chidden: Continuous-time Hidden Markov Chain Models

In repeated: Non-Normal Repeated Measurements Models

Continuous-time Hidden Markov Chain Models

Description

chidden fits a two or more state hidden Markov chain model with a variety of distributions in continuous time. All series on different individuals are assumed to start at the same time point. If the time points are equal, discrete steps, use hidden.

Usage

chidden(
  response = NULL,
  totals = NULL,
  times = 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)
)

Arguments

response	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.
totals	If response is a matrix, a corresponding matrix of totals if the distribution is binomial. Ignored if response has class, response or repeated.
times	If response is a matrix, a vector of corresponding times, when they are the same for all individuals. Ignored if response has class, response or repeated.
distribution	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, Student t, or (time-)discretized Poisson process. (For definitions of distributions, see the corresponding [dpqr]distribution help.)
mu	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).
cmu	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.
tvmu	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.
pgamma	A square mxm matrix of initial estimates of the continuous-time hidden Markov transition matrix, where m is the number of hidden states. Rows can either sum to zero or the diagonal elements can be zero, in which case they will be replaced by minus the sum of the other values on the rows. If the matrix contains zeroes off diagonal, these are fixed and not estimated.
pmu	Initial estimates of the unknown parameters in mu.
pcmu	Initial estimates of the unknown parameters in cmu.
ptvmu	Initial estimates of the unknown parameters in tvmu.
pshape	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.
pfamily	Initial estimate of the family parameter, for those distributions having one.
par	Initial estimate of the autoregression parameter.
pintercept	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.
delta	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.
envir	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.
print.level	Arguments for nlm.
ndigit	Arguments for nlm.
gradtol	Arguments for nlm.
steptol	Arguments for nlm.
fscale	Arguments for nlm.
iterlim	Arguments for nlm.
typsize	Arguments for nlm.
stepmax	Arguments for nlm.

Details

The time-discretized Poisson process is a continuous-time hidden Markov model for Poisson processes where time is then discretized and only presence or absence of one or more events is recorded in each, perhaps unequally-spaced, discrete interval.

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. Those for intensities of the discretized Poisson process are on the log scale.

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 algorithm will run more quickly if the most frequently occurring time step is scaled to be equal to unity.

The object returned can be plotted to give the probabilities of being in each hidden state at each time point. See hidden for details. For distributions other than the multinomial, proportional odds, and continuation ratio, the (recursive) predicted values can be plotted using mprofile and iprofile.

Value

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.

Author(s)

J.K. Lindsey

References

MacDonald, I.L. and Zucchini, W. (1997) Hidden Markov and other Models for Discrete-valued Time Series. Chapman & Hall.

For time-discretized Poisson processes, see

Davison, A.C. and Ramesh, N.I. (1996) Some models for discretized series of events. JASA 91: 601-609.

Examples

# model for one randomly-generated binary series
y <- c(rbinom(10,1,0.1), rbinom(10,1,0.9))
mu <- function(p) array(p, c(1,2))
print(z <- chidden(y, times=1:20, dist="Bernoulli",
	pgamma=matrix(c(-0.1,0.2,0.1,-0.2),ncol=2),
	cmu=mu, pcmu=c(-2,2)))
# or equivalently
print(z <- chidden(y, times=1:20, dist="Bernoulli",
	pgamma=matrix(c(-0.1,0.2,0.1,-0.2),ncol=2),
	cmu=~1, pcmu=c(-2,2)))
# or
print(z <- chidden(y, times=1:20, dist="Bernoulli",
	pgamma=matrix(c(-0.1,0.2,0.1,-0.2),ncol=2),
	mu=~rep(a,20), pmu=c(-2,2)))
mexp(z$gamma)
par(mfcol=c(2,2))
plot(z)
plot(iprofile(z), lty=2)
plot(mprofile(z), add=TRUE)
print(z <- chidden(y, times=(1:20)*2, dist="Bernoulli",
	pgamma=matrix(c(-0.05,0.1,0.05,-0.1),ncol=2),
	cmu=~1, pcmu=c(-2,2)))
mexp(z$gamma) %*% mexp(z$gamma)
plot(z)
plot(iprofile(z), lty=2)
plot(mprofile(z), add=TRUE)

repeated documentation built on Aug. 8, 2023, 5:07 p.m.