FactoMineR (version 1.01)

GPA: Generalised Procrustes Analysis

Description

Performs Generalised Procrustes Analysis (GPA) that takes into account missing values.

Usage

GPA(df, tolerance=10^-10, nbiteration=200, scale=TRUE, 
    coord=c(1,2), group, name.group = NULL, graph = TRUE)

Arguments

df

a data frame with n rows (individuals) and p columns (quantitative varaibles)

tolerance

a threshold with respect to which the algorithm stops, i.e. when the difference between the GPA loss function at step n and n+1 is less than tolerance

nbiteration

the maximum number of iterations until the algorithm stops

scale

a boolean, if TRUE (which is the default value) scaling is required

coord

a length 2 vector specifying the components to plot

group

a vector indicating the number of variables in each group

name.group

a vector indicating the name of the groups (the groups are successively named group.1, group.2 and so on, by default)

graph

boolean, if TRUE a graph is displayed

Value

• A list containing the following components:
• RV
  a matrix of RV coefficients between partial configurations
• RVs
  a matrix of standardized RV coefficients between partial configurations
• simi
  a matrix of Procrustes similarity indexes between partial configurations
• scaling
  a vector of isotropic scaling factors
• dep
  an array of initial partial configurations
• consensus
  a matrix of consensus configuration
• Xfin
  an array of partial configurations after transformations
• correlations
  correlation matrix between initial partial configurations and consensus dimensions
• PANOVA
  a list of "Procrustes Analysis of Variance" tables, per assesor (config), per product(objet), per dimension (dimension)

Details

Performs a Generalised Procrustes Analysis (GPA) that takes into account missing values: some data frames of df may have non described or non evaluated rows, i.e. rows with missing values only. The algorithm used here is the one developed by Commandeur.

References

Commandeur, J.J.F (1991) Matching configurations.DSWO press, Leiden University. Dijksterhuis, G. & Punter, P. (1990) Interpreting generalized procrustes analysis "Analysis of Variance" tables, Food Quality and Preference, 2, 255--265 Gower, J.C (1975) Generalized Procrustes analysis, Psychometrika, 40, 33--50 Kazi-Aoual, F., Hitier, S., Sabatier, R., Lebreton, J.-D., (1995) Refined approximations to permutations tests for multivariate inference. Computational Statistics and Data Analysis, 20, 643--656 Qannari, E.M., MacFie, H.J.H, Courcoux, P. (1999) Performance indices and isotropic scaling factors in sensory profiling, Food Quality and Preference, 10, 17--21

Examples

data(wine)
res.gpa <- GPA(wine[,-(1:2)], group=c(5,3,10,9,2),
    name.group=c("olf","vis","olfag","gust","ens"))

### If you want to construct the partial points for some individuals only
plot.GPApartial (res.gpa)