forwardbackward: Forward and backward variables

In depmixS4: Dependent Mixture Models - Hidden Markov Models of GLMs and Other Distributions in S4

Forward and backward variables

Description

Compute the forward and backward variables of a depmix object.

Usage

	## 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.

Value

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.

Author(s)

Maarten Speekenbrink & Ingmar Visser

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.

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)

depmixS4 documentation built on June 8, 2025, 1:29 p.m.