newton_raphson_mstep

Implements the maximization step of the EM algorithm based on a ridge-stabilized version of the Newton-Raphson algorithm, see Goldfeld et al. (1966).

Methods for model-based clustering of multinomial counts under the presence of covariates using mixtures of multinomial logit models, as implemented in Papastamoulis (2023) <DOI:10.1007/s11634-023-00547-5>. These models are estimated under a frequentist as well as a Bayesian setup using the Expectation-Maximization algorithm and Markov chain Monte Carlo sampling (MCMC), respectively. The (unknown) number of clusters is selected according to the Integrated Completed Likelihood criterion (for the frequentist model), and estimating the number of non-empty components using overfitting mixture models after imposing suitable sparse prior assumptions on the mixing proportions (in the Bayesian case), see Rousseau and Mengersen (2011) <DOI:10.1111/j.1467-9868.2011.00781.x>. In the latter case, various MCMC chains run in parallel and are allowed to switch states. The final MCMC output is suitably post-processed in order to undo label switching using the Equivalence Classes Representatives (ECR) algorithm, as described in Papastamoulis (2016) <DOI:10.18637/jss.v069.c01>.

Panagiotis Papastamoulis

multinomialLogitMix

Clustering Multinomial Count Data under the Presence of
Covariates

newton_raphson_mstep function

<dl> <dt>y</dt>
<dd>count data matrix</dd> <dt>X</dt>
<dd>design matrix (including const).</dd> <dt>b</dt>
<dd>coefficients of the multinomial logit mixture</dd> <dt>w</dt>
<dd>mixing proportions</dd> <dt>maxNR</dt>
<dd>threshold</dd> <dt>R0</dt>
<dd>inital value for the parameter that controls the step-size of the update.</dd> <dt>method</dt>
<dd>set to 5. Always.</dd> <dt>verbose</dt>
<dd>Boolean.</dd></dl>

Arguments

Author

M-step of the EM algorithm — newton_raphson_mstep

<dl>

 <dt>y</dt>
<dd>count data matrix</dd>

 <dt>X</dt>
<dd>design matrix (including const).</dd>

 <dt>b</dt>
<dd>coefficients of the multinomial logit mixture</dd>

 <dt>w</dt>
<dd>mixing proportions</dd>

 <dt>maxNR</dt>
<dd>threshold</dd>

 <dt>R0</dt>
<dd>inital value for the parameter that controls the step-size of the update.</dd>

 <dt>method</dt>
<dd>set to 5. Always.</dd>

 <dt>verbose</dt>
<dd>Boolean.</dd>

</dl>

newton_raphson_mstep: M-step of the EM algorithm

Description

Usage

Value

Arguments

Author

References