Type:	Package
Title:	Multivariate Analysis
Version:	2.2.7
Date:	2025-04-19
Imports:	graphics, grDevices, MASS, stats
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.
License:	GPL-3
Encoding:	UTF-8
LazyData:	true
NeedsCompilation:	yes
Author:	Paulo Cesar Ossani [aut, cre], Marcelo Angelo Cirillo [aut]
Maintainer:	Paulo Cesar Ossani <ossanipc@hotmail.com>
Repository:	CRAN
Packaged:	2025-04-18 18:29:07 UTC; Ossan
Date/Publication:	2025-04-18 18:40:09 UTC

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

Author(s)

Paulo Cesar Ossani and Marcelo Angelo Cirillo.

Maintainer: Paulo Cesar Ossani <ossanipc@hotmail.com>

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

Value

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

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.

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

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.

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

Value

Several graphics.

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

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

Value

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

Value

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)

Generalized Singular Value Decomposition (GSVD).

Description

Given the matrix A of order nxm, the generalized singular value decomposition (GSVD) involves the use of two sets of positive square matrices of order nxn and mxm respectively. These two matrices express constraints imposed, respectively, on the lines and columns of A.

Usage

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

Arguments

Details

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

Value

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)) 

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

Value

Graphs with rotations.

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

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

Value

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

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

Value

Multidimensional Scaling.

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

Value

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

Value

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

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

Value

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)

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

Value

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

Value

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

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, axes = TRUE,
        savptc = FALSE, width = 3236, height = 2000, res = 300, 
        casc = TRUE)

Arguments

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, axes = TRUE,
        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, 
        axes = TRUE, 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, axes = TRUE, savptc = FALSE, 
         width = 3236, height = 2000, res = 300, casc = TRUE)

Arguments

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, axes = TRUE,
         casc = FALSE)

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

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

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

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

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

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

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)

Linear regression.

Description

Performs linear regression on a data set.

Usage

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

Arguments

Value

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

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)