Control parameters for the EM algorithm

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Description

Set control parameters for the EM algorithm.

Usage

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	em.control(maxit = 500, tol = 1e-08, crit = c("relative","absolute"), 
	random.start = TRUE, classification = c("soft","hard"))
	

Arguments

maxit

The maximum number of iterations.

tol

The tolerance level for convergence. See Details.

crit

Sets the convergence criterion to "relative" or "absolute" change of the log-likelihood. See Details.

random.start

This is used for a (limited) random initialization of the parameters. See Details.

classification

Type of classification to states used. See Details.

Details

The argument crit sets the convergence criterion to either the relative change in the log-likelihood or the absolute change in the log-likelihood. The relative likelihood criterion (the default) assumes convergence on iteration i when (log L(i) - log L(i-1))/(log L(i-1)) < tol. The absolute likelihood criterion assumes convergence on iteration i when (log L(i) - log L(i-1)) < tol. Use crit="absolute" to invoke the latter convergence criterion. Note that in that case, optimal values of the tolerance parameter tol scale with the value of the log-likelihood (and these are not changed automagically).

Argument random.start This is used for a (limited) random initialization of the parameters. In particular, if random.start=TRUE, the (posterior) state probabilities are randomized at iteration 0 (using a uniform distribution), i.e. the γ variables (Rabiner, 1989) are sampled from the Dirichlet distribution with a (currently fixed) value of α=0.1; this results in values for each row of γ that are quite close to zero and one; note that when these values are chosen at zero and one, the initialization is similar to that used in kmeans. Random initialization is useful when no initial parameters can be given to distinguish between the states. It is also useful for repeated estimation from different starting values.

Argument classification is used to choose either soft (default) or hard classification of observations to states. When using soft classification, observations are assigned to states with a weight equal to the posterior probability of the state. When using hard classification, observations are assigned to states according to the maximum a posteriori (MAP) states (i.e., each observation is assigned to one state, which is determined by the Viterbi algorithm in the case of depmix models). As a result, the EM algorithm will find a local maximum of the classification likelihood (Celeux & Govaert, 1992). Warning: hard classification is an experimental feature, especially for hidden Markov models, and its use is currently not advised.

Value

em.control returns a list of the control parameters.

Author(s)

Ingmar Visser & Maarten Speekenbrink

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.

Gilles Celeux and Gerard Govaert (1992). A classification EM algorithm for clustering and two stochastic versions. Computational Statistics and Data Analysis, 14, p. 315-332.

Examples

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# using "hard" assignment of observations to the states, we can maximise the
# classification likelihood instead of the usual marginal likelihood
data(speed)  
mod <- depmix(list(rt~1,corr~1),data=speed,nstates=2,
    family=list(gaussian(),multinomial("identity")),ntimes=c(168,134,137))
set.seed(1)
# fit the model by calling fit
fmod <- fit(mod,emcontrol=em.control(classification="hard"))
# can get rather different solutions with different starting values...
set.seed(3)
fmod2 <- fit(mod,emcontrol=em.control(classification="hard"))