seqici: Complexity index of individual 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

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

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.

silent

logical: should messages about running operations be displayed?

Value

a single-column matrix of length equal to the number of sequences in seqdata containing the complexity index value of each sequence.

Details

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 $\ell$.

References

Gabadinho, A., G. Ritschard, N. S. M<U+00FC>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<U+00FC>ller, N.S. (2010). "Indice de complexit<U+00E9> pour le tri et la comparaison de s<U+00E9>quences cat<U+00E9>gorielles", In Extraction et gestion des connaissances (EGC 2010), Revue des nouvelles technologies de l'information RNTI. Vol. E-19, pp. 61-66.

Examples

Run this code

# NOT RUN {
## 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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