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

seqstatd {TraMineR} | R Documentation

## Sequence of transversal state distributions and their entropies

### Description

Returns the state 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 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

    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)

[Package TraMineR version 2.2-2 Index]