# seqcost: Generate substitution and indel costs In TraMineR: Trajectory Miner: a Sequence Analysis Toolkit

 seqcost R Documentation

## Generate substitution and indel costs

### Description

The function `seqcost` proposes different ways to generate substitution costs (supposed to represent state dissimilarities) and possibly indel costs. Proposed methods are: `"CONSTANT"` (same cost for all substitutions), `"TRATE"` (derived from the observed transition rates), `"FUTURE"` (Chi-squared distance between conditional state distributions `lag` positions ahead), `"FEATURES"` (Gower distance between state features), `"INDELS"`, `"INDELSLOG"` (based on estimated indel costs). The substitution-cost matrix is intended to serve as `sm` argument in the `seqdist` function that computes distances between sequences. `seqsubm` is an alias that returns only the substitution cost matrix, i.e., no indel.

### Usage

``````seqcost(seqdata, method, cval = NULL, with.missing = FALSE, miss.cost = NULL,
time.varying = FALSE, weighted = TRUE, transition = "both", lag = 1,
miss.cost.fixed = NULL, state.features = NULL, feature.weights = NULL,
feature.type = list(), proximities = FALSE)

seqsubm(...)
``````

### Arguments

 `seqdata` A sequence object as returned by the seqdef function. `method` String. How to generate the costs. One of `"CONSTANT"` (same cost for all substitutions), `"TRATE"` (derived from the observed transition rates), `"FUTURE"` (Chi-squared distance between conditional state distributions `lag` positions ahead), `"FEATURES"` (Gower distance between state features), `"INDELS"`, `"INDELSLOG"` (based on estimated indel costs). `cval` Scalar. For method `"CONSTANT"`, the single substitution cost. For method `"TRATE"`, a base value from which transition probabilities are subtracted. If `NULL`, `cval=2` is used, unless `transition` is `"both"` and `time.varying` is `TRUE`, in which case `cval=4`. `with.missing` Logical. Should an additional entry be added in the matrix for the missing states? If `TRUE`, the ‘missing’ state is also added to the alphabet. Set as `TRUE` if you want to use the costs for distances between sequences containing non deleted (non void) missing values. Forced as `FALSE` when there are no non-void missing values in `seqdata`. See Gabadinho et al. (2010) for more details on the options for handling missing values when creating the state sequence object with `seqdef`. `miss.cost` Scalar or vector. Cost for substituting the missing state. Default is `cval`. `miss.cost.fixed` Logical. Should the substitution cost for missing be set as the `miss.cost` value. When `NULL` (default) it will be set as `FALSE` when `method = "INDELS"` or `"INDELSLOG"`, and `TRUE` otherwise. `time.varying` Logical. If `TRUE` return an `array` with a distinct matrix for each time unit. Time is the third dimension (subscript) of the returned array. Time varying works only with `method='CONSTANT'`, `'TRATE'`, `'INDELS'`, and `'INDELSLOG'`. `weighted` Logical. Should weights in `seqdata` be used when applicable? `transition` String. Only used if `method="TRATE"` and `time.varying=TRUE`. On which transition are rates based? Should be one of `"previous"` (from previous state), `"next"` (to next state) or `"both"`. `lag` Integer. For methods `TRATE` and `FUTURE` only. Time ahead to which transition rates are computed (default is `lag=1`). `state.features` Data frame with features values for each state. `feature.weights` Vector of feature weights with a weight per column of `state.features`. `feature.type` List of feature types. See `daisy` for details. `proximities` Logical: should state proximities be returned instead of substitution costs? `...` Arguments passed to `seqcost`

### Details

The substitution-cost matrix has dimension `ns*ns`, where `ns` is the number of states in the alphabet of the sequence object. The element `(i,j)` of the matrix is the cost of substituting state `i` with state `j`. It represents the dissimilarity between the states `i` and `j`. The indel cost of the cost of inserting or deleting a state.

With method `CONSTANT`, the substitution costs are all set equal to the `cval` value, the default value being 2.

With method `TRATE` (transition rates), the transition probabilities between all pairs of states is first computed (using the seqtrate function). Then, the substitution cost between states `i` and `j` is obtained with the formula

`SC(i,j) = cval - P(i|j) -P(j|i)`

where `P(i|j)` is the probability of transition from state `j` to `i` `lag` positions ahead. Default `cval` value is 2. When `time.varying=TRUE` and `transition="both"`, the substitution cost at position `t` is set as

`SC(i,j,t) = cval - P(i|j,t-1) -P(j|i,t-1) - P(i|j,t) - P(j|i,t)`

where `P(i|j,t-1)` is the probability to transit from state `j` at `t-1` to `i` at `t`. Here, the default `cval` value is 4.

With method `FUTURE`, the cost between `i` and `j` is the Chi-squared distance between the vector (`d(alphabet | i)`) of probabilities of transition from states `i` and `j` to all the states in the alphabet `lag` positions ahead:

`SC(i,j) = ChiDist(d(alphabet | i), d(alphabet | j))`

With method `FEATURES`, each state is characterized by the variables `state.features`, and the cost between `i` and `j` is computed as the Gower distance between their vectors of `state.features` values.

With methods `INDELS` and `INDELSLOG`, values of indels are first derived from the state relative frequencies `f_i`. For `INDELS`, `indel_i = 1/f_i` is used, and for `INDELSLOG`, `indel_i = \log[2/(1 + f_i)]`. Substitution costs are then set as `SC(i,j) = indel_i + indel_j`.

For all methods but `INDELS` and `INDELSLOG`, the indel is set as `\max(sm)/2` when `time.varying=FALSE` and as `1` otherwise.

### Value

For `seqcost`, a list of two elements, `indel` and `sm` or `prox`:

 `indel` The indel cost. Either a scalar or a vector of size `ns`. When `time.varying=TRUE` and `method` is one of `"INDELS"` or `"INDELSLOG"`, a matrix with indels per time point in columns. `sm` The substitution-cost matrix (or array) when `proximities = FALSE` (default). `prox` The state proximity matrix when `proximities = TRUE`.

`sm` and `prox` are, when `time.varying = FALSE`, a matrix of size `ns * ns`, where `ns` is the number of states in the alphabet of the sequence object. When `time.varying = TRUE`, they are a three dimensional array of size `ns * ns * L`, where `L` is the maximum sequence length.

For `seqsubm`, only one element, the matrix (or array) `sm`.

### Author(s)

Gilbert Ritschard and Matthias Studer (and Alexis Gabadinho for first version of `seqsubm`)

### References

Gabadinho, A., G. Ritschard, N. S. Müller and M. Studer (2011). Analyzing and Visualizing State Sequences in R with TraMineR. Journal of Statistical Software 40(4), 1-37.

Gabadinho, A., G. Ritschard, M. Studer and N. S. Müller (2010). Mining Sequence Data in `R` with the `TraMineR` package: A user's guide. Department of Econometrics and Laboratory of Demography, University of Geneva.

Studer, M. & Ritschard, G. (2016), "What matters in differences between life trajectories: A comparative review of sequence dissimilarity measures", Journal of the Royal Statistical Society, Series A. 179(2), 481-511. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/rssa.12125")}

Studer, M. and G. Ritschard (2014). "A Comparative Review of Sequence Dissimilarity Measures". LIVES Working Papers, 33. NCCR LIVES, Switzerland, 2014. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.12682/lives.2296-1658.2014.33")}

`seqtrate`, `seqdef`, `seqdist`.

### Examples

``````## Defining a sequence object with columns 10 to 25
## of a subset of the 'biofam' example data set.
data(biofam)
biofam.seq <- seqdef(biofam[501:600,10:25])

## Indel and substitution costs based on log of inverse state frequencies
lifcost <- seqcost(biofam.seq, method="INDELSLOG")
## Here lifcost\$indel is a vector
biofam.om <- seqdist(biofam.seq, method="OM", indel=lifcost\$indel, sm=lifcost\$sm)

## Optimal matching using transition rates based substitution-cost matrix
## and the associated indel cost
## Here trcost\$indel is a scalar
trcost <- seqcost(biofam.seq, method="TRATE")
biofam.om <- seqdist(biofam.seq, method="OM", indel=trcost\$indel, sm=trcost\$sm)

## Using costs based on FUTURE with a forward lag of 4
fucost <- seqcost(biofam.seq, method="FUTURE", lag=4)
biofam.om <- seqdist(biofam.seq, method="OM", indel=fucost\$indel, sm=fucost\$sm)

## Optimal matching using a unique substitution cost of 2
## and an insertion/deletion cost of 3
ccost <- seqsubm(biofam.seq, method="CONSTANT", cval=2)
biofam.om.c2 <- seqdist(biofam.seq, method="OM",indel=3, sm=ccost)

## Displaying the distance matrix for the first 10 sequences
biofam.om.c2[1:10,1:10]

## =================================
## Example with weights and missings
## =================================
data(ex1)
ex1.seq <- seqdef(ex1[,1:13], weights=ex1\$weights)

## Unweighted
subm <- seqcost(ex1.seq, method="INDELSLOG", with.missing=TRUE, weighted=FALSE)
ex1.om <- seqdist(ex1.seq, method="OM", indel=subm\$indel, sm=subm\$sm, with.missing=TRUE)

## Weighted
subm.w <- seqcost(ex1.seq, method="INDELSLOG", with.missing=TRUE, weighted=TRUE)
ex1.omw <- seqdist(ex1.seq, method="OM", indel=subm.w\$indel, sm=subm.w\$sm, with.missing=TRUE)

ex1.om == ex1.omw
``````

TraMineR documentation built on May 29, 2024, 5 a.m.