seqstatd {TraMineR} | R Documentation |

## 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 |

`weighted` |
if |

`with.missing` |
If |

`norm` |
if |

### 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*, 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*version 2.2-10 Index]