hmodel argument to msm. The initial values
for the parameters of the distribution should be given as arguments.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)
hmmNBinom(disp, prob)
hmmBeta(shape1,shape2)
hmmT(mean,scale,df)hmmCat) Vector of probabilities of observing
category 1, 2, ..., length(prob) respectively. Or
the probability governing a binomial or negative binomial
distribution.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 probabilityhmmIdent) Code in the data which denotes the exactly-observed state.hmmNorm,hmmLNorm,hmmTNorm) Mean defining a Normal, or truncated Normal
distribution.hmmNorm,hmmLNorm,hmmTNorm) Standard deviation defining a
Normal, or truncated Normal distribution.hmmNorm,hmmLNorm,hmmTNorm) Mean on the log
scale, for a log Normal distribution.hmmNorm,hmmLNorm,hmmTNorm) Standard deviation on
the log scale, for a log Normal distribution.dbeta).hmmGamma) Scale parameter of a Gamma
distribution (see dgamma), or unstandardised Student t
distribution.dbinom).size or order. (see
dnbinom).hmmUnif,hmmTNorm,hmmMEUnif) Lower limit for an Uniform or truncated Normal distribution.hmmUnif,hmmTNorm,hmmMEUnif) Upper limit for an Uniform or truncated Normal
distribution.hmmMETNorm,hmmUnif) Standard deviation of the Normal measurement error
distribution.hmmMETNorm,hmmUnif) Additional shift in the
measurement error, fixed to 0 by default. This may
be modelled in terms of covariates.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.hmmCat represents a categorical response distribution on the
set 1, 2, ..., length(prob). The
Markov model with misclassification is an example of this type of model. The
categories in this case are (some subset of) the underlying states.
The hmmIdent distribution is used for underlying states which are
observed exactly without error. hmmUnif, hmmNorm, hmmLNorm, hmmExp,
hmmGamma, hmmWeibull, hmmPois, hmmBinom,
hmmTNorm, hmmNBinom and hmmBeta represent Uniform, Normal,
log-Normal, exponential, Gamma, Weibull, Poisson, Binomial, truncated Normal,
negative binomial and beta distributions, respectively, with parameterisations
the same as the default parameterisations in the corresponding base R
distribution functions.
hmmT is the Student t distribution with general mean
$\mu$, scale $\sigma$ and degrees of freedom
df.
The variance is $\sigma^2 df/(df + 2)$.
Note the t distribution in base R dt is a standardised one with
mean 0 and scale 1. These allow any positive (integer or non-integer)
df. By default, all three
parameters, including df, are estimated when fitting a hidden
Markov model, but in practice, df might need to be fixed for identifiability - this can be done
using the fixedpars argument to msm.
The hmmMETNorm and hmmMEUnif distributions are
truncated Normal and Uniform distributions, but with additional Normal measurement error on the
response. These are generalisations of the distributions proposed by
Satten and Longini (1996) for modelling the progression of CD4 cell
counts in monitoring HIV disease. See medists for
density, distribution, quantile and random generation functions for
these distributions. See also tnorm for
density, distribution, quantile and random generation functions for
the truncated Normal distribution.
See the PDF manual
mean identity
meanlog identity
rate log
scale log
meanerr identity
prob (multinomial logistic regression)
}
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 via multinomial
logistic regression (relative to basecat).
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).
msm