seqici | R Documentation |

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.

```
seqici(seqdata, with.missing=FALSE, silent=TRUE)
```

`seqdata` |
a sequence object as returned by the the |

`with.missing` |
if set to |

`silent` |
logical: should messages about running operations be displayed? |

The *complexity index* `C(s)`

of a sequence
`s`

is

` C(s)= \sqrt{\frac{q(s)}{q_{max}} \,\frac{h(s)}{h_{max}}} `

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|`

with `|A|`

the size of the alphabet.

The index `C(s)`

is the geometric mean of its two normalized components and is,
therefore, itself normalized.
The minimum value of 0 can only be reached by a
sequence made of one distinct state, thus containing 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, i.e. each state occurs `\ell/|A|`

times, and ii) the number
of transitions in the sequence is `\ell-1`

, meaning that the length `\ell_d`

of the DSS is equal to the length of the sequence `\ell`

.

a single-column matrix of length equal to the number of sequences in
`seqdata`

containing the complexity index value of each
sequence.

Alexis Gabadinho (with Gilbert Ritschard for the help page)

Gabadinho, A., G. Ritschard, N. S. Müller 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 Müller,
N.S. (2010). "Indice de complexité pour le tri et la comparaison de
séquences catégorielles", In *Extraction et gestion des
connaissances (EGC 2010), Revue des nouvelles technologies de
l'information RNTI*. Vol. E-19, pp. 61-66.

Ritschard, G. (2023), "Measuring the nature of individual sequences", *Sociological Methods and Research*, 52(4), 2016-2049. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1177/00491241211036156")}.

`seqindic`

, `seqient`

, `seqipos`

.

For alternative measures of sequence complexity see `seqST`

, `seqivolatility`

.

```
## 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)
```

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