Confidence ellipses around products based on panelists descriptions

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Description

Virtual panels are generated using Boostrap techniques in order to display confidence ellipses around products.

Usage

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panellipse(donnee, col.p, col.j, firstvar, lastvar = ncol(donnee),
    alpha = 0.05, coord = c(1,2), scale.unit = TRUE, nbsimul = 500,
    nbchoix = NULL, group = NULL, name.group = NULL,
    level.search.desc = 0.2, centerbypanelist = TRUE,
    scalebypanelist = FALSE, name.panelist = FALSE,
    variability.variable = TRUE, cex = 1, color = NULL)

Arguments

donnee

a data frame made up of at least two qualitative variables (product, panelist) and a set of quantitative variables (sensory descriptors)

col.p

the position of the product variable

col.j

the position of the panelist variable

firstvar

the position of the first sensory descriptor

lastvar

the position of the last sensory descriptor (by default the last column of donnee)

alpha

the confidence level of the ellipses

coord

a length 2 vector specifying the components to plot

scale.unit

boolean, if T the descriptors are scaled to unit variance

nbsimul

the number of simulations (corresponding to the number of virtual panels) used to compute the ellipses

nbchoix

the number of panelists forming a virtual panel, by default the number of panelists in the original panel

group

the number of variables in each group of variables when multiple factor analysis is performed (by default this parameter equals NULL and a PCA is performed)

name.group

the names of the groups of variables when mfa is performed (if group differs from NULL)

level.search.desc

the threshold above which a descriptor is not considered as discriminant according to AOV model "descriptor=Product+Panelist"

centerbypanelist

boolean, if T center the data by panelist before the construction of the axes

scalebypanelist

boolean, if T scale the data by panelist before the construction of the axes (by default, FALSE is assigned to that parameter)

name.panelist

boolean, if T then the name of each panelist is displayed on the plotpanelist graph (by default, FALSE is assigned to that parameter)

variability.variable

boolean, if T a plot with the variability of the variable is drawn and a confidence intervals of the correlations between descriptors are calculated

cex

cf. function par in the graphics package

color

a vector with the colors used; by default there are 35 colors defined

Details

Panellipse, step by step:
Step 1 Performs a selection of discriminating descriptors with respect to a threshold set by users
Step 2 Virtual panels are generated using Boostrap techniques; the number of panels as well as their size are set by users with the nbsimul and nbchoix parameters
Step 3 Coordinates of the products with respect to each virtual panels are computed
Step 4 Each product is then circled by its confidence ellipse generated by virtual panels and comprising (1-alpha)*100 percent of the virtual products
Step 5 Variability of the variables is drawn and confidence interval of the correlation coefficient between descriptors are calculated by bootstrap

Value

A list containing the following elements:

eig

a matrix with the component of the factor analysis (in row) and the eigenvalues, the inertia and the cumulative inertia for each component

coordinates

a list with: the coordinates of the products with respect to the panel and to each panelists and the coordinates of the partial products with respect to the panel and to each panelists

hotelling

Returns a matrix with the P-values of the Hotelling's T2 tests for each pair of products: this matrix allows to find the product which are significantly different for the 2-components sensory description; if an MFA is done, hotelling returns as many matrices as there are group, these matrices allows to find the product which are significantly different for the 2-components sensory description of the group, and it returns also a global matrix corresponding to the P-values for the tests corresponding to the mean product.

correl

a list with: the matrix of the estimated correlation coefficients and two matrices corresponding to the confidence intervals, min and max, of the correlation coefficients calculated by bootstrap.

Returns a graph of the products as well as a correlation circle of the descriptors.

Returns a graph where each product is displayed with respect to a panel and to each panelist composing the panel; products described by the panel are displayed as square, they are displayed as circle when they are described by each panelist.

Returns a graph where each product is circled by its confidence ellipse generated by virtual panels. When a Multiple Factor Analysis is performed, returns a graph where each partial product is circled by its confidence ellipse generated by virtual panels.

Returns a graph where the variability of each variable is drawn on the correlation circle graph.

Author(s)

Fran<e7>ois Husson

References

Husson F., Le Dien S. & Pag<e8>s J. (2005). Confidence ellipse for the sensory profiles obtained by Principal Components Analysis. Food Quality and Preference. 16 (3), 245-250.
Pag<e8>s J. & Husson F. (2005). Multiple Factor Analysis with confidence ellipses: a methodology to study the relationships between sensory and instrumental data. To be published in Journal of Chemometrics.
Husson F., L<ea> S. & Pag<e8>s J. Variability of the representation of the variables resulting from PCA in the case of a conventional sensory profile. Food Quality and Preference. 16 (3), 245-250.

See Also

panellipse.session, panelmatch

Examples

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## Not run: 
## Example 1: PCA
data(chocolates)
res <- panellipse(sensochoc, col.p = 4, col.j = 1, firstvar = 5)
coltable(res$hotelling, main.title = "P-values for the Hotelling's T2 tests")

## If we consider only 12 panelists in a virtual panel, 
## what would be the size of the ellipses
res2 <- panellipse(sensochoc, col.p = 4, col.j = 1, nbchoix = 12, firstvar = 5)
coltable(res2$hotelling, main.title = "P-values for the Hotelling's T2 tests")

## If we want the confidence ellipses around the individual descriptions
panellipse(sensochoc, col.p = 4, col.j = 1, nbchoix = 1, firstvar = 5)


## Example 2: MFA
data(chocolates)
res <- panellipse(sensochoc, col.p = 4, col.j = 1, firstvar = 5, 
    group = c(6,8), name.group = c("G1","G2"))
for (i in 1:dim(res$hotelling$bygroup)[3]) coltable(res$hotelling$bygroup[,,i], 
    main.title = paste("P-values for the Hotelling's T2 tests (",
    dimnames(res$hotelling$bygroup)[3][[1]][i],")",sep=""))

## End(Not run)

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