tpm_g

In an HMM, we can model the influence of covariates on the state process, by linking them to the transition probabiltiy matrix. 
Most commonly, this is done by specifying a linear predictor 
\( \eta_{ij}^{(t)} = \beta^{(ij)}_0 + \beta^{(ij)}_1 z_{t1} + \dots + \beta^{(ij)}_p z_{tp} \) 
for each off-diagonal element (\(i \neq j\)) and then applying the inverse multinomial logistic link to each row.
This function efficiently calculates all transition probabilty matrices for a given design matrix \(Z\) and parameter matrix beta.

The class of latent Markov models, including hidden Markov models,
hidden semi-Markov models, state space models, and point processes, is a very popular and powerful framework for inference of time series driven by latent processes.
Furthermore, all these models can be fitted using direct numerical maximum likelihood estimation using the so-called forward algorithm as discussed in
Zucchini et al. (2016) <doi:10.1201/b20790>.
However, due to their great flexibility, researchers using these models in applied work often need to build highly customized models for which standard software implementation is lacking,
or the construction of such models in said software is as complicated as writing fully tailored 'R' code.
While providing greater flexibility and control, the latter suffers from slow estimation speeds that make custom solutions inconvenient.
We address the above issues in two ways. First, standard blocks of code, common to all these model classes, are implemented as simple-to-use functions that can be added like Lego blocks to an otherwise fully custom likelihood function, making writing custom code much easier.
Second, under the hood, these functions are written in 'C++', allowing for 10-20 times faster evaluation time, and thus drastically speeding up model estimation.
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_g function

<dl><dt>Z</dt>
<dd>Covariate design matrix (excluding intercept column) of dimension c(n, p), where p can also be one (i.e. Z can be a vector).</dd>
<dt>beta</dt>
<dd>Matrix of coefficients for the off-diagonal elements of the transition probability matrix.
Needs to be of dimension c(N*(N-1), p+1), where the first column contains the intercepts.</dd>
<dt>byrow</dt>
<dd>Logical that indicates if each transition probability matrix should be filled by row. 
Defaults to FALSE, but should be set to TRUE if one wants to work with a matrix of beta parameters returned by popular HMM packages like moveHMM, momentuHMM, or hmmTMB.</dd></dl>

Arguments

In an HMM, we can model the influence of covariates on the state process, by linking them to the transition probabiltiy matrix. 
Most commonly, this is done by specifying a linear predictor 
\( \eta_{ij}^{(t)} = \beta^{(ij)}_0 + \beta^{(ij)}_1 z_{t1} + \dots + \beta^{(ij)}_p z_{tp} \) 
for each off-diagonal element (\(i \neq j\)) and then applying the inverse multinomial logistic link to each row.
This function efficiently calculates all transition probabilty matrices for a given design matrix \(Z\) and parameter matrix beta.

Build all transition probability matrices of an inhomogeneous HMM — tpm_g

<dl>

<dt>Z</dt>
<dd>Covariate design matrix (excluding intercept column) of dimension c(n, p), where p can also be one (i.e. Z can be a vector).</dd>


<dt>beta</dt>
<dd>Matrix of coefficients for the off-diagonal elements of the transition probability matrix.
Needs to be of dimension c(N*(N-1), p+1), where the first column contains the intercepts.</dd>


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

</dl>

tpm_g: Build all transition probability matrices of an inhomogeneous HMM

Description

Usage

Value

Arguments

Examples