MFA {MFAg}

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)