hsmm {hsmm} | R Documentation |
Fitting Hidden Semi-Markov Models
hsmm(x, od, rd, pi.par, tpm.par, od.par, rd.par, M = NA, Q.max = 500, epsilon = 1e-08, censoring = 1, prt = TRUE, detailed = FALSE, r.lim = c(0.01, 100), p.log.lim = c(0.001, 0.999), nu.lim = c(0.01, 100))
x |
the observed process, a vector of length tau |
od |
character with the name of the conditional distribution of the observations: "bern" = Bernoulli, "norm" = Normal, "pois" = Poisson, "t" = Student-t |
rd |
character with the name of the runlength distribution (or sojourn time, dwell time distribution): "nonp" = Non-parametric, "geom" = Geometric, "nbinom" = Negative Binomial, "log" = Logarithmic, , "pois" = Poisson |
pi.par |
vector of length J with the initial values for the initial probabilities of the semi-Markov chain |
tpm.par |
matrix of dimension J x J with the initial values for the transition probability matrix of the embedded Markov chain. The diagonal entries must all be zero; absorbing states are not permitted |
rd.par |
list with the initial values for the parameters of the runlength distributions. See further details below (section 'List Objects rd.par and od.par') |
od.par |
list with the initial values for the parameters of the conditional observation distributions. See further details below (section 'List Objects rd.par and od.par') |
M |
positive integer containing the maximum runlength |
Q.max |
positive integer containing the maximum number of iterations |
epsilon |
positive scalar giving the tolerance at which the relative change of log-likelihood is considered close enough to zero to terminate the algorithm. |
censoring |
integer. if equal to 1, the last visited state contributes to the likelihood. If equal to 0, the partial likelihood estimator, which ignores the contribution of the last visited state, is used. For details see Guedon (2003) |
prt |
logical. if TRUE, the log-likelihood and number of iterations carried out are printed for each iteration |
detailed |
logical. if TRUE, a list of the parameters at every iteration step is written into the ctrl list |
r.lim |
upper and lower bound for the r parameter of the negative binomial distribution in the M-step, bisection is applied to determine this parameter |
p.log.lim |
upper and lower bound for the parameter of the logarithmic distribution in the M-step, bisection is applied to determine this parameter |
nu.lim |
upper and lower bound for the degrees of freedom of parameter of the t distribution in the M-step, bisection is applied to determine this parameter |
The function hsmm
fits a Hidden Semi-Markov Model using the EM-Algorithm for parameter estimation. The estimation algorithms are based on the right-censored approach initially described in Guedon (2003).
call |
call |
iter |
positive integer containing the number of iterations carried out |
logl |
double containing log-likelihood of the fitted model |
para |
list object containing the parameter estimates |
ctrl |
list object containing additional control variables. These are solution.reached , error , and details .
solution.reached is TRUE, if the stopping criterion is fulfilled.
error returns an error code: 0 = no error, 1 = internal probability less or equal to zero, 2 = memory exception,
3 = file error (internal output from C routine, disabled by default).
details contains the parameter values of every iteration. |
The list objects rd.par
and od.par
contain parameter values for the runlength and conditional
observation distribution, respectively. For a model with J states, the length of all parameter vectors
is equal to J. For non-parametric runlength distribution, the corresponding entry is
a matrix of dimension M x J.
The names of the list entries have to be as follows.
od.par
"bern" (Bernoulli): "b"
"norm" (Normal): "mean", "var"
"pois" (Poisson): "lambda"
"t" (Student-t): "mean", "var", "df"
rd.par
"nonp" (Non-parametric): "np"
"geom" (Geometric): "p"
"nbinom" (Negative Binomial): "r", "pi"
"log" (Logarithmic): "p"
"pois" (Poisson): "lambda"
Bulla, J. (2006), Stylized facts of financial time series and hidden semi-Markov models. Ph.D. thesis, Goettingen.
Guedon, Y. (2003), Estimating Hidden Semi-Markov Chains From Discrete Sequences. JCGS, 12 (3), pp 604-639.
hsmm.smooth
, hsmm.viterbi
, hsmm.sim