GPA {FactoMineR} | R Documentation |

## 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,
group, name.group = NULL, graph = TRUE, axes = c(1,2))
```

### Arguments

`df` |
a data frame with |

`tolerance` |
a threshold with respect to which the algorithm stops, i.e. when the difference between
the GPA loss function at step |

`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.

### 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) |

### Author(s)

Elisabeth Morand

### 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

```
## 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)
```

*FactoMineR*version 2.11 Index]