# Fast Numerical Maximum Likelihood Estimation for Latent Markov Models

## Documentation for package ‘LaMa’ version 2.1.1

- DESCRIPTION file.
- User guides, package vignettes and other documentation.
- Package NEWS.

## Help Pages

%sp% | Sparsity-retaining matrix multiplication
calc_trackInd | Calculate the index of the first observation of each track based on an ID variable
cosinor | Trigonometric basis expansion
ddwell | State dwell-time distributions of periodically inhomogeneous Markov chains
dgamma2 | Reparametrised gamma distribution
dgmrf2 | Reparametrised multivariate Gaussian distribution
dskewnorm | Skew normal distribution
dvm | Von Mises distribution
dwrpcauchy | Wrapped Cauchy distribution
forward | Forward algorithm to calculate the HMM log-likelihood
forward_g | Forward algorithm with time-varying transition probability matrix
forward_hsmm | Forward algorithm for homogeneous hidden semi-Markov models
forward_ihsmm | Forward algorithm for hidden semi-Markov models with inhomogeneous state durations and/ or conditional transition probabilities
forward_p | Forward algorithm with for periodically varying transition probability matrices
forward_phsmm | Forward algorithm for hidden semi-Markov models with periodically inhomogeneous state durations and/ or conditional transition probabilities
forward_s | Forward algorithm for hidden semi-Markov models with homogeneous transition probability matrix
forward_sp | Forward algorithm for hidden semi-Markov models with periodically varying transition probability matrices
gamma2 | Reparametrised gamma distribution
gdeterminant | Computes generalised determinant
generator | Build the generator matrix of a continuous-time Markov chain
generator_g | Build generator matrices of a continuous-time Markov chain
LaMaColors | Generate a colour-blind-friendly palette
logLik.LaMaModel | Extract log-likelihood from LaMaModel object
logLik.qremlModel | Extract log-likelihood from qremlModel object
make_matrices | Build the design and the penalty matrix for models involving penalised splines based on a formula and a data set
make_matrices_dens | Build a standardised P-Spline design matrix and the associated P-Spline penalty matrix
make_matrices_old | Build the design and the penalty matrix for models involving penalised splines based on a formula and a data set
max0_smooth | Smooth approximations to max(x, 0) and min(x, 0)
max2 | AD-compatible minimum and maximum functions
MCreport | Sample parameters from approximate Gaussian posterior distribution
min0_smooth | Smooth approximations to max(x, 0) and min(x, 0)
min2 | AD-compatible minimum and maximum functions
minmax | AD-compatible minimum and maximum functions
minmax0_smooth | Smooth approximations to max(x, 0) and min(x, 0)
nessi | Loch Ness Monster Acceleration Data
penalty | Computes penalty based on quadratic form
penalty2 | Computes generalised quadratic-form penalties
penalty_uni | Penalty approximation of unimodality constraints for univariates smooths
pgamma2 | Reparametrised gamma distribution
plot.LaMaResiduals | Plot pseudo-residuals
predict.LaMa_matrices | Build the prediction design matrix based on new data and model_matrices object created by 'make_matrices'
pred_matrix | Build the prediction design matrix based on new data and model_matrices object created by 'make_matrices'
process_hid_formulas | Process and standardise formulas for the state process of hidden Markov models
pseudo_res | Calculate pseudo-residuals
pskewnorm | Skew normal distribution
pvm | Von Mises distribution
qgamma2 | Reparametrised gamma distribution
qreml | Quasi restricted maximum likelihood (qREML) algorithm for models with penalised splines or simple i.i.d. random effects
qreml_old | Quasi restricted maximum likelihood (qREML) algorithm for models with penalised splines or simple i.i.d. random effects
qskewnorm | Skew normal distribution
report | Get reported quantities from and 'RTMB' object and return a 'LaMaModel'
rgamma2 | Reparametrised gamma distribution
rskewnorm | Skew normal distribution
rvm | Von Mises distribution
rwrpcauchy | Wrapped Cauchy distribution
sdreportMC | Monte Carlo version of 'sdreport'
sdreport_outer | Report uncertainty of the estimated smoothing parameters or variances
skewnorm | Skew normal distribution
smooth_dens_construct | Build the design and penalty matrices for smooth density estimation
stateprobs | Calculate conditional local state probabilities in HMMs
stateprobs_g | Calculate conditional local state probabilities for inhomogeneous HMMs
stateprobs_p | Calculate conditional local state probabilities for periodically inhomogeneous HMMs
stationary | Compute the stationary distribution of a homogeneous Markov chain
stationary_cont | Compute the stationary distribution of a continuous-time Markov chain
stationary_ct | Compute the stationary distribution of a continuous-time Markov chain
stationary_p | Periodically stationary distribution of a periodically inhomogeneous Markov chain
stationary_p_sparse | Sparse version of 'stationary_p'
stationary_sparse | Sparse version of 'stationary'
summary.qremlModel | Summary method for 'qremlModel' objects
tpm | Build the transition probability matrix from unconstrained parameter vector
tpm_cont | Calculate continuous time transition probabilities
tpm_ct | Calculate continuous time transition probabilities
tpm_emb | Build the embedded transition probability matrix of an HSMM from unconstrained parameter vector
tpm_emb_g | Build all embedded transition probability matrices of an inhomogeneous HSMM
tpm_g | Build all transition probability matrices of an inhomogeneous HMM
tpm_g2 | Build all transition probability matrices of an inhomogeneous HMM
tpm_hsmm | Builds the transition probability matrix of an HSMM-approximating HMM
tpm_hsmm2 | Build the transition probability matrix of an HSMM-approximating HMM
tpm_ihsmm | Builds all transition probability matrices of an inhomogeneous-HSMM-approximating HMM
tpm_p | Build all transition probability matrices of a periodically inhomogeneous HMM
tpm_phsmm | Builds all transition probability matrices of an periodic-HSMM-approximating HMM
tpm_phsmm2 | Build all transition probability matrices of an periodic-HSMM-approximating HMM
tpm_thinned | Compute the transition probability matrix of a thinned periodically inhomogeneous Markov chain.
trex | T-Rex Movement Data
trigBasisExp | Compute the design matrix for a trigonometric basis expansion
viterbi | Viterbi algorithm for state decoding in HMMs
viterbi_g | Viterbi algorithm for state decoding in inhomogeneous HMMs
viterbi_p | Viterbi algorithm for state decoding in periodically inhomogeneous HMMs
vm | Von Mises distribution
wrpcauchy | Wrapped Cauchy distribution
zero_inflate | Zero-inflated density constructer