depmixS4 (version 0.1-1)

fit: Fit depmix models

Description

fit optimizes parameters of depmix models, optionally subject to general linear (in)equality constraints.

Usage

## S3 method for class 'depmix':
fit(object, fixed=NULL, equal=NULL, conrows=NULL,
		conrows.upper=0, conrows.lower=0, method=NULL,...)
	
	## S3 method for class 'depmix.fitted':
posterior(object)
	## S3 method for class 'depmix.fitted':
summary(object)

Arguments

object

An object of class depmix.

fixed

Vector of mode logical indicating which parameters should be fixed.

equal

Vector indicating equality constraints; see details.

conrows

Rows of a general linear constraint matrix; see details.

conrows.upper, conrows.lower

Upper and lower bounds for the linear constraints; see details.

method

The optimization method; mostly determined by constraints.

...

Further arguments passed on to the optimization methods.

Value

• fit returns an object of class depmix.fitted which contains the original depmix object, and further has slots:
• message
  : Convergence information.
• conMat
  : The constraint matrix A, see details.
• posterior
  : Returns a data.frame with nstates(object) + 1 columns; the first column has the viterbi states, the other columns have the delta probabilities, see Rabiner (1989).
• The print method shows the message and the summary method shows the parameter estimates.

Details

The method fits depmix models by the EM algorithm if there are no linear constraints on the parameters and if the transition model has no covariates. Otherwise the general optimizer donlp is used which handles general linear (in-)equality constraints. Three types of constraints can be specified on the parameters: fixed, equality, and general constraints. Constraint vectors should be of length npar(object). See help on getpars and setpars about the ordering of parameters. The equal argument is used to specify equality constraints: parameters that get the same integer number in this vector are estimated to be equal. Any integers can be used in the vector except 0 and 1, which indicate fixed and free parameters respectively.

Using the donlp optimizer a Newton-Raphson scheme is employed to estimate parameters subject to linear constraints by imposing: bl <= a*x="" <="bu," where="" x="" is="" the="" parameter="" vector,="" bl="" a="" vector="" of="" lower="" bounds,="" bu="" upper="" and="" constraint="" matrix.="" p="">

The conrows argument is used to specify rows of A directly, and the conrows.lower and conrows.upper arguments to specify the bounds on the constraints. conrows is a matrix of npar(object) columns and one row for each constraint (ie a vector in the case of a single constraint). llratio performs a log-likelihood ratio test on two fitted models; the first object should have the largest degrees of freedom.

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 the RTs of the speed data with random 
# starting values for the transition pars (without those EM does not get off the ground)
set.seed(1)
mod <- depmix(rt~1,data=speed,nstates=2,trstart=runif(4))
# fit the model
mod1 <- fit(mod)
mod1 # to see the logLik and optimization information
# to see the parameters
summary(mod1)


data(balance)
# four binary items on the balance scale task

# now fit some latent class models
trstart=c(1,0,0,1) # as this is a latent class model, the transition are not optimized
instart=c(0.5,0.5)
set.seed(1)
respstart=runif(16)
# note that ntimes argument is used to make this a mixture model
mod <- depmix(list(d1~1,d2~1,d3~1,d4~1), data=balance, nstates=2,
	family=list(multinomial(),multinomial(),multinomial(),multinomial()),
	respstart=respstart,trstart=trstart,instart=instart,
	ntimes=rep(1,nrow(balance)))

mod1 <- fit(mod)

# add age as covariate on class membership by using the prior argument
trstart=c(1,0,0,1) # as this is a latent class model, the transition are not optimized
instart=c(0.5,0.5,0,0) # we need the initial probs and the coefficients of age 
set.seed(2)
respstart=c(runif(16))
trstart=c(1,0,0,1)
mod2 <- depmix(list(d1~1,d2~1,d3~1,d4~1), data=balance, nstates=2,
	family=list(multinomial(),multinomial(),multinomial(),multinomial()),
	trstart=trstart, instart=instart, respstart=respstart,
	ntimes=rep(1,nrow(balance)), prior=~age, initdata=balance)

mod3 <- fit(mod2)

# check the likelihood ratio; adding age significantly improves the goodness-of-fit
llratio(mod3,mod1)