SMM (version 1.0.2)

LoglikelihoodSM: Loglikelihood (semi-Markov model)

Description

Computation of the loglikelihood starting from sequence(s), alphabet, initial distribution, transition matrix and type of sojourn times

Usage

## parametric case
LoglikelihoodSM(seq, E, mu, Ptrans, distr, param, laws = NULL, TypeSojournTime)
## non-parametric case
LoglikelihoodSM(seq, E, mu, Ptrans, distr, param = NULL, laws, TypeSojournTime)

Arguments

seq

List of sequence(s)

E

Vector of state space

mu

Vector of initial distribution of length S

Ptrans

Matrix of transition probabilities of the embedded Markov chain \(J=(J_m)_{m}\) of size SxS

distr

- "NP" for nonparametric case, laws have to be used, param is useless

- Matrix of distributions of size SxS if TypeSojournTime is equal to "fij";

- Vector of distributions of size S if TypeSojournTime is equal to "fi" or "fj";

- A distribution if TypeSojournTime is equal to "f".

The distributions to be used in distr must be one of "uniform", "geom", "pois", "dweibull", "nbinom".

param

- Useless if distr = "NP"

- Array of distribution parameters of size SxSx2 (2 corresponds to the maximal number of distribution parameters) if TypeSojournTime is equal to "fij";

- Matrix of distribution parameters of size Sx2 if TypeSojournTime is equal to "fi" or "fj";

- Vector of distribution parameters of length 2 if TypeSojournTime is equal to "f".

laws

- Useless if distr \(\neq\) "NP"

- Array of size SxSxKmax if TypeSojournTime is equal to "fij";

- Matrix of size SxKmax if TypeSojournTime is equal to "fi" or "fj";

- Vector of length Kmax if the TypeSojournTime is equal to "f".

Kmax is the maximum length of the sojourn times.

TypeSojournTime

Character: "fij", "fi", "fj", "f" (for more explanations, see Details)

Value

L

Value of loglikelihood for each sequence

Kmax

The maximal observed sojourn time

Details

In this package we can choose differents types of sojourn time. Four options are available for the sojourn times:

• depending on the present state and on the next state ("fij");

• depending only on the present state ("fi");

• depending only on the next state ("fj");

• depending neither on the current, nor on the next state ("f").

See Also

simulSM, estimMk, simulMk, estimSM

Examples

# NOT RUN {
alphabet = c("a","c","g","t")
S = length(alphabet)
# creation of the transition matrix
Pij = matrix(c(0,0.2,0.3,0.5,0.4,0,0.2,0.4,0.1,0.2,0,0.7,0.8,0.1,0.1,0), 
nrow = S, ncol = S, byrow = TRUE)

Pij
#     [,1] [,2] [,3] [,4]
#[1,]  0.0  0.2  0.3  0.5
#[2,]  0.4  0.0  0.2  0.4
#[3,]  0.1  0.2  0.0  0.7
#[4,]  0.8  0.1  0.1  0.0

################################
## Parametric estimation of a trajectory (of length equal to 5000), 
## where the sojourn times depend neither on the present state nor on the next state.
################################
## Simulation of a sequence of length 5000
seq5000 = simulSM(E = alphabet, NbSeq = 1, lengthSeq = 5000, TypeSojournTime = "f", 
                init = c(1/4,1/4,1/4,1/4), Ptrans = Pij, distr = "pois", param = 2)
                
#################################
## Computation of the loglikelihood
#################################
LoglikelihoodSM(seq = seq5000, E = alphabet, mu = rep(1/4,4), Ptrans = Pij, 
distr = "pois", param = 2, TypeSojournTime = "f")

#$L
#$L[[1]]
#[1] -1475.348
#
#
#$Kmax
#[1] 10

#------------------------------#
################################
## Non-parametric simulation of several trajectories (3 trajectories of length 1000, 
## 10 000 and 2000 respectively),
## where the sojourn times depend on the present state and on the next state.
################################
## creation of a matrix corresponding to the conditional sojourn time distributions
lengthSeq3 = c(1000, 10000, 2000)
Kmax = 4 
mat1 = matrix(c(0,0.5,0.4,0.6,0.3,0,0.5,0.4,0.7,0.2,0,0.3,0.4,0.6,0.2,0), 
nrow = S, ncol = S, byrow = TRUE)
mat2 = matrix(c(0,0.2,0.3,0.1,0.2,0,0.2,0.3,0.1,0.4,0,0.3,0.2,0.1,0.3,0), 
nrow = S, ncol = S, byrow = TRUE)
mat3 = matrix(c(0,0.1,0.3,0.1,0.3,0,0.1,0.2,0.1,0.2,0,0.3,0.3,0.3,0.4,0), 
nrow = S, ncol = S, byrow = TRUE)
mat4 = matrix(c(0,0.2,0,0.2,0.2,0,0.2,0.1,0.1,0.2,0,0.1,0.1,0,0.1,0), 
nrow = S, ncol = S, byrow = TRUE)
f <- array(c(mat1,mat2,mat3,mat4), c(S,S,Kmax))
### Simulation of 3 sequences
seqNP3 = simulSM(E = alphabet, NbSeq = 3, lengthSeq = lengthSeq3, 
TypeSojournTime = "fij", init = rep(1/4,4), Ptrans = Pij, laws = f, 
File.out = NULL)

#################################
## Computation of the loglikelihood
#################################
LoglikelihoodSM(seq = seqNP3, E = alphabet, mu = rep(1/4,4), Ptrans = Pij, laws = f, 
TypeSojournTime = "fij")

#$L
#$L[[1]]
#[1] -429.35
#
#$L[[2]]
#[1] -4214.521
#
#$L[[3]]
#[1] -818.6451
#
#
#$Kmax
#[1] 4
# }