hmm-dists | R Documentation |
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. Note the
initial values should be supplied as literal values - supplying them as
variables is currently not supported.
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)
hmmBetaBinom(size, meanp, sdp)
hmmNBinom(disp, prob)
hmmBeta(shape1, shape2)
hmmTNorm(mean, sd, lower = -Inf, upper = Inf)
hmmMETNorm(mean, sd, lower, upper, sderr, meanerr = 0)
hmmMEUnif(lower, upper, sderr, meanerr = 0)
hmmT(mean, scale, df)
prob |
( |
basecat |
( |
x |
( |
lower |
( |
upper |
( |
mean |
( |
sd |
( |
meanlog |
( |
sdlog |
( |
rate |
( |
shape |
( |
scale |
( |
size |
Order of a Binomial distribution (see |
meanp |
Mean outcome probability in a beta-binomial distribution |
sdp |
Standard deviation describing the overdispersion of the outcome probability in a beta-binomial distribution |
disp |
Dispersion parameter of a negative binomial distribution, also
called |
shape1 , shape2 |
First and second parameters of a beta distribution (see
|
sderr |
( |
meanerr |
( |
df |
Degrees of freedom of the Student t 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. For hidden Markov models with multiple
outcomes, (see hmmMV
), the outcome in the data which takes the
special hmmIdent
value must be the first of the multiple outcomes.
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 ‘msm-manual.pdf’ in the ‘doc’ subdirectory for algebraic definitions of all these distributions. New hidden Markov model response distributions can be added to msm by following the instructions in Section 2.17.1.
Parameters which can be modelled in terms of covariates, on the scale of a link function, are as follows.
PARAMETER NAME | LINK FUNCTION |
mean | identity |
meanlog | identity |
rate | log |
scale | log |
meanerr | identity |
meanp | logit |
prob | logit or multinomial 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 via multinomial logistic regression
(relative to basecat
).
Each function returns an object of class hmmdist
, 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.
C. H. Jackson chris.jackson@mrc-bsu.cam.ac.uk
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).
msm
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