hidden fits a two or more state hidden Markov chain model with a
variety of distributions. All series on different individuals are assumed
to start at the same time point. Time points are equal, discrete steps.
hidden(
response = NULL,
totals = NULL,
distribution = "Bernoulli",
mu = NULL,
cmu = NULL,
tvmu = NULL,
pgamma,
pmu = NULL,
pcmu = NULL,
ptvmu = NULL,
pshape = NULL,
pfamily = NULL,
par = NULL,
pintercept = NULL,
delta = NULL,
envir = parent.frame(),
print.level = 0,
ndigit = 10,
gradtol = 1e-05,
steptol = 1e-05,
fscale = 1,
iterlim = 100,
typsize = abs(p),
stepmax = 10 * sqrt(p %*% p)
)A list of classes hidden and recursive (unless
multinomial, proportional odds, or continuation ratio) is returned that
contains all of the relevant information calculated, including error codes.
A list of two or three column matrices with counts or
category indicators, times, and possibly totals (if the distribution is
binomial), for each individual, one matrix or dataframe of counts, or an
object of class, response (created by
restovec) or repeated (created by
rmna or lvna). If the
repeated data object contains more than one response variable, give
that object in envir and give the name of the response variable to
be used here. If there is only one series, a vector of responses may be
supplied instead.
Multinomial and ordinal categories must be integers numbered from 0.
If response is a matrix, a corresponding matrix of totals if
the distribution is binomial. Ignored if response has class,
response or repeated.
Bernoulli, Poisson, multinomial, proportional odds, continuation ratio, binomial, exponential, beta binomial, negative binomial, normal, inverse Gauss, logistic, gamma, Weibull, Cauchy, Laplace, Levy, Pareto, gen(eralized) gamma, gen(eralized) logistic, Hjorth, Burr, gen(eralized) Weibull, gen(eralized) extreme value, gen(eralized) inverse Gauss, power exponential, skew Laplace, or Student t. (For definitions of distributions, see the corresponding [dpqr]distribution help.)
A general location function with two possibilities: (1) a list of formulae (with parameters having different names) or functions (with one parameter vector numbering for all of them) each returning one value per observation; or (2) a single formula or function which will be used for all states (and all categories if multinomial) but with different parameter values in each so that pmu must be a vector of length the number of unknowns in the function or formula times the number of states (times the number of categories minus one if multinomial).
A time-constant location function with three possibilities: (1)
a list of formulae (with parameters having different names) or functions
(with one parameter vector numbering for all of them) each returning one
value per individual; (2) a single formula or function which will be used
for all states (and all categories if multinomial) but with different
parameter values in each so that pcmu must be a vector of length the number
of unknowns in the function or formula times the number of states (times
the number of categories minus one if multinomial); or (3) a function
returning an array with one row for each individual, one column for each
state of the hidden Markov chain, and, if multinomial, one layer for each
category but the last. If used, this function or formula should contain the
intercept. Ignored if mu is supplied.
A time-varying location function with three possibilities: (1)
a list of formulae (with parameters having different names) or functions
(with one parameter vector numbering for all of them) each returning one
value per time point; (2) a single formula or function which will be used
for all states (and all categories if multinomial) but with different
parameter values in each so that ptvmu must be a vector of length the
number of unknowns in the function or formula times the number of states
(times the number of categories minus one if multinomial); or (3) a
function returning an array with one row for each time point, one column
for each state of the hidden Markov chain, and, if multinomial, one layer
for each category but the last. This function or formula is usually a
function of time; it is the same for all individuals. It only contains the
intercept if cmu does not. Ignored if mu is supplied.
A square mxm matrix of initial estimates of the hidden
Markov transition matrix, where m is the number of hidden states.
Rows must sum to one. If the matrix contains zeroes or ones, these are
fixed and not estimated. (Ones cannot appear on the diagonal.) If a
1x1 matrix or a scalar value of 1 is given, the independence model
is fitted.
Initial estimates of the unknown parameters in mu.
Initial estimates of the unknown parameters in cmu.
Initial estimates of the unknown parameters in tvmu.
Initial estimate(s) of the dispersion parameter, for those distributions having one. This can be one value or a vector with a different value for each state.
Initial estimate of the family parameter, for those distributions having one.
Initial estimate of the autoregression parameter.
For multinomial, proportional odds, and continuation
ratio models, p-2 initial estimates for intercept contrasts from the
first intercept, where p is the number of categories.
Scalar or vector giving the unit of measurement (always one
for discrete data) for each response value, set to unity by default. For
example, if a response is measured to two decimals, delta=0.01. If the
response is transformed, this must be multiplied by the Jacobian. For
example, with a log transformation, delta=1/response. Ignored if
response has class, response or repeated.
Environment in which model formulae are to be interpreted or a
data object of class, repeated, tccov, or tvcov; the
name of the response variable should be given in response. If
response has class repeated, it is used as the environment.
Arguments for nlm.
Arguments for nlm.
Arguments for nlm.
Arguments for nlm.
Arguments for nlm.
Arguments for nlm.
Arguments for nlm.
Arguments for nlm.
J.K. Lindsey and P.J. Lindsey
To fit an `observed' Markov chain, as well, with Bernoulli or multinomial
responses, use the lagged response as a time-varying covariate. For
quantitative responses, specifying par allows an `observed"
autoregression to be fitted as well as the hidden Markov chain.
All functions and formulae for the location parameter are on the (generalized) logit scale for the Bernoulli, binomial, and multinomial distributions.
If cmu and tvmu are used, these two mean functions are
additive so that interactions between time-constant and time-varying
variables are not possible.
The object returned can be plotted to give the probabilities of being in
each hidden state at each time point. For distributions other than the
multinomial, proportional odds, and continuation ratio, the (recursive)
predicted values can be plotted using mprofile and
iprofile.
See MacDonald, I.L. and Zucchini, W. (1997) Hidden Markov and Other Models for Discrete-valued Time Series. Chapman and Hall.
MacDonald, I.L. and Zucchini, W. (1997) Hidden Markov and other Models for Discrete-valued Time Series. Chapman & Hall.
# generate two random Poisson sequences with change-points
set.seed(8)
y <- rbind(c(rpois(5,1), rpois(15,5)), c(rpois(15,1), rpois(5,5)))
print(z <- hidden(y,dist="Poisson", cmu=~1, pcmu=c(1,5),
pgamma=matrix(c(0.95,0.05,0.05,0.95),ncol=2)))
# or equivalently
mu <- function(p) array(rep(p[1:2],rep(2,2)), c(2,2))
print(z <- hidden(y,dist="Poisson", cmu=mu, pcmu=c(1,5),
pgamma=matrix(c(0.95,0.05,0.05,0.95),ncol=2)))
# or
# param nind For plotting: numbers of individuals to plot.
# param state For plotting: states to plot.
print(z <- hidden(y,dist="Poisson", mu=~rep(a,40), pmu=c(1,5),
pgamma=matrix(c(0.95,0.05,0.05,0.95),ncol=2)))
par(mfrow=c(3,2))
plot(z, nind=1:2)
plot(z, nind=1:2, smooth=TRUE)
plot(iprofile(z), lty=2)
plot(mprofile(z), add=TRUE)
plot(iprofile(z), nind=2, lty=2)
plot(mprofile(z), nind=2, add=TRUE)
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