in the PDA index (default = 0.1).
r

Used in the Lr index (default = 1).
cooling

Cooling rate (default = 0.9).
eps

Approximation accuracy for cooling (default = 1e-3).
maxiter

Maximum number of iterations of the algorithm (default = 3000).
half

Number of steps without incrementing the index, then decreasing the cooling value (default = 30).

Value

num.class

Number of classes.
class.names

Class names.
proj.data

Projected data.
vector.opt

Projection vectors found.
index

Vector with the projection indices found in the process, converging to the maximum, or the minimum.
findex

Projection index function used.

Author(s)

Paulo Cesar Ossani

Marcelo Angelo Cirillo

References

Cook, D.; Lee, E. K.; Buja, A.; Wickmam, H. Grand tours, projection pursuit guided tours and manual controls. In Chen, Chunhouh, Hardle, Wolfgang, Unwin, e Antony (Eds.), Handbook of data Visualization, Springer Handbooks of Computational Statistics, chapter III.2, p. 295-314. Springer, 2008.

Lee, E.; Cook, D.; Klinke, S.; Lumley, T. Projection pursuit for exploratory supervised classification. Journal of Computational and Graphical Statistics, 14(4):831-846, 2005.

See Also

Plot.PP and PP_Index

Examples

data(iris) # data set

# Example 1 - Without the classes in the data
data <- iris[,1:4]

class <- NA # data class

findex <- "kurtosismax" # index function

dim <- 1 # dimension of data projection

sphere <- TRUE # spherical data

res <- PP_Optimizer(data = data, class = class, findex = findex,
                    optmethod = "GTSA", dimproj = dim, sphere = sphere, 
                    weight = TRUE, lambda = 0.1, r = 1, cooling = 0.9, 
                    eps = 1e-3, maxiter = 1000, half = 30)
 
print("Number of classes:"); res$num.class
print("class Names:"); res$class.names
print("Projection index function:"); res$findex
print("Projected data:"); res$proj.data
print("Projection vectors:"); res$vector.opt
print("Projection index:"); res$index


# Example 2 - With the classes in the data
class <- iris[,5] # classe dos dados

res <- PP_Optimizer(data = data, class = class, findex = findex,
                    optmethod = "GTSA", dimproj = dim, sphere = sphere, 
                    weight = TRUE, lambda = 0.1, r = 1, cooling = 0.9, 
                    eps = 1e-3, maxiter = 1000, half = 30)

print("Number of classes:"); res$num.class
print("class Names:"); res$class.names
print("Projection index function:"); res$findex
print("Projected data:"); res$proj.data
print("Projection vectors:"); res$vector.opt
print("Projection index:"); res$index

Linear regression.

Description

Performs linear regression on a data set.

Usage

Regr(Y, X, namevarx = NA, intercept = TRUE, sigf = 0.05)

Arguments

Y

Variable response.
X

Regression variables.
namevarx

Name of the variable, or variables X, if not set, assumes the default text.
intercept

Consider the intercept in the regression (default = TRUE).
sigf

Level of significance of residue tests(default = 5%).

Value

Betas

Regression coefficients.
CovBetas

Covariance matrix of the regression coefficients.
ICc

Confidence interval of the regression coefficients.
hip.test

Hypothesis test of the regression coefficients.
ANOVA

Regression analysis of the variance.
R

Determination coefficient.
Rc

Corrected coefficient of determination.
Ra

Adjusted coefficient of determination.
QME

Variance of the residues.
ICQME

Confidence interval of the residue variance.
prev

Prediction of the regression fit.
IPp

Predictions interval
ICp

Interval of prediction confidence
error

Residuals of the regression fit.
error.test

It returns to 5% of significance the test of independence, normality and homogeneity of the variance of the residues.

Author(s)

Paulo Cesar Ossani

References

Charnet, R.; at al.. Analise de modelos de regressao lienar, 2a ed. Campinas: Editora da Unicamp, 2008. 357 p.

Rencher, A. C.; Schaalje, G. B. Linear models in statisctic. 2th. ed. New Jersey: John & Sons, 2008. 672 p.

Rencher, A. C. Methods of multivariate analysis. 2th. ed. New York: J.Wiley, 2002. 708 p.

See Also

Plot.Regr

Examples

data(DataMix)

Y <- DataMix[,2]

X <- DataMix[,6:7]

name.x <- c("Special Coffees", "Commercial Coffees")

res <- Regr(Y, X, namevarx = name.x , intercept = TRUE, sigf = 0.05)

print("Regression Coefficients:"); round(res$Betas,4)
print("Analysis of Variance:"); res$ANOVA
print("Hypothesis test of regression coefficients:"); round(res$hip.test,4)
print("Determination coefficient:"); round(res$R,4)
print("Corrected coefficient of determination:"); round(res$Rc,4) 
print("Adjusted coefficient of determination:"); round(res$Ra,4)
print("Tests of the residues"); res$error.test

Scatter plot.

Description

Performs the scatter plot.

Usage

Scatter(data, ellipse = TRUE, ellipse.level = 0.95, rectangle = FALSE,  
        title = NA, xlabel = NA, ylabel = NA,  posleg = 2, boxleg = TRUE, 
        axes = TRUE, size = 1.1, grid = TRUE, color = TRUE, linlab = NA,   
        class = NA, classcolor = NA, savptc = FALSE, width = 3236, 
        height = 2000, res = 300)

Arguments

data

Data with x and y coordinates.
ellipse

Place an ellipse around the classes (default = TRUE).
ellipse.level

Significance level of the ellipse (defaul = 0.95).
rectangle

Place rectangle to differentiate classes (default = FALSE).
title

Titles of the graphics, if not set, assumes the default text.
xlabel

Names the X axis, if not set, assumes the default text.
ylabel

Names the Y axis, if not set, assumes the default text.
posleg

0 with no caption,
1 for caption in the left upper corner,
2 for caption in the right upper corner (default),
3 for caption in the right lower corner,
4 for caption in the left lower corner.
boxleg

Puts the frame in the caption (default = TRUE).
axes

Plots the X and Y axes (default = TRUE).
size

Size of the points in the graphs.
grid

Put grid on graphs (default = TRUE).
color

Colored graphics (default = TRUE).
linlab

Vector with the labels for the observations.
class

Vector with names of data classes.
classcolor

Vector with the colors of the classes.
savptc

Saves graphics images to files (default = FALSE).
width

Graphics images width when savptc = TRUE (defaul = 3236).
height

Graphics images height when savptc = TRUE (default = 2000).
res

Nominal resolution in ppi of the graphics images when savptc = TRUE (default = 300).

Value

Scatter plot.

Author(s)

Paulo Cesar Ossani

References

Rencher, A. C. Methods of multivariate analysis. 2th. ed. New York: J.Wiley, 2002. 708 p.

Anton, H.; Rorres, C. Elementary linear algebra: applications version. 10th ed. New Jersey: John Wiley & Sons, 2010. 768 p.

Examples

data(iris) # data set

data <- iris[,3:4]

cls <- iris[,5] # data class

Scatter(data, ellipse = TRUE, ellipse.level = 0.95, rectangle = FALSE,  
        title = NA, xlabel = NA, ylabel = NA,  posleg = 1, boxleg = FALSE, 
        axes = FALSE, size = 1.1, grid = TRUE, color = TRUE, linlab = NA, 
        class = cls, classcolor = c("goldenrod3","blue","red"),
        savptc = FALSE, width = 3236, height = 2000, res = 300)

Scatter(data, ellipse = FALSE, ellipse.level = 0.95, rectangle = TRUE,  
        title = NA, xlabel = NA, ylabel = NA,  posleg = 1, boxleg = TRUE, 
        axes = FALSE, size = 1.1, grid = TRUE, color = TRUE, linlab = NA, 
        class = cls, classcolor = c("goldenrod3","blue","red"),
        savptc = FALSE, width = 3236, height = 2000, res = 300)