forwardbackward function

Forward and backward variables

Compute the forward and backward variables of a depmix object.

## S4 method for signature 'mix'
forwardbackward(object, return.all=TRUE, useC=TRUE, ...)

Arguments

• object: A depmix object.
• return.all: If FALSE, only gamma and xi and the log likelihood are returned (which are the only variables needed in using EM).
• useC: Flag used to set whether the C-code is used to compute the forward, backward, gamma and xi variables or not; the R-code is basically obsolete (but retained for now for debugging purposes).
• ...: Not currently used.

Returns

forwardbackward returns a list of the following (the variables are named after the notation from Rabiner, 1989):

• alpha: The forward variables.

• beta: The backward variables.

• gamma: The smoothed state probabilities.

• xi: The smoothed transition probabilities.

• sca: The scale factors (called lambda in Rabiner, 1989).

• logLike: The log likelihood (computed as -sum(log(sca)).

If return.all=FALSE, only gamma, xi and the log likelihood are returned.

References

Lawrence R. Rabiner (1989). A tutorial on hidden Markov models and selected applications in speech recognition. Proceedings of IEEE, 77-2, p. 267-295.

Author(s)

Maarten Speekenbrink & Ingmar Visser

Examples

data(speed)

# 2-state model on rt and corr from speed data set 
# with Pacc as covariate on the transition matrix
# ntimes is used to specify the lengths of 3 separate series
mod1 <- depmix(list(rt~1,corr~1),data=speed,transition=~Pacc,nstates=2,
        family=list(gaussian(),multinomial("identity")),ntimes=c(168,134,137))

fb <- forwardbackward(mod1)
all.equal(-sum(log(fb$sca)),fb$logLike)