# Simple and Canonical Correspondence Analysis

### Description

This function performs simple and canonical CA for incomplete tables based on SVD. Different scaling methods for row and column scores are provided.

### Usage

1 2 3 4 5 6 7 |

### Arguments

`tab` |
Data frame of dimension n times m with frequencies. Missings are coded as |

`ndim` |
Number of dimensions. |

`row.covariates` |
Matrix with n rows containing covariates for the row scores. |

`col.covariates` |
Matrix with m rows containing covariates for the column scores. |

`scaling` |
A vector with two elements. The first one corresponds to the method for row scaling, the second one for column scaling. Available scaling methods are |

`ellipse` |
If |

`eps` |
Convergence criterion for reconstitution algorithm. |

`x` |
Object of class |

`object` |
Object of class |

`...` |
Additional arguments ignored. |

### Details

Missing values in `tab`

are imputed using the reconstitution algorithm.
Setting `scaling`

to `"standard"`

leads to standard coordinates.
Principal coordinates can be computed by means of Benzecri decomposition.
Furthermore, scores can be scaled around their centroid.
Goodman scaling is based on Fisher-Maung decomposition.

For large datasets it is suggested to set `ellipse = FALSE`

. If `conf = TRUE`

, make sure
that there are no rows and columns that have full 0 entries.

### Value

`row.scores` |
Scaled row scores. |

`col.scores` |
Scaled column scores. |

`ndim` |
Number of dimensions extracted. |

`chisq` |
Total chi-square value. |

`chisq.decomp` |
Chi-square decomposition across dimensions with p-values. |

`singular.values` |
Singular values without trivial solution. |

`se.singular.values` |
Standard errors for the singular values. |

`left.singvec` |
Left singular vectors without trivial solution. |

`right.singvec` |
Right singular vectors without trivial solution. |

`eigen.values` |
Eigenvalues without trivial solution. |

`datname` |
Name of the dataset. |

`tab` |
Table with imputed frequencies in case of missings. |

`row.covariates` |
Matrix with row covariates. |

`col.covariates` |
Matrix with column covariates. |

`scaling` |
Scaling Method. |

`bdmat` |
List of matrices with observed and fitted Benzecri distances for rows and columns. |

`rmse` |
Root mean squared error of Bezencri distances (rows and columns). |

`row.acov` |
Covariance matrix for row scores. |

`col.acov` |
Covariance matrix for column scores. |

`cancoef` |
List containing canonical coefficients (CCA only). |

`sitescores` |
List containing the site scores (CCA only). |

`isetcor` |
List containing the intraset correlations (CCA only). |

### Author(s)

Jan de Leeuw, Patrick Mair

### References

De Leeuw, J. and Mair, P. (2009). Simple and Canonical Correspondence Analysis Using the R Package anacor. Journal of Statistical Software, 31(5), 1-18. http://www.jstatsoft.org/v31/i05/

### See Also

`plot.anacor`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 | ```
## simple CA on Tocher data, asymmetric coordinates
data(tocher)
res <- anacor(tocher, scaling = c("standard", "centroid"))
res
summary(res)
## 2- and 5-dimensional solutions for bitterling data, Benzecri scaling
data(bitterling)
res1 <- anacor(bitterling, ndim = 2, scaling = c("Benzecri", "Benzecri"))
res2 <- anacor(bitterling, ndim = 5, scaling = c("Benzecri", "Benzecri"))
res1
res2
## Canonical CA on Maxwell data, Goodman scaling
data(maxwell)
res <- anacor(maxwell$table, row.covariates = maxwell$row.covariates,
scaling = c("Goodman", "Goodman"))
res
summary(res)
``` |