fHMM (version 1.2.2)

ll_hmm: Log-likelihood function of an (H)HMM

Description

This function computes the log-likelihood value of a (hierarchical) hidden Markov model for given observations and parameter values.

Usage

ll_hmm(
  parUncon,
  observations,
  controls = list(),
  hierarchy = FALSE,
  states = if (!hierarchy) 2 else c(2, 2),
  sdds = if (!hierarchy) "normal" else c("normal", "normal"),
  negative = FALSE,
  check_controls = TRUE
)

Value

The (negative) log-likelihood value.

Arguments

parUncon

An object of class parUncon, which is a numeric vector with identified and unconstrained model parameters in the following order:

1. non-diagonal transition probabilities gammasUncon

2. expectations muUncon

3. standard deviations sigmaUncon (if any)

4. degrees of freedom dfUncon (if any)

5. fine-scale parameters for each coarse-scale state, in the same order (if any)

observations

A numeric vector of time-series data.

In the hierarchical case (hierarchy = TRUE), a matrix with coarse-scale data in the first column and corresponding fine-scale data in the rows.

controls

Either a list or an object of class fHMM_controls.

The list can contain the following elements, which are described in more detail below:

• hierarchy, defines an hierarchical HMM,

• states, defines the number of states,

• sdds, defines the state-dependent distributions,

• horizon, defines the time horizon,

• period, defines a flexible, periodic fine-scale time horizon,

• data, a list of controls that define the data,

• fit, a list of controls that define the model fitting

Either none, all, or selected elements can be specified.

Unspecified parameters are set to their default values, see below.

Specifications in controls override individual specifications.

hierarchy

A logical, set to TRUE for an hierarchical HMM.

If hierarchy = TRUE, some of the other controls must be specified for the coarse-scale and the fine-scale layer.

By default, hierarchy = FALSE.

states

An integer, the number of states of the underlying Markov chain.

If hierarchy = TRUE, states must be a vector of length 2. The first entry corresponds to the coarse-scale layer, while the second entry corresponds to the fine-scale layer.

By default, states = 2 if hierarchy = FALSE and states = c(2, 2) if hierarchy = TRUE.

sdds

A character, specifying the state-dependent distribution. One of

• "normal" (the normal distribution),

• "lognormal" (the log-normal distribution),

• "t" (the t-distribution),

• "gamma" (the gamma distribution),

• "poisson" (the Poisson distribution).

The distribution parameters, i.e. the

• mean mu,

• standard deviation sigma (not for the Poisson distribution),

• degrees of freedom df (only for the t-distribution),

can be fixed via, e.g., "t(df = 1)" or "gamma(mu = 0, sigma = 1)". To fix different values of a parameter for different states, separate by "|", e.g. "poisson(mu = 1|2|3)".

If hierarchy = TRUE, sdds must be a vector of length 2. The first entry corresponds to the coarse-scale layer, while the second entry corresponds to the fine-scale layer.

By default, sdds = "normal" if hierarchy = FALSE and sdds = c("normal", "normal") if hierarchy = TRUE.

negative

Either TRUE to return the negative log-likelihood value (useful for optimization) or FALSE (default), else.

check_controls

Either TRUE to check the defined controls or FALSE to not check them (which saves computation time), else.

Examples

### HMM log-likelihood 
controls <- set_controls(states = 2, sdds = "normal")
parameters <- fHMM_parameters(controls)
parUncon <- par2parUncon(parameters, controls)
observations <- 1:10
ll_hmm(parUncon, observations, controls)

### HHMM log-likelihood 
controls <- set_controls(
  hierarchy = TRUE, states = c(2, 2), sdds = c("normal", "normal")
)
parameters <- fHMM_parameters(controls)
parUncon <- par2parUncon(parameters, controls)
observations <- matrix(dnorm(110), ncol = 11, nrow = 10)
ll_hmm(parUncon, observations, controls)