Abstract
Optimization of mixture models such as the mixture transition distribution (MTD) model is notoriously difficult because of the high complexity of their solution space. The best approach comprises combining features of two types of algorithms: an algorithm that can explore as completely as possible the whole solution space (e.g., an evolutionary algorithm), and another that can quickly identify an optimum starting from a set of initial conditions (for instance, an EM algorithm). The march package for the R environment is a library dedicated to the computation of Markovian models for categorical variables. It includes different algorithms that can manage the complexity of the MTD model, including an ad hoc hill-climbing procedure. In this article, we first discuss the problems related to the optimization of the MTD model, and then we show how march can be used to solve these problems; further, we provide different syntaxes for the computation of other models, including homogeneous Markov chains, hidden Markov models, and double chain Markov models.
Highlights
Despite their long history and use in many scientific fields, Markovian models are difficult to apply in practice because of the lack of empirical tools
Markovian models are not included in the base versions of statistical environments such as SPSS, SAS, and Stata, and researchers need to either adopt a log-linear approach or rely on ad hoc toolboxes developed by third parties such as MARKOV [1] and mixmcm [2] for Stata, or PTRANSIT [3]
Mixture models are notoriously difficult to optimize [16], and the mixture transition distribution (MTD) model is not an exception, especially when a different transition matrix is used for each lag and/or when covariates are added to the model
Summary
Despite their long history and use in many scientific fields, Markovian models are difficult to apply in practice because of the lack of empirical tools. Symmetry 2020, 12, 2031 but whose development was definitively stopped in 2010 This lack of options when using the MTD model is not surprising, because to other mixture models, this model is notoriously difficult to optimize. There is a need for an R package dedicated to the computation of Markovian models for categorical variables and one that can handle the MTD model. We decided to rewrite the old march for Windows software (originally developed in the MATLAB language) as an R package and improve it. This package is freely available from CRAN (https://cran.r-project.org/). An appendix provides additional syntax with which to optimize other Markovian models
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