# seqici: Complexity index of individual sequences In TraMineR: Trajectory Miner: a Toolbox for Exploring and Rendering Sequences

## Description

Computes the complexity index, a composite measure of sequence complexity. The index uses the number of transitions in the sequence as a measure of the complexity induced by the state ordering and the longitudinal entropy as a measure of the complexity induced by the state distribution in the sequence.

## Usage

 ```1 2``` ``` seqici(seqdata, with.missing=FALSE) ```

## Arguments

 `seqdata` a sequence object as returned by the the `seqdef` function. `with.missing` if set to `TRUE`, missing status (gaps in sequences) is handled as an additional state when computing the state distribution and the number of transitions in the sequence.

## Details

The complexity index C(s) of a sequence s is

C(s) = ([q(s) h(s)]/[q_{max} h_{max}])^(.5)

where q(s) is the number of transitions in the sequence, q_{max} the maximum number of transitions, h(s) the within entropy, and h_{max} the theoretical maximum entropy which is h_max = -log 1/|A|.

The index C(s) is the geometric mean of its two components which are normalized. The minimum value of 0 can only be reached by a sequence made of one distinct state, containing thus 0 transitions and having an entropy of 0. The maximum 1 of C(s) is reached when the two following conditions are fulfilled: i) Each of the state in the alphabet is present in the sequence and the total durations are uniform, that is, equal to l/a and ii) The number of transitions in the sequence is equal to l-1, that is, the length l_d of the DSS is equal to the length of the sequence l

## Value

a vector of length equal to the number of sequences in `seqdata` containing the complexity index value of each sequence.

## Author(s)

Alexis Gabadinho (with Gilbert Ritschard for the help page)

## References

Gabadinho, A., G. Ritschard, N. S. M<c3><bc>ller and M. Studer (2011). Analyzing and Visualizing State Sequences in R with TraMineR. Journal of Statistical Software 40(4), 1-37.

Gabadinho, A., Ritschard, G., Studer, M. and M<c3><bc>ller, N.S. (2010). "Indice de complexit<c3><a9> pour le tri et la comparaison de s<c3><a9>quences cat<c3><a9>gorielles", In Extraction et gestion des connaissances (EGC 2010), Revue des nouvelles technologies de l'information RNTI. Vol. E-19, pp. 61-66.

`seqient`, `seqST`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```## Creating a sequence object from the mvad data set data(mvad) mvad.labels <- c("employment", "further education", "higher education", "joblessness", "school", "training") mvad.scodes <- c("EM","FE","HE","JL","SC","TR") mvad.seq <- seqdef(mvad, 15:86, states=mvad.scodes, labels=mvad.labels) ## mvad.ci <- seqici(mvad.seq) summary(mvad.ci) hist(mvad.ci) ## Example using with.missing argument data(ex1) ex1.seq <- seqdef(ex1, 1:13) seqici(ex1.seq) seqici(ex1.seq, with.missing=TRUE) ```