# dissassoc: Analysis of discrepancy from dissimilarity measures In TraMineR: Trajectory Miner: a Toolbox for Exploring and Rendering Sequences

## Description

Compute and test the share of discrepancy (defined from a dissimilarity matrix) explained by a categorical variable.

## Usage

 ```1 2``` ```dissassoc(diss, group, weights=NULL, R=1000, weight.permutation="replicate", squared=FALSE) ```

## Arguments

 `diss` A dissimilarity matrix or a dist object (see `dist`) `group` A categorical variable. For a numerical variable use `dissmfacw`. `weights` optional numerical vector containing weights. `R` Number of permutations for computing the p-value. If equal to 1, no permutation test is performed. `weight.permutation` Weighted permutation method: `"diss"` (attach weights to the dissimilarity matrix), `"replicate"` (replicate case using `weights`), `"rounded-replicate"` (replicate case using rounded `weights`), `"random-sampling"` (random assignment of covariate profiles to the objects using distributions defined by the weights.) `squared` Logical. If `TRUE` the dissimilarities `diss` are squared.

## Details

The `dissassoc` function assesses the association between objects characterized by their dissimilarity matrix and a discrete covariate. It provides a generalization of the ANOVA principle to any kind of distance metric. The function returns a pseudo R-square that can be interpreted as a usual R-square. The statistical significance of the association is computed by means of permutation tests. The function performs also a test of discrepancy homogeneity (equality of within variances) using a generalization of the Levene statistic and Bartlett's statistics.
There are `print` and `hist` methods (the latter producing an histogram of the permuted values used for testing the significance).

If a numeric `group` variable is provided, it will be treated as categorical, i.e., each different value will be considered as a different category. To measure the ‘linear’ effect of a numerical variable, use `dissmfacw`.

## Value

An object of class `dissassoc` with the following components:

 `groups` A data frame with the number of cases and the discrepancy of each group `anova.table` The pseudo ANOVA table `stat` The value of the statistics and their p-values `perms` The permutation object, containing the values computed for each permutation

## Author(s)

Matthias Studer (with Gilbert Ritschard for the help page)

## References

Studer, M., G. Ritschard, A. Gabadinho and N. S. M<c3><bc>ller (2011). Discrepancy analysis of state sequences, Sociological Methods and Research, Vol. 40(3), 471-510.

Studer, M., G. Ritschard, A. Gabadinho and N. S. M<c3><bc>ller (2010) Discrepancy analysis of complex objects using dissimilarities. In F. Guillet, G. Ritschard, H. Briand, and D. A. Zighed (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. M<c3><bc>ller (2009). Analyse de dissimilarit<c3><a9>s 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.

`dissvar` to compute the pseudo variance from dissimilarities and for a basic introduction to concepts of pseudo variance analysis.
`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.
 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```## 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") ## R=1 implies no permutation test da <- dissassoc(mvad.ham, group=mvad\$gcse5eq, R=10) print(da) hist(da) ```