R: Generate substitution and indel costs

seqcost {TraMineR} | 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 length equal to the number of columns 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. 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. doi: 10.12682/lives.2296-1658.2014.33

### See Also

`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

[Package TraMineR version 2.2-3 Index]