seqstatd: Sequence of transversal state distributions and their...

In TraMineR: Trajectory Miner: a Sequence Analysis Toolkit

Sequence of transversal state distributions and their entropies

Description

Returns the state relative frequencies, the number of valid states and the entropy of the state distribution at each position in the sequence.

Usage

 seqstatd(seqdata, weighted=TRUE, with.missing=FALSE, norm=TRUE)

Arguments

seqdata	a state sequence object as defined by the seqdef function.
weighted	if TRUE, distributions account for the weights assigned to the state sequence object (see seqdef). Set as FALSE if you want ignore the weights.
with.missing	If FALSE (default value), returned distributions ignore missing values.
norm	if TRUE (default value), entropy is normalized, ie divided by the entropy of the alphabet. Set as FALSE if you want the entropy without normalization.

Details

In addition to the state distribution at each position in the sequence, the seqstatd function provides also for each time point the number of valid states and the Shannon entropy of the observed cross-sectional state distribution. Letting p_i denote the proportion of cases in state i at the considered position, the entropy is

h(p_1,\ldots,p_s) = -\sum_{i=1}^{s} p_i \log(p_i)

where s is the size of the alphabet. The log is here the natural (base e) logarithm. The entropy is 0 when all cases are in the same state and is maximal when the same proportion of cases are in each state. The entropy is a measure of the diversity of states observed at the considered position. First studies using sequence of cross-sectional entropies (but with aggregated transversal data) are Billari (2001) and Fussell (2005).

Value

A list with three elements: Frequencies (relative frequencies), ValidStates (number of valid states at each position), and Entropy (cross-sectional entropy at each position).

The returned list has attributes nbseq (number of sequences), cpal, xtlab, xtstep, tick.last, weighted, and norm.

Author(s)

Alexis Gabadinho and Gilbert Ritschard

References

Ritschard, G. (2021), "Measuring the nature of individual sequences", Sociological Methods and Research, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1177/00491241211036156")}.

Billari, F. C. (2001). The analysis of early life courses: complex descriptions of the transition to adulthood. Journal of Population Research 18 (2), 119-24.

Fussell, E. (2005). Measuring the early adult life course in Mexico: An application of the entropy index. In R. Macmillan (Ed.), The Structure of the Life Course: Standardized? Individualized? Differentiated?, Advances in Life Course Research, Vol. 9, pp. 91-122. Amsterdam: Elsevier.

See Also

plot.stslist.statd the plot method for objects of class stslist.statd,
seqdplot for higher level chronograms (state distribution plots)),
seqHtplot for transversal entropy line over sequence positions, and
seqdHplot for chronograms with overlayed entropy line.

Examples

data(biofam)
biofam.seq <- seqdef(biofam,10:25)
sd <- seqstatd(biofam.seq)
## Plotting the state distribution
plot(sd, type="d")

## Line of cross-sectional entropies
plot(sd, type="Ht")

## ====================
## example with weights
## ====================
data(ex1)
ex1.seq <- seqdef(ex1, 1:13, weights=ex1$weights)

## Unweighted
seqstatd(ex1.seq, weighted=FALSE)

seqstatd(ex1.seq, weighted=TRUE)

TraMineR documentation built on Sept. 19, 2023, 1:07 a.m.