seqstatd: Sequence of transversal state distributions and their... In TraMineR: Trajectory Miner: a Toolbox for Exploring and Rendering Sequences

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.

`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.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19``` ```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) ```