# How does fHMM process model parameters?

#### Lennart Oelschläger

#### 2021-06-16

In **fHMM**, four types of model parameters are estimated:

non-diagonal elements (column-wise) `gammas`

of transition probability matrices `Gamma`

,

expected values `mus`

,

standard deviations `sigmas`

,

degrees of freedom `dfs`

.

All of these parameters have to fulfill constraints. Constrained parameters get the suffix `Con`

, unconstrained parameters the suffix `Uncon`

. Fine-scale parameters additionally get the suffix `_star`

. Internally, collections of model parameters are processed using the following structures:

`thetaFull`

: A named list of all unconstrained model parameters.

`thetaUncon`

: A vector of all unconstrained model parameters to be estimated (in the above order).

`thetaCon`

: Constrained elements of `thetaUncon`

.

`thetaUnconSplit`

: Splitted `thetaUncon`

by fine-scale models.

`thetaListOrdered`

: `thetaList`

in ordered form with respect to estimated expected values.

The package **fHMM** provides functions to transform these structures. Their names follow the logic `x2y`

, where `x`

and `y`

are two structures.