parameter_transformations function

Parameter transformations

These helper functions transform model parameters between

• constrained spaces (suffix *Con)
• and unconstrained spaces (suffix *Uncon).

The former is useful for interpretation, the latter for unconstrained optimization.

par2parUncon(par, controls, use_parameter_labels = TRUE)

parUncon2parCon(
  parUncon,
  controls,
  use_parameter_labels = TRUE,
  numerical_safeguard = FALSE
)

parCon2par(parCon, controls, use_parameter_labels = TRUE)

par2parCon(par, controls, use_parameter_labels = TRUE)

parCon2parUncon(parCon, controls, use_parameter_labels = TRUE)

parUncon2par(
  parUncon,
  controls,
  use_parameter_labels = TRUE,
  numerical_safeguard = FALSE
)

muCon2muUncon(muCon, link, prefix = "muUncon_", use_parameter_labels = TRUE)

muUncon2muCon(muUncon, link, prefix = "muCon_", use_parameter_labels = TRUE)

sigmaCon2sigmaUncon(
  sigmaCon,
  prefix = "sigmaUncon_",
  use_parameter_labels = TRUE
)

sigmaUncon2sigmaCon(
  sigmaUncon,
  prefix = "sigmaCon_",
  use_parameter_labels = TRUE,
  numerical_safeguard = FALSE
)

dfCon2dfUncon(dfCon, prefix = "dfUncon_", use_parameter_labels = TRUE)

dfUncon2dfCon(
  dfUncon,
  prefix = "dfCon_",
  use_parameter_labels = TRUE,
  numerical_safeguard = FALSE
)

Gamma2gammasCon(
  Gamma,
  prefix = "gammasCon_",
  use_parameter_labels = TRUE,
  numerical_safeguard = FALSE
)

Gamma2gammasUncon(Gamma, prefix = "gammasUncon_", use_parameter_labels = TRUE)

gammasCon2Gamma(gammasCon, dim, prefix = "state_", use_parameter_labels = TRUE)

gammasCon2gammasUncon(
  gammasCon,
  dim,
  prefix = "gammasUncon_",
  use_parameter_labels = TRUE
)

gammasUncon2Gamma(
  gammasUncon,
  dim,
  prefix = "state_",
  use_parameter_labels = TRUE,
  numerical_safeguard = FALSE
)

gammasUncon2gammasCon(
  gammasUncon,
  dim,
  prefix = "gammasCon_",
  use_parameter_labels = TRUE,
  numerical_safeguard = FALSE
)

Arguments

• par: An object of class fHMM_parameters, which is a list

  of model parameters.

• 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.

  Important: Specifications in controls always override individual specifications.

• use_parameter_labels: Either TRUE to label the parameters or FALSE, if not (this can save computation time).

• 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)

• numerical_safeguard: Either TRUE or FALSE, determining whether to apply the following small corrections to boundary parameters to improve numerical performance when calculating and optimizing the likelihood function:

  • transition probabilities equal to 0 or 1 are shifted towards the center by 1e-3
  • standard deviations and degrees of freedom are bounded above by 100

• parCon: An object of class parCon, which is a numeric vector

  with identified (and constrained) model parameters in the following order:

  1. non-diagonal transition probabilities gammasCon
  2. expectations muCon
  3. standard deviations sigmaCon (if any)
  4. degrees of freedom dfCon (if any)
  5. fine-scale parameters for each coarse-scale state, in the same order (if any)

• muCon, muUncon: A vector of (un-) constrained expected values.

• link: Either TRUE or FALSE, determining whether to apply the link function.

• prefix: A character prefix for labeling the parameters.

• sigmaCon, sigmaUncon: A vector of (un-) constrained standard deviations.

• dfCon, dfUncon: A vector of (un-) constrained degrees of freedom.

• gammasCon, gammasUncon: A vector of (un-) constrained non-diagonal transition probabilities.

• dim: An integer, the dimension of the transition probability matrix.

Returns

For par2parUncon: a vector of unconstrained model parameters.

For parUncon2parCon: a vector of constrained model parameters.

For parCon2par: an object of class fHMM_parameters.

For par2parCon: a vector of constrained model parameters.

For parCon2parUncon: a vector of unconstrained model parameters.

For parUncon2par: an object of class fHMM_parameters.

For muCon2muUncon: a vector of unconstrained expected values.

For muUncon2muCon: a vector of constrained expected values.

For sigmaCon2sigmaUncon: a vector of unconstrained standard deviations.

For sigmaUncon2sigmaCon: a vector of constrained standard deviations.

For dfCon2dfUncon: a vector of unconstrained degrees of freedom.

For dfUncon2dfCon: a vector of constrained degrees of freedom.

For Gamma2gammasCon: a vector of constrained non-diagonal matrix elements (column-wise).

For Gamma2gammasUncon: a vector of unconstrained non-diagonal matrix elements (column-wise).

For gammasCon2Gamma: a transition probability matrix.

For gammasCon2gammasUncon: a vector of unconstrained non-diagonal elements of the transition probability matrix.

For gammasUncon2Gamma: a transition probability matrix.

For gammasUncon2gammasCon: a vector of constrained non-diagonal elements of a transition probability matrix.