fitted.hmm.discnp: Fitted values of a discrete non-parametric hidden Markov...

In hmm.discnp: Hidden Markov Models with Discrete Non-Parametric Observation Distributions

Fitted values of a discrete non-parametric hidden Markov model.

Description

Calculates the fitted values of a discrete non-parametric hidden Markov model. If the data are numeric these are the conditional expectations of the observations, given the entire observation sequence (and the estimated parameters of the model). If the data are categorical (whence “expectations” make no sense) the “fitted values” are taken to be the probabilities of each of the possible values of the observations, at each time point.

Usage

## S3 method for class 'hmm.discnp'
fitted(object, warn=TRUE, drop=TRUE, ...)

Arguments

object	An object of class hmm.discnp as returned by hmm().
warn	Logical scalar. See the help for sp().
drop	Logical scalar. If there is a single sequence of observations (i.e. if object[["y"]] consists of a matrix or a list of length 1) and if drop is TRUE then the returned value is a single entity (matrix, list of two matrices, or 3-dimensional array, depending on circumstances. Otherwise the returned value is a list of such entities, one for each observation sequence.
...	Not used.

Details

The observation sequence(s) must be present in object (which will be the case if object was returned by hmm() and if the argument keep.y was set to TRUE). If it is not present an error is thrown.

However, if such an error is thrown, do not despair! You do not have to start from scratch when fitting your model with keep.y==TRUE. If fit is your fitted model that you obtained without setting keep.y==TRUE, then you can just re-fit the model using fit as the starting values:

      fit2 <- hmm(<whatever>,par0=fit,keep.y=TRUE)
  

This will of course converge instantaneously. You could also do:

      fit2 <- update(fit,data=<whatever>,keep.y=TRUE)
  

Value

If the observations consist of a single sequence and if drop is TRUE then the returned value consists of a single object (matrix, list of two matrices, or 3-dimensional array, depending on circumstances; see below). Otherwise the returned value is a list of such objects, one for each observation sequence.

If the observations are numeric then the object corresponding to each observation sequence is a matrix. If the model is univariate (see hmm()) then matrix has a single column constituting the sequence of fitted values corresponding to the observations in the given sequence. The number of rows is the number of observations and the entry in row t is the fitted value (conditional expection) corresponding to the observation made at time t. If the model is bivariate (either independent or dependent) then the matrix has two columns corresponding respectively to the two variables in the bivariate model.

If the observations are categorical then the nature of the object returned changes substantially depending on whether the data are univariate, bivariate independent or bivariate dependent. (See hmm().

In the unvariate case the object corresponding to each sequence is a matrix, the number of rows of which is the number of observations and the number of columns of which is the number of unique possible values of the observations. The entry of this matrix in row t and column j is the conditional probability that an emission, at time t, is equal to u[i] where u[1], …, u[m] are the unique possible values.

In the bivariate independent case the object is a list of two matrices, each of which is of the same nature as that produced in the univariate case, corresponding respectively to the first and second of the two variables.

In the bivariate dependent case the object is a 3-dimensional array of dimension m1 x m2 x n where m1 is the number of unique possible values of the first variable, m2 is the number of unique possible values of the second variable, and n is the number of observations. The (i,j,t)-th entry of this array is the conditional probability that an emission, at time t, is equal to (u[i],v[j]) where the u[i] are the unique possible values of the first variable and the v[j] are the unique possible values of the second variable.

Author(s)

Rolf Turner [e-mail]

See Also

sp() link{predict.hmm.discnp}()

Examples

P <- matrix(c(0.7,0.3,0.1,0.9),2,2,byrow=TRUE)
R <- matrix(c(0.5,0,0.1,0.1,0.3,
              0.1,0.1,0,0.3,0.5),5,2)
set.seed(42)
lll <- sample(250:350,20,TRUE)
y   <- rhmm(ylengths=lll,nsim=1,drop=TRUE,tpm=P,Rho=R)
fit <- hmm(y,K=2,verb=TRUE,keep.y=TRUE,itmax=10)
fv  <- fitted(fit)

hmm.discnp documentation built on Sept. 26, 2022, 5:05 p.m.