Sequence of transversal state distributions and their entropies

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Description

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

Usage

1
 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 state distribution. Letting p_i denote the proportion of cases in state i at the considered time point, the entropy is

h(p_1,…,p_s) = -∑_{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 can be seen as a measure of the diversity of states observed at the considered time point. An application of such a measure (but with aggregated transversal data) can be seen in Billari (2001) and Fussell (2005).

Author(s)

Alexis Gabadinho (with Gilbert Ritschard for the help page)

References

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 plot of transversal distributions and
seqHtplot for plotting the transversal entropy over sequence positions.

Examples

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

## Plotting the entropy indexes
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)

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