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 |

`cval` |
Scalar. For method |

`with.missing` |
Logical. Should an additional entry be added in the matrix for the missing states?
If |

`miss.cost` |
Scalar or vector. Cost for substituting the missing state. Default is |

`miss.cost.fixed` |
Logical. Should the substitution cost for missing be set as the |

`time.varying` |
Logical. If |

`weighted` |
Logical. Should weights in |

`transition` |
String. Only used if |

`lag` |
Integer. For methods |

`state.features` |
Data frame with features values for each state. |

`feature.weights` |
Vector of feature weights with a weight per column of |

`feature.type` |
List of feature types. See |

`proximities` |
Logical: should state proximities be returned instead of substitution costs? |

`...` |
Arguments passed to |

### 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 |

`sm` |
The substitution-cost matrix (or array) when |

`prox` |
The state proximity matrix when |

`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

### 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*version 2.2-10 Index]