msm (version 0.5.1)

hmm-dists: Hidden Markov model constructors

Description

These functions are used to specify the distribution of the response conditionally on the underlying state in a hidden Markov model. A list of these function calls, with one component for each state, should be used for the hmodel argument to msm. The initial values for the parameters of the distribution should be given as arguments.

Usage

hmmCat(prob, basecat)
hmmIdent(x)
hmmUnif(lower, upper)
hmmNorm(mean, sd)
hmmLNorm(meanlog, sdlog)
hmmExp(rate)
hmmGamma(shape, rate)
hmmWeibull(shape, scale)
hmmPois(rate)
hmmBinom(size, prob)
hmmTNorm(mean, sd, lower, upper)
hmmMETNorm(mean, sd, lower, upper, sderr, meanerr=0)
hmmMEUnif(lower, upper, sderr, meanerr=0)

Arguments

prob
(hmmCat) Vector of probabilities of observing category 1, 2, ..., length(prob) respectively.
basecat
(hmmCat) Category which is considered to be the "baseline", so that during estimation, the probabilities are parameterised as probabilities relative to this baseline category. By default, the category with the greatest probability
x
(hmmIdent) Code in the data which denotes the exactly-observed state.
mean
(hmmNorm,hmmLNorm,hmmTNorm) Mean defining a Normal, or truncated Normal distribution.
sd
(hmmNorm,hmmLNorm,hmmTNorm) Standard deviation defining a Normal, or truncated Normal distribution.
meanlog
(hmmNorm,hmmLNorm,hmmTNorm) Mean on the log scale, for a log Normal distribution.
sdlog
(hmmNorm,hmmLNorm,hmmTNorm) Standard deviation on the log scale, for a log Normal distribution.
rate
(hmmPois,hmmExp,hmmGamma) Rate of a Poisson, Exponential or Gamma distribution (see dpois, dexp, dgamma<
shape
(hmmPois,hmmExp,hmmGamma) Shape parameter of a Gamma or Weibull distribution (see dgamma, dweibull).
scale
(hmmGamma) Shape parameter of a Gamma distribution (see dgamma).
size
Order of a Binomial distribution (see dbinom).
lower
(hmmUnif,hmmTNorm,hmmMEUnif) Lower limit for an Uniform or truncated Normal distribution.
upper
(hmmUnif,hmmTNorm,hmmMEUnif) Upper limit for an Uniform or truncated Normal distribution.
sderr
(hmmMETNorm,hmmUnif) Standard deviation of the Normal measurement error distribution.
meanerr
(hmmMETNorm,hmmUnif) Additional shift in the measurement error, fixed to 0 by default. This may be modelled in terms of covariates.

Value

  • Each function returns an object of class hmodel, which is a list containing information about the model. The only component which may be useful to end users is r, a function of one argument n which returns a random sample of size n from the given distribution.

Details

See the PDF manual msm-manual.pdf in the doc subdirectory for algebraic definitions of all these distributions.

Parameters which can be modelled in terms of covariates, on the scale of a link function, are as follows.

ll{ PARAMETER NAME LINK FUNCTION mean identity meanlog identity rate log scale log meanerr identity prob logit }

Parameters basecat, lower, upper, size, meanerr are fixed at their initial values. All other parameters are estimated while fitting the hidden Markov model, unless the appropriate fixedpars argument is supplied to msm.

For categorical response distributions (hmmCat) the outcome probabilities initialized to zero are fixed at zero, and the probability corresponding to basecat is fixed to one minus the sum of the remaining probabilities. These remaining probabilities are estimated, and can be modelled in terms of covariates.

References

Satten, G.A. and Longini, I.M. Markov chains with measurement error: estimating the 'true' course of a marker of the progression of human immunodeficiency virus disease (with discussion) Applied Statistics 45(3): 275-309 (1996). Jackson, C.H. and Sharples, L.D. Hidden Markov models for the onset and progresison of bronchiolitis obliterans syndrome in lung transplant recipients Statistics in Medicine, 21(1): 113--128 (2002).

Jackson, C.H., Sharples, L.D., Thompson, S.G. and Duffy, S.W. and Couto, E. Multi-state Markov models for disease progression with classification error. The Statistician, 52(2): 193--209 (2003).

See Also

msm