R: Sequences turbulence

seqST {TraMineR} | R Documentation

## Sequences turbulence

### Description

Elzinga's turbulence for each sequence in a sequence data set.

### Usage

     seqST(seqdata, norm=FALSE, silent=TRUE, with.missing=FALSE, type=1)

### Arguments

`seqdata` | a state sequence object as returned by the the `seqdef` function.
`norm` | logical: should the turbulence index be normalized?
`silent` | logical: should messages about running operations (extracting dss and durations, computing turbulence) be displayed?
`with.missing` | logical: should non-void missing values be treated as a regular state? If `FALSE` (default) missing values are ignored.
`type` | either 1 or 2. Type of duration variance. The default `type=1` ignores non visited states. Type 2 takes into account the 0-time spent in non-visited states (see `seqivardur`).

### Details

Sequence turbulence is a measure proposed by Elzinga & Liefbroer (2007). It is based on the number phi(x) of distinct subsequences that can be extracted from the distinct successive state (DSS) sequence and the variance of the consecutive times t_i spent in the distinct states. For a sequence x, the formula is

T(x) = log_2 [phi(x) (s_{t,max}^2(x) + 1)/(s_t^2(x) + 1)]

where s_t^2(x) is the variance of the successive state durations in sequence x and s_{t,max}^2(x) is the maximum value that this variance can take given the number of spells and the total duration of the sequence. For `type=1`, this maximum is computed as

s_{t,max}^2 = (d-1)(1- bar{t})^2

where bar{t} is the mean consecutive time spent in the distinct states, i.e. the sequence duration t divided by the number d of distinct states in the sequence. For `type=2`, the variance takes into account the 0-time spent in non-visited states and the maximum is adjusted for the maximum number of non-visited states for the number of spells (see Ritschard, 2021).

When `with.missing=TRUE`, the function searches for missing states in the sequences and if found, adds the missing state to the alphabet for the computation of the turbulence. In this case the `seqdss` and `seqdur` functions for extracting the distinct successive state sequences and the associated durations are called with the `{with.missing=TRUE}` argument. Thus, a missing state in a sequence is considered as the occurrence of an additional symbol of the alphabet and two or more consecutive missing states are considered as two or more occurrences of this additional state. E.g. the DSS of `A-A-*-*-*-B-B-C-C-D` is `A-*-B-C-D` and the associated durations are `2-3-2-2-1`.

The normalized value is obtained by subtracting 1 to the index and then dividing by the resulting value for a sequence made by the successive repetition of the alphabet up to the maximal length in `seqdata` (Ritschard, 2021)).

### Value

a sinlge-column matrix of length equal to the number of sequences in `seqdata` containing the turbulence value of each sequence. Normalized values are returned when `norm=TRUE`.

### Author(s)

Alexis Gabadinho and Gilbert Ritschard

### References

Elzinga, Cees H. and Liefbroer, Aart C. (2007). De-standardization of Family-Life Trajectories of Young Adults: A Cross-National Comparison Using Sequence Analysis. European Journal of Population, 23, 225-250.

Ritschard, Gilbert (2021) Measuring the nature of state sequences, Sociological Methods and Research, forthcoming.

### See Also

`seqdss`, `seqdur`, `seqsubsn`. For alternative measures of sequence complexity see `seqivolatility`, `seqici`, `seqindic`.

### Examples

      ## Loading the 'actcal' example data set
      data(actcal)
      ## Here we consider only the first 10 sequences
      actcal <- actcal[1:10,]

      ## Defining a sequence object with data in columns 13 to 24
      ## (activity status from January to December 2000)
      actcal.seq <- seqdef(actcal[,13:24], informat='STS')

      ## Computing the sequences turbulence
      turb <- seqST(actcal.seq)

      ## Normalized turbulence
      turb.norm <- seqST(actcal.seq, norm=TRUE)

      ## Normalized turbulence taking non-visited states into account.
      turb2.norm <- seqST(actcal.seq, norm=TRUE, type=2)

[Package TraMineR version 2.2-2 Index]