# logLik: Log-Likelihood of a variable length Markov chain model In PST: Probabilistic Suffix Trees and Variable Length Markov Chains

## Description

Retrieve the log-likelihood of a fitted VLMC. This is the `logLik` method for objects of class `PSTf` returned by the `pstree` and `prune` functions.

## Usage

 ```1 2``` ```## S4 method for signature 'PSTf' logLik(object) ```

## Arguments

 `object` a probabilistic suffix tree, i.e., an object of class `"PSTf"` as returned by the `pstree`, `prune` or `tune` function.

## Details

The likelihood of a learning sample containing n sequences, given a model S fitted to it, is

L(S)=∏_{i=1}^{n} P^{S}(x^{i})

where P^{S}(x^{i}) is the probability of the ith observed sequence predicted by S. Note that the log-likelihood of a VLMC model is not used in the estimation of the model's parameters (see `pstree`). It is obtained once the model is estimated by calling the `predict` function. The value is stored in the `logLik` slot of the probabilistic suffix tree representing the model (a `PSTf` object returned by the `pstree` or `prune` function). The `AIC` and `BIC` values can also be obtained with the corresponding generic functions, which call `logLik` and use its result. For more details, see Gabadinho 2016.

## Value

An object of class `logLik`, a negative numeric value with the `df` (degrees of freedom) attribute containing the number of free parameters of the model.

## References

Gabadinho, A. & Ritschard, G. (2016). Analyzing State Sequences with Probabilistic Suffix Trees: The PST R Package. Journal of Statistical Software, 72(3), pp. 1-39.

`AIC`, `BIC`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24``` ```## activity calendar for year 2000 ## from the Swiss Household Panel ## see ?actcal data(actcal) ## selecting individuals aged 20 to 59 actcal <- actcal[actcal\$age00>=20 & actcal\$age00 <60,] ## defining a sequence object actcal.lab <- c("> 37 hours", "19-36 hours", "1-18 hours", "no work") actcal.seq <- seqdef(actcal,13:24,labels=actcal.lab) ## building a PST actcal.pst <- pstree(actcal.seq, nmin=2, ymin=0.001) logLik(actcal.pst) ## Cut-offs for 5% and 1% (see ?prune) C99 <- qchisq(0.99,4-1)/2 ## pruning actcal.pst.C99 <- prune(actcal.pst, gain="G2", C=C99) ## Comparing AIC AIC(actcal.pst, actcal.pst.C99) ```