dissvar {TraMineR} | R Documentation |

## Dissimilarity based discrepancy

### Description

Compute the discrepancy from the pairwise dissimilarities between objects. The discrepancy is a measure of dispersion of the set of objects.

### Usage

```
dissvar(diss, weights=NULL, squared = FALSE)
```

### Arguments

`diss` |
A dissimilarity matrix or a |

`weights` |
optional numerical vector containing weights. |

`squared` |
Logical. If |

### Details

The discrepancy is an extension of the concept of variance to any kind of objects for which we can compute pairwise dissimilarities.
The discrepancy `s^2`

is defined as:

`s^2=\frac{1}{2n^2}\sum_{i=1}^{n}\sum_{j=1}^{n}d_{ij}`

*Mathematical ground*:
In the Euclidean case, the sum of squares can be expressed as:

`SS=\sum_{i=1}^{n}(y_i-\bar{y})^2=\frac{1}{2n}\sum_{i=1}^{n}\sum_{j=1}^{n}(y_i-y_j)^2`

The concept of discrepancy generalizes the equation by allowing to replace the `(y_i - y_j)^2`

term with any measure of dissimilarity `d_{ij}`

.

### Value

The discrepancy.

### Author(s)

Matthias Studer (with Gilbert Ritschard for the help page)

### References

Studer, M., G. Ritschard, A. Gabadinho and N. S. Müller (2011). Discrepancy analysis of state sequences, *Sociological Methods and Research*, Vol. 40(3), 471-510, doi:10.1177/0049124111415372.

Studer, M., G. Ritschard, A. Gabadinho and N. S. Müller (2010)
Discrepancy analysis of complex objects using dissimilarities.
In F. Guillet, G. Ritschard, D. A. Zighed and H. Briand (Eds.),
*Advances in Knowledge Discovery and Management*,
Studies in Computational Intelligence, Volume 292, pp. 3-19. Berlin: Springer.

Studer, M., G. Ritschard, A. Gabadinho and N. S. Müller (2009)
Analyse de dissimilarités par arbre d'induction. In EGC 2009,
*Revue des Nouvelles Technologies de l'Information*, Vol. E-15, pp. 7-18.

Anderson, M. J. (2001) A new method for non-parametric multivariate analysis of variance.
*Austral Ecology* **26**, 32-46.

Batagelj, V. (1988) Generalized ward and related clustering problems. In H. Bock (Ed.),
*Classification and related methods of data analysis*, Amsterdam: North-Holland, pp. 67-74.

### See Also

`dissassoc`

to test association between objects represented by their dissimilarities and a covariate.

`disstree`

for an induction tree analyse of objects characterized by a dissimilarity matrix.

`disscenter`

to compute the distance of each object to its group center from pairwise dissimilarities.

`dissmfacw`

to perform multi-factor analysis of variance from pairwise dissimilarities.

### Examples

```
## Defining a state sequence object
data(mvad)
mvad.seq <- seqdef(mvad[, 17:86])
## Building dissimilarities (any dissimilarity measure can be used)
mvad.ham <- seqdist(mvad.seq, method="HAM")
## Pseudo variance of the sequences
print(dissvar(mvad.ham))
```

*TraMineR*version 2.2-10 Index]