Define substitution and indel costs

Description

The function seqcost proposes different ways to generate substitution costs (supposed to reflect 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 return only the substitution cost matrix, i.e., no indel.

Usage

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

seqsubm(...)

Arguments

seqdata

a sequence object as returned by the seqdef function.

method

Character 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 state alphabet. Use this if you want to compute distances with missing values inside the sequences. See Gabadinho et al. (2010) for more details on the options for handling missing values when computing distances between sequences.

miss.cost

Scalar or vector. Cost for substituting the missing state. Default is cval.

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.

weighted

Logical. Should weights in seqdata be used when applicable?

transition

Character 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).

missing.trate

Logical. For methods TRATE and FUTURE only. If TRUE, substitution costs with missing state are also based on transition rates. If FALSE (default value), the substitution cost for the missing state are set as miss.cost.

state.prop

???

prop.weights

???

prop.type

A list, ???

,

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 defines the dissimilarity between

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 rates 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 rate of transition from state i to j lag positions ahead.

With method FUTURE, the cost between i and j is the Chi-squared distance between the vector (d(alphabet | i)) of rates 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.prop, and the cost between i and j is computed as the Gower distance between their vectors of state.prop 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, 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

A list of two elements indel and sm with

indel

The indel cost. Either a scalar or a vector of size ns.

sm

The substitution cost matrix of size ns*ns, where ns is the number of states in the alphabet of the sequence object.

For seqsubm, the matrix sm.

Author(s)

Matthias Studer and Alexis Gabadinho (first version) (with Gilbert Ritschard for the help page)

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. (2015), "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: http://dx.doi.org/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: http://dx.doi.org/10.12682/lives.2296-1658.2014.33

See Also

seqtrate, seqdef, seqdist.

Examples

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## Defining a sequence object with columns 10 to 25
## in the 'biofam' example data set
data(biofam)
biofam.seq <- seqdef(biofam,10:25)

## Optimal matching using transition rates based substitution-cost matrix
## and insertion/deletion costs of 3
trcost <- seqcost(biofam.seq, method="TRATE")
biofam.om <- seqdist(biofam.seq, method="OM", indel=3, sm=trcost$sm)

## Using the insertion/deletion cost returned by seqcost
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="TRATE", with.missing=TRUE, weighted=FALSE)
ex1.om <- seqdist(ex1.seq, method="OM", sm=subm$sm, with.missing=TRUE)

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

ex1.om == ex1.omw

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