Table 2.

Features of HMM packages available in the R environment for statistical computing, including capabilities for multiple observation sequences (‘Multiple sequences’), multivariate HMMs (‘Multivariate’), mixed HMMs (‘Mixed’), hierarchical HMMs (‘Hierarchical’), hidden semi‐Markov models (‘Semi‐Markov’), parameter covariate modelling (‘Covariates’), parameter constraints (‘Constraints’), missing observations (‘Missing data’) and state‐dependent probability distributions

Package	Multiple sequences	Multivariate	Mixed	Hierarchical	Semi‐Markov	Covariates	Constraints	Missing data	Reference
aphid	✓								Wilkinson (2019)
depmixS4	✓	✓				$\mathrm{\delta },f,\mathrm{\gamma }$	$\mathrm{\delta },f,\mathrm{\gamma }$	✓	Visser and Speenkenbrink (2010)
HiddenMarkov						$f^{\ast }$			Harte (2017)
HMM									Himmelmann (2010)
hsmm					✓				Bulla and Bulla (2013)
LMest	✓	✓	✓			$f^{†}$ or $\mathrm{\delta },\mathrm{\gamma }$		✓	Bartolucci et al., (2017)
mhsmm	✓				✓			✓	O'Connell and Hojsgaard (2011)
momentuHMM	✓	✓	✓	✓		$\mathrm{\delta },f,\mathrm{\gamma },\mathrm{\pi }$	$\mathrm{\delta },f,\mathrm{\gamma },\mathrm{\pi }$	✓	McClintock and Michelot (2018)
msm	✓	✓				$f^{‡},\mathrm{\gamma }$	$f,\mathrm{\gamma }$	✓	Jackson (2011)
RcppHMM									Cardenas‐Ovando et al., (2017)
seqHMM	✓	✓	✓			$\mathrm{\pi }$	$\mathrm{\delta },\mathrm{\gamma }$	✓	Helske and Helske (2019)

	State‐dependent probability distributions
	Bernoulli	Beta	Binomial	Categorical	Custom	Exponential	Gamma	Lognormal	Logistic	Negative binomial	Normal	Multivariate normal	Truncated normal	Poisson	Student's $\mathit{t}$	Von Mises	Weibull	Wrapped Cauchy
aphid				✓
depmixS4			✓	✓	✓		✓				✓			✓
HiddenMarkov		✓	✓		✓	✓	✓	✓	✓		✓			✓
HMM				✓
hsmm	✓										✓			✓	✓
LMest				✓							✓	✓
mhsmm					✓						✓	✓		✓
momentuHMM	✓	✓		✓		✓	✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓
msm	✓	✓	✓	✓		✓	✓	✓		✓	✓		✓	✓	✓		✓
RcppHMM				✓							✓	✓		✓
seqHMM				✓

‘Covariates’ and ‘Constraints’ can pertain to initial distribution $\left(\mathrm{\delta }\right)$, state‐dependent probability distribution $\left(f\right)$, state transition probability $\left(\mathrm{\gamma }\right)$ and/or mixture probability $\left(\mathrm{\pi }\right)$ parameters. Several packages facilitate extensions for user‐specified state‐dependent probability distributions that require no modifications to the package source code (‘custom’).

^*Covariates are only permitted on state‐dependent distribution location parameters for the binomial, gamma, normal and Poisson distributions.

^†Covariates are only permitted on state‐dependent categorical distribution parameters.

^‡Covariates are only permitted on state‐dependent distribution location parameters.

[Corrections added on 10 November 2020, after first online publication: Table 2 has been updated.]