Sequences turbulence
Elzinga's turbulence for each sequence in a sequence data set.
seqST(seqdata, norm=FALSE, silent=TRUE, with.missing=FALSE, type=1)
seqdata |
a state sequence object as returned by the the |
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 |
type |
either 1 or 2. Type of duration variance. |
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. This maximum is
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.
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 dividing by the turbulence value of a sequence made by the successive repetition of the alphabet up to the maximal length in seqdata.
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.
Alexis Gabadinho and Gilbert Ritschard
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.
## 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) ## Histogram for the turbulence hist(turb) ## Normalized turbulence turb.norm <- seqST(actcal.seq, norm=TRUE)
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