Markov chains are parametrised in terms of a transition probability matrix \(\Gamma\), for which each row contains a conditional probability distribution of the next state given the current state.
Hence, each row has entries between 0 and 1 that need to sum to one.
For numerical optimisation, we parametrise in terms of unconstrained parameters, thus this function computes said matrix from an unconstrained parameter vector via the inverse multinomial logistic link (also known as softmax) applied to each row.

A variety of latent Markov models, including hidden Markov models, hidden semi-Markov models,
state-space models and continuous-time variants can be formulated and estimated within the same framework via directly maximising the likelihood function using the so-called forward algorithm.
Applied researchers often need custom models that standard software does not easily support.
Writing tailored 'R' code offers flexibility but suffers from slow estimation speeds.
We address these issues by providing easy-to-use functions (written in 'C++' for speed) for common tasks like the forward algorithm.
These functions can be combined into custom models in a Lego-type approach, offering up to 10-20 times faster estimation via standard numerical optimisers.
To aid in building fully custom likelihood functions, several vignettes are included that show how to simulate data from and estimate all the above model classes.

Jan-Ole Koslik

LaMa

Fast Numerical Maximum Likelihood Estimation for Latent Markov
Models

tpm function

<dl><dt>param</dt>
<dd>unconstrained parameter vector of length N*(N-1) where N is the number of states of the Markov chain</dd>
<dt>byrow</dt>
<dd>logical indicating if the transition probability matrix should be filled by row
Defaults to <code>FALSE</code>, but should be set to <code>TRUE</code> if one wants to work with a matrix of beta parameters returned by popular HMM packages like <code>moveHMM</code>, <code>momentuHMM</code>, or <code>hmmTMB</code>.</dd></dl>

Arguments

Build the transition probability matrix from unconstrained parameter vector — tpm

<dl>

<dt>param</dt>
<dd>unconstrained parameter vector of length N*(N-1) where N is the number of states of the Markov chain</dd>


<dt>byrow</dt>
<dd>logical indicating if the transition probability matrix should be filled by row
Defaults to <code>FALSE</code>, but should be set to <code>TRUE</code> if one wants to work with a matrix of beta parameters returned by popular HMM packages like <code>moveHMM</code>, <code>momentuHMM</code>, or <code>hmmTMB</code>.</dd>

</dl>

tpm: Build the transition probability matrix from unconstrained parameter vector

Description

Usage

Value

Arguments

See Also

Examples