gpa function

Generalised Procrustes Analysis

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

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

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
• 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
• axes: a length 2 vector specifying the components to plot

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.

Returns

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)

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

Author(s)

Elisabeth Morand

Examples

## Not run:

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
plotGPApartial (res.gpa)
## End(Not run)