# Confidence ellipses around products based on panelists descriptions

### Description

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

### Usage

1 2 3 4 5 6 | ```
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
( |

`col.p` |
the position of the |

`col.j` |
the position of the |

`firstvar` |
the position of the first sensory descriptor |

`lastvar` |
the position of the last sensory descriptor (by default the last column of |

`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 |

`level.search.desc` |
the threshold above which a descriptor is not considered as discriminant according to AOV model |

`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 |

`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 |

`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 |

`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, |

`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

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 | ```
## 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)
``` |