Date: 2024-09-04
Title: Hidden Hybrid Markov/Semi-Markov Model Fitting
Version: 0.4.2
Description: Develops algorithms for fitting, prediction, simulation and initialization of the following models (1)- hidden hybrid Markov/semi-Markov model, introduced by Guedon (2005) <doi:10.1016/j.csda.2004.05.033>, (2)- nonparametric mixture of B-splines emissions (Langrock et al., 2015 <doi:10.1111/biom.12282>), (3)- regime switching regression model (Kim et al., 2008 <doi:10.1016/j.jeconom.2007.10.002>) and auto-regressive hidden hybrid Markov/semi-Markov model, (4)- spline-based nonparametric estimation of additive state-switching models (Langrock et al., 2018 <doi:10.1111/stan.12133>) (5)- robust emission model proposed by Qin et al, 2024 <doi:10.1007/s10479-024-05989-4> (6)- several emission distributions, including mixture of multivariate normal (which can also handle missing data using EM algorithm) and multi-nomial emission (for modeling polymer or DNA sequences) (7)- tools for prediction of future state sequence, computing the score of a new sequence, splitting the samples and sequences to train and test sets, computing the information measures of the models, computing the residual useful lifetime (reliability) and many other useful tools ... (read for more description: Amini et al., 2022 <doi:10.1007/s00180-022-01248-x> and its arxiv version: <doi:10.48550/arXiv.2109.12489>).
License: GPL-3
Imports: Rcpp, Rdpack, MASS, mice, progress, magic, splines2
RdMacros: Rdpack
Depends: R (≥ 4.3.0), CMAPSS, mvtnorm
Encoding: UTF-8
BugReports: https://github.com/mortamini/hhsmm/issues
RoxygenNote: 7.3.0
LinkingTo: Rcpp
Suggests: testthat (≥ 3.0.0)
NeedsCompilation: yes
Packaged: 2024-09-04 07:26:31 UTC; LENOVO.PIESC
Author: Morteza Amini [aut, cre, cph], Afarin Bayat [aut], Reza Salehian [aut]
Maintainer: Morteza Amini <morteza.amini@ut.ac.ir>
Repository: CRAN
Date/Publication: 2024-09-04 09:00:10 UTC

the M step function of the EM algorithm

Description

The M step function of the EM algorithm for the Gaussian linear (Markov-switching) regression as the emission distribution using the responses and covariates matrices and the estimated weight vectors

Usage

additive_reg_mstep(x, wt, control = list(K = 5, lambda0 = 0.01, resp.ind = 1))

Arguments

x

the observation matrix

wt

the state probabilities matrix (number of observations times number of states)

control

the parameters to control the M-step function. The simillar name is chosen with that of dnorm_additive_reg, to be used in ... argument of the hhsmmfit function. Here, it contains the following items:

  • K the degrees of freedom for the B-spline, default is K=5

  • lambda0 the initial value of the smoothing parameter, default is lambda0=0.01

  • resp.ind a vector of the column numbers of x which contain response variables. The default is 1, which means that the first column of x is the univariate response variable

Value

list of emission (nonparametric mixture of splines) parameters:

Author(s)

Morteza Amini, morteza.amini@ut.ac.ir, Reza Salehian, reza.salehian@ut.ac.ir

References

Langrock, R., Adam, T., Leos-Barajas, V., Mews, S., Miller, D. L., and Papastamatiou, Y. P. (2018). Spline-based nonparametric inference in general state-switching models. Statistica Neerlandica, 72(3), 179-200.

Examples

J <- 3
initial <- c(1, 0, 0)
semi <- rep(FALSE, 3)
P <- matrix(c(0.5, 0.2, 0.3, 0.2, 0.5, 0.3, 0.1, 0.4, 0.5), nrow = J, 
byrow = TRUE)
par <- list(intercept = list(3, list(-10, -1), 14),
coefficient = list(-1, list(1, 5), -7),
csigma = list(1.2, list(2.3, 3.4), 1.1),
mix.p = list(1, c(0.4, 0.6), 1))
model <- hhsmmspec(init = initial, transition = P, parms.emis = par,
dens.emis = dmixlm, semi = semi)
train <- simulate(model, nsim = c(20, 30, 42, 50), seed = 1234, 
remission = rmixlm, covar = list(mean = 0, cov = 1))
clus = initial_cluster(train = train, nstate = 3, nmix = NULL,
ltr = FALSE, final.absorb = FALSE, verbose = TRUE, regress = TRUE)
initmodel = initialize_model(clus = clus ,mstep = additive_reg_mstep,
dens.emission = dnorm_additive_reg, sojourn = NULL, semi = rep(FALSE, 3),
M = max(train$N),verbose = TRUE)
fit1 = hhsmmfit(x = train, model = initmodel, mstep = additive_reg_mstep,
M = max(train$N))
plot(train$x[, 1] ~ train$x[, 2], col = train$s, pch = fit1$yhat, 
xlab = "x", ylab = "y")
text(0,30, "colors are real states",col="red")
text(0,28, "characters are predicted states")
pred <- addreg_hhsmm_predict(fit1, train$x[, 2], 5)
yhat1 <- pred[[1]]
yhat2 <- pred[[2]]
yhat3 <- pred[[3]]

lines(yhat1[order(train$x[, 2])]~sort(train$x[, 2]),col = 2)
lines(yhat2[order(train$x[, 2])]~sort(train$x[, 2]),col = 1)
lines(yhat3[order(train$x[, 2])]~sort(train$x[, 2]),col = 3)

predicting the response values for the regime switching model

Description

This function computes the predictions of the response variable for the Gaussian linear (Markov-switching) regression model for different states for any observation matrix of the covariates

Usage

addreg_hhsmm_predict(object, x, K)

Arguments

object

a fitted model of class "hhsmm" estimated by hhsmmfit

x

the observation matrix of the covariates

K

the degrees of freedom for the B-spline

Value

list of predictions of the response variable

Author(s)

Morteza Amini, morteza.amini@ut.ac.ir

Examples

J <- 3
initial <- c(1, 0, 0)
semi <- rep(FALSE, 3)
P <- matrix(c(0.5, 0.2, 0.3, 0.2, 0.5, 0.3, 0.1, 0.4, 0.5), nrow = J, 
byrow = TRUE)
par <- list(intercept = list(3, list(-10, -1), 14),
coefficient = list(-1, list(1, 5), -7),
csigma = list(1.2, list(2.3, 3.4), 1.1),
mix.p = list(1, c(0.4, 0.6), 1))
model <- hhsmmspec(init = initial, transition = P, parms.emis = par,
dens.emis = dmixlm, semi = semi)
train <- simulate(model, nsim = c(20, 30, 42, 50), seed = 1234, 
remission = rmixlm, covar = list(mean = 0, cov = 1))
clus = initial_cluster(train = train, nstate = 3, nmix = NULL,
ltr = FALSE, final.absorb = FALSE, verbose = TRUE, regress = TRUE)
initmodel = initialize_model(clus = clus ,mstep = additive_reg_mstep,
dens.emission = dnorm_additive_reg, sojourn = NULL, semi = rep(FALSE, 3),
M = max(train$N),verbose = TRUE)
fit1 = hhsmmfit(x = train, model = initmodel, mstep = additive_reg_mstep,
M = max(train$N))
plot(train$x[, 1] ~ train$x[, 2], col = train$s, pch = fit1$yhat, 
xlab = "x", ylab = "y")
text(0,30, "colors are real states",col="red")
text(0,28, "characters are predicted states")
pred <- addreg_hhsmm_predict(fit1, train$x[, 2], 5)
yhat1 <- pred[[1]]
yhat2 <- pred[[2]]
yhat3 <- pred[[3]]

lines(yhat1[order(train$x[, 2])]~sort(train$x[, 2]),col = 2)
lines(yhat2[order(train$x[, 2])]~sort(train$x[, 2]),col = 1)
lines(yhat3[order(train$x[, 2])]~sort(train$x[, 2]),col = 3)

weighted covariance for data with missing values

Description

The weighted means and variances using the observation matrix and the estimated weight vectors for a data matrix containing missing values (NA or NaN)

Usage

cov.miss.mix.wt(
  x,
  means,
  secm,
  wt1 = rep(1/nrow(x), nrow(x)),
  wt2 = rep(1/nrow(x), nrow(x)),
  cor = FALSE,
  center = TRUE,
  method = c("unbiased", "ML")
)

Arguments

x

the observation matrix, which can contain missing values (NA or NaN)

means

a list containing the means of the missing values given observed values

secm

a list containing the second moments of the missing values given observed values

wt1

the state probabilities matrix (number of observations times number of states)

wt2

the mixture components probabilities list (of length nstate) of matrices (number of observations times number of mixture components)

cor

logical. if TRUE the weighted correlation is also given

center

logical. if TRUE the weighted mean is also given

method

with two possible entries:

  • "unbiased" the unbiased estimator is given

  • "ML" the maximum likelihood estimator is given

Value

list containing the following items:

Author(s)

Morteza Amini, morteza.amini@ut.ac.ir

Examples

data(CMAPSS)
x0 = CMAPSS$train$x[1:CMAPSS$train$N[1], ]
n = nrow(x0)
wt1 = runif(n)
wt2 = runif(n)
p = ncol(x0)
sammissall = sample(1:n, trunc(n / 20))
means = secm = list()
for(ii in 1:n){ 
	if(ii %in% sammissall){
   means[[ii]] = colMeans(x0[sammissall, ])
   secm[[ii]] = t(x0[sammissall, ]) %*% x0[sammissall, ]
 }else{
  means[[ii]] = secm[[ii]] = NA
 }
}
x0[sammissall,] = NA

cov.miss.mix.wt(x0, means, secm, wt1, wt2)

weighted covariance

Description

The weighted means and variances using the observation matrix and the estimated weight vectors

Usage

cov.mix.wt(
  x,
  wt1 = rep(1/nrow(x), nrow(x)),
  wt2 = rep(1/nrow(x), nrow(x)),
  cor = FALSE,
  center = TRUE,
  method = c("unbiased", "ML")
)

Arguments

x

the observation matrix

wt1

the state probabilities matrix (number of observations times number of states)

wt2

the mixture components probabilities list (of length nstate) of matrices (number of observations times number of mixture components)

cor

logical. if TRUE the weighted correlation is also given

center

logical. if TRUE the weighted mean is also given

method

with two possible entries:

  • "unbiased" the unbiased estimator is given

  • "ML" the maximum likelihood estimator is given

Value

list containing the following items:

Author(s)

Morteza Amini, morteza.amini@ut.ac.ir, Afarin Bayat, aftbayat@gmail.com

Examples

data(CMAPSS)
n = nrow(CMAPSS$train$x)
wt1 = runif(n)
wt2 = runif(n)
cov.mix.wt(CMAPSS$train$x, wt1, wt2)

pdf of the mixture of Gaussian linear (Markov-switching) models for hhsmm

Description

The probability density function of a mixture Gaussian linear (Markov-switching) models for a specified observation vector, a specified state and a specified model's parameters

Usage

dmixlm(x, j, model, resp.ind = 1)

Arguments

x

the observation matrix including responses and covariates

j

a specified state between 1 to nstate

model

a hhsmmspec model

resp.ind

a vector of the column numbers of x which contain response variables. The default is 1, which means that the first column of x is the univariate response variable

Value

the probability density function value

Author(s)

Morteza Amini, morteza.amini@ut.ac.ir

References

Kim, C. J., Piger, J. and Startz, R. (2008). Estimation of Markov regime-switching regression models with endogenous switching. Journal of Econometrics, 143(2), 263-273.

Examples

J <- 3
initial <- c(1, 0, 0)
semi <- rep(FALSE, 3)
P <- matrix(c(0.5, 0.2, 0.3, 0.2, 0.5, 0.3, 0.1, 0.4, 0.5), 
nrow = J, byrow = TRUE)
par <- list(intercept = list(3, list(-10, -1), 14),
coefficient = list(-1, list(1, 5), -7),
csigma = list(1.2, list(2.3, 3.4), 1.1),
mix.p = list(1, c(0.4, 0.6), 1))
model <- hhsmmspec(init = initial, transition = P, parms.emis = par,
dens.emis = dmixlm, semi = semi)
train <- simulate(model, nsim = c(20, 30, 42, 50), seed = 1234, 
remission = rmixlm, covar = list(mean = 0, cov = 1))
clus = initial_cluster(train = train, nstate = 3, nmix = c(1, 2, 1), 
ltr = FALSE, final.absorb = FALSE, verbose = TRUE, regress = TRUE)
initmodel = initialize_model(clus = clus, mstep = mixlm_mstep,
dens.emission = dmixlm, sojourn = NULL, semi = rep(FALSE, 3), 
M = max(train$N),verbose = TRUE)
fit1 = hhsmmfit(x = train, model = initmodel, mstep = mixlm_mstep,
M = max(train$N))
plot(train$x[,1] ~ train$x[, 2], col = train$s, pch = 16, 
xlab = "x", ylab = "y")
abline(fit1$model$parms.emission$intercept[[1]],
fit1$model$parms.emission$coefficient[[1]], col = 1)
abline(fit1$model$parms.emission$intercept[[2]][[1]],
fit1$model$parms.emission$coefficient[[2]][[1]], col = 2)
abline(fit1$model$parms.emission$intercept[[2]][[2]],
fit1$model$parms.emission$coefficient[[2]][[2]], col = 2)
abline(fit1$model$parms.emission$intercept[[3]],
fit1$model$parms.emission$coefficient[[3]], col = 3)

pdf of the mixture of multivariate normals for hhsmm

Description

The probability density function of a mixture multivariate normal for a specified observation vector, a specified state and a specified model's parameters

Usage

dmixmvnorm(x, j, model)

Arguments

x

an observation vector or matrix

j

a specified state between 1 to nstate

model

a hhsmmspec model

Value

the probability density function value

Author(s)

Morteza Amini, morteza.amini@ut.ac.ir, Afarin Bayat, aftbayat@gmail.com

Examples

J <- 3
initial <- c(1, 0, 0)
semi <- c(FALSE, TRUE, FALSE)
P <- matrix(c(0.8, 0.1, 0.1, 0.5, 0, 0.5, 0.1, 0.2, 0.7), 
nrow = J, byrow = TRUE)
par <- list(mu = list(list(7, 8),list(10, 9, 11), list(12, 14)),
sigma = list(list(3.8, 4.9), list(4.3, 4.2, 5.4), list(4.5, 6.1)),
mix.p = list(c(0.3, 0.7), c(0.2, 0.3, 0.5), c(0.5, 0.5)))
sojourn <- list(shape = c(0, 3, 0), scale = c(0, 10, 0), type = "gamma")
model <- hhsmmspec(init = initial, transition = P, parms.emis = par,
dens.emis = dmixmvnorm, sojourn = sojourn, semi = semi)
train <- simulate(model, nsim = c(10, 8, 8, 18), seed = 1234, 
remission = rmixmvnorm)
p = dmixmvnorm(train$x, 1, model)

pdf of the multinomial emission distribution for hhsmm

Description

The probability density function of a multinomial emission distribution for a specified observation vector, a specified state and a specified model's parameters

Usage

dmultinomial.hhsmm(x, j, model, n)

Arguments

x

the observation vector

j

a specified state between 1 to nstate

model

a hhsmmspec model

n

the maximum possible level of the multinomial vector (i.e. from 1 to n)

Value

the probability density function value

Author(s)

Morteza Amini, morteza.amini@ut.ac.ir

Examples

J <- 2
initial <- c(1, 0)
semi <- rep(TRUE, 2)
P <- matrix(c(0, 1, 1, 0), 
nrow = J, byrow = TRUE)
par <- list(prob = list(c(0.6,  0.2, 0.2),
                           c(0.2, 0.6,  0.2)))
sojourn <- list(shape = c(1, 3), scale = c(2, 10), type = "gamma")
model <- hhsmmspec(init = initial, transition = P, parms.emis = par,
dens.emis = dmultinomial.hhsmm, remission = rmultinomial.hhsmm,
 mstep = mstep.multinomial,sojourn = sojourn, semi = semi)
train <- simulate(model, nsim = c(20, 30, 42, 50), seed = 1234, 
remission = rmultinomial.hhsmm)
clus = initial_cluster(train = train, nstate = 2, nmix = NULL,
ltr = FALSE, final.absorb = FALSE, verbose = TRUE)
initmodel = initialize_model(clus = clus, mstep = mstep.multinomial, n = 3,
dens.emission = dmultinomial.hhsmm, sojourn = "gamma", semi = rep(TRUE, 2), 
M = max(train$N),verbose = TRUE)
fit1 = hhsmmfit(x = train, model = initmodel, mstep = mstep.multinomial, n = 3, 
M = max(train$N))
homogeneity(fit1$yhat,train$s)

pdf of the mixture of B-splines for hhsmm

Description

The probability density function of a mixture of B-splines for a specified observation vector, a specified state and a specified model's parameters

Usage

dnonpar(x, j, model, control = list(K = 5))

Arguments

x

an observation vector or matrix

j

a specified state between 1 to nstate

model

a hhsmmspec model

control

the parameters to control the density function. The simillar name is chosen with that of nonpar_mstep, to be used in ... argument of the hhsmmfit function. Here, it contains only the parameter K which is the degrees of freedom for the B-spline, default is K=5

Value

the probability density function value

Author(s)

Morteza Amini, morteza.amini@ut.ac.ir, Reza Salehian, reza.salehian@ut.ac.ir

Examples

J <- 3
initial <- c(1, 0, 0)
semi <- c(FALSE, TRUE, FALSE)
P <- matrix(c(0.8, 0.1, 0.1, 0.5, 0, 0.5, 0.1, 0.2, 0.7), 
nrow = J, byrow = TRUE)
par <- list(mu = list(list(7, 8), list(10, 9, 11), list(12, 14)),
sigma = list(list(3.8, 4.9), list(4.3, 4.2, 5.4), list(4.5, 6.1)),
mix.p = list(c(0.3, 0.7), c(0.2, 0.3, 0.5), c(0.5, 0.5)))
sojourn <- list(shape = c(0, 3, 0), scale = c(0, 10, 0), type = "gamma")
model <- hhsmmspec(init = initial, transition = P, parms.emis = par,
dens.emis = dmixmvnorm, sojourn = sojourn, semi = semi)
train <- simulate(model, nsim = c(10, 8, 8, 18), seed = 1234, 
remission = rmixmvnorm)
clus = initial_cluster(train, nstate = 3, nmix = NULL, ltr = FALSE,
final.absorb = FALSE, verbose = TRUE)
semi <- c(FALSE, TRUE, FALSE)
initmodel = initialize_model(clus = clus, mstep = nonpar_mstep,
	sojourn = "gamma", M = max(train$N), semi = semi)
p = dnonpar(train$x, 1, initmodel)

pdf of the Gaussian additive (Markov-switching) model for hhsmm

Description

The probability density function of a Gaussian additive (Markov-switching) model for a specified observation vector, a specified state and a specified model's parameters

Usage

dnorm_additive_reg(x, j, model, control = list(K = 5, resp.ind = 1))

Arguments

x

the observation matrix including responses and covariates

j

a specified state between 1 to nstate

model

a hhsmmspec model

control

the parameters to control the density function. The simillar name is chosen with that of additive_reg_mstep, to be used in ... argument of the hhsmmfit function. Here, it contains the following items:

  • K the degrees of freedom for the B-spline, default is K=5

  • resp.ind a vector of the column numbers of x which contain response variables. The default is 1, which means that the first column of x is the univariate response variable

Value

the probability density function value

Author(s)

Morteza Amini, morteza.amini@ut.ac.ir, Reza Salehian, reza.salehian@ut.ac.ir

References

Langrock, R., Adam, T., Leos-Barajas, V., Mews, S., Miller, D. L., and Papastamatiou, Y. P. (2018). Spline-based nonparametric inference in general state-switching models. Statistica Neerlandica, 72(3), 179-200.

Examples

J <- 3
initial <- c(1, 0, 0)
semi <- rep(FALSE, 3)
P <- matrix(c(0.5, 0.2, 0.3, 0.2, 0.5, 0.3, 0.1, 0.4, 0.5), nrow = J, 
byrow = TRUE)
par <- list(intercept = list(3, list(-10, -1), 14),
coefficient = list(-1, list(1, 5), -7),
csigma = list(1.2, list(2.3, 3.4), 1.1),
mix.p = list(1, c(0.4, 0.6), 1))
model <- hhsmmspec(init = initial, transition = P, parms.emis = par,
dens.emis = dmixlm, semi = semi)
train <- simulate(model, nsim = c(20, 30, 42, 50), seed = 1234, 
remission = rmixlm, covar = list(mean = 0, cov = 1))
clus = initial_cluster(train = train, nstate = 3, nmix = NULL,
ltr = FALSE, final.absorb = FALSE, verbose = TRUE, regress = TRUE)
initmodel = initialize_model(clus = clus ,mstep = additive_reg_mstep,
dens.emission = dnorm_additive_reg, sojourn = NULL, semi = rep(FALSE, 3),
M = max(train$N),verbose = TRUE)
fit1 = hhsmmfit(x = train, model = initmodel, mstep = additive_reg_mstep,
M = max(train$N))
plot(train$x[, 1] ~ train$x[, 2], col = train$s, pch = fit1$yhat, 
xlab = "x", ylab = "y")
text(0,30, "colors are real states",col="red")
text(0,28, "characters are predicted states")
pred <- addreg_hhsmm_predict(fit1, train$x[, 2], 5)
yhat1 <- pred[[1]]
yhat2 <- pred[[2]]
yhat3 <- pred[[3]]

lines(yhat1[order(train$x[, 2])]~sort(train$x[, 2]),col = 2)
lines(yhat2[order(train$x[, 2])]~sort(train$x[, 2]),col = 1)
lines(yhat3[order(train$x[, 2])]~sort(train$x[, 2]),col = 3)

pdf of the mixture of the robust emission proposed by Qin et al. (2024)

Description

The probability density function of the robust emission proposed by Qin et al. (2024) for a specified observation vector, a specified state and a specified model's parameters

Usage

drobust(x, j, model, control = list(k = 1.345))

Arguments

x

an observation vector or matrix

j

a specified state between 1 to nstate

model

a hhsmmspec model

control

a list containing the control parameter k with the default value equal to 1.345

Value

the probability density function value

Author(s)

Morteza Amini, morteza.amini@ut.ac.ir

References

Qin, S., Tan, Z., and Wu, Y. (2024). On robust estimation of hidden semi-Markov regime-switching models. Annals of Operations Research, 1-33.

Examples

J <- 3
initial <- c(1, 0, 0)
semi <- c(FALSE, TRUE, FALSE)
P <- matrix(c(0.8, 0.1, 0.1, 0.5, 0, 0.5, 0.1, 0.2, 0.7), 
nrow = J, byrow = TRUE)
par <- list(mu = list(list(7, 8),list(10, 9, 11), list(12, 14)),
sigma = list(list(3.8, 4.9), list(4.3, 4.2, 5.4), list(4.5, 6.1)),
mix.p = list(c(0.3, 0.7), c(0.2, 0.3, 0.5), c(0.5, 0.5)))
sojourn <- list(shape = c(0, 3, 0), scale = c(0, 10, 0), type = "gamma")
model <- hhsmmspec(init = initial, transition = P, parms.emis = par,
dens.emis = dmixmvnorm, sojourn = sojourn, semi = semi)
train <- simulate(model, nsim = c(10, 8, 8, 18), seed = 1234, 
remission = rmixmvnorm)
mu = list(0,1)
sigma = list(1,2)
robustmodel = list(parms.emission = list(mu = mu,sigma = sigma))
p = drobust(train$x, 1, robustmodel)

convert to hhsmm data

Description

Converts a matrix of data and its associated vector of sequence lengths to a data list of class "hhsmmdata"

Usage

hhsmmdata(x, N = NULL)

Arguments

x

a matrix of data

N

a vector of sequence lengths. If NULL then N = nrow(x)

Value

a data list of class "hhsmmdata" containing x and N

Author(s)

Morteza Amini, morteza.amini@ut.ac.ir

Examples

x = sapply(c(1, 2), function(i) rnorm(100, i, i/2))
N = c(10, 15, 50, 25)
data = hhsmmdata(x, N)

hhsmm model fit

Description

Fits a hidden hybrid Markov-semi-Markov model to a data of class "hhsmmdata" and using an initial model created by hhsmmspec or initialize_model

Usage

hhsmmfit(
  x,
  model,
  mstep = NULL,
  ...,
  M = NA,
  par = list(maxit = 100, lock.transition = FALSE, lock.d = FALSE, lock.init = FALSE,
    graphical = FALSE, verbose = TRUE)
)

Arguments

x

a data of class "hhsmmdata", which can also contain missing values (NA or NaN)

model

an initial model created by hhsmm.spec or initialize_model

mstep

the M step function for the EM algorithm, which also can be given in the model

...

additional parameters for the dens.emission and mstep functions

M

the maximum duration in each state

par

additional list of control parameters of the hhsmmfit function including the following items:

  • maxit the maximum number of iterations for the EM algorithm

  • lock.transition logical. if TRUE the transition matrix will not be updated through the EM algorithm

  • lock.d logical. if TRUE the sojourn probability matrix d will not be updated through the EM algorithm

  • lock.init logical. if TRUE the initial probability vector will not be updated through the EM algorithm

  • graphical logical. if TRUE a plot of the sojourn probabilities will be plotted through the EM algorithm

  • verbose logical. if TRUE the outputs will be printed

Value

a list of class "hhsmm" containing the following items:

Author(s)

Morteza Amini, morteza.amini@ut.ac.ir, Afarin Bayat, aftbayat@gmail.com

References

Guedon, Y. (2005). Hidden hybrid Markov/semi-Markov chains. Computational statistics and Data analysis, 49(3), 663-688.

OConnell, J., & Hojsgaard, S. (2011). Hidden semi Markov models for multiple observation sequences: The mhsmm package for R. Journal of Statistical Software, 39(4), 1-22.

Examples

J <- 3
initial <- c(1, 0, 0)
semi <- c(FALSE, TRUE, FALSE)
P <- matrix(c(0.8, 0.1, 0.1, 0.5, 0, 0.5, 0.1, 0.2, 0.7), nrow = J, 
byrow = TRUE)
par <- list(mu = list(list(7, 8), list(10, 9, 11), list(12, 14)),
sigma = list(list(3.8, 4.9), list(4.3, 4.2, 5.4), list(4.5, 6.1)),
mix.p = list(c(0.3, 0.7), c(0.2, 0.3, 0.5), c(0.5, 0.5)))
sojourn <- list(shape = c(0, 3, 0), scale = c(0, 10, 0), type = "gamma")
model <- hhsmmspec(init = initial, transition = P, parms.emis = par,
dens.emis = dmixmvnorm, sojourn = sojourn, semi = semi)
train <- simulate(model, nsim = c(10, 8, 8, 18), seed = 1234, 
remission = rmixmvnorm)
clus = initial_cluster(train, nstate = 3, nmix = c(2 ,2, 2),ltr = FALSE,
final.absorb = FALSE, verbose = TRUE)
initmodel1 = initialize_model(clus = clus, sojourn = "gamma", 
M = max(train$N), semi = semi)
fit1 = hhsmmfit(x = train, model = initmodel1, M = max(train$N))

hhsmm specification

Description

Specify a model of class "hhsmmspec" using the model parameters

Usage

hhsmmspec(
  init,
  transition,
  parms.emission,
  sojourn = NULL,
  dens.emission,
  remission = NULL,
  mstep = NULL,
  semi = NULL
)

Arguments

init

vector of initial probabilities

transition

the transition matrix

parms.emission

the parameters of the emission distribution

sojourn

the sojourn distribution, which is one of the following cases:

  • a list containing d, which is a nobs (number of observations) times nstates (number of states) matrix of probabilities, and type = "nonparametric" for non-parametric sojourn distribution

  • a list containing the parameters mu, shift and size of a shifted negative binomial distribution, for each semi-Markovian state, and type = "nbinom" for negative binomial sojourn distribution

  • a list containing the parameters shape and shift of a shifted logarithmic distribution, for each semi-Markovian state, and type = "logarithmic" for logarithmic sojourn distribution

  • a list containing the parameters lambda and shift of the shifted poisson distribution, for each semi-Markovian state, and type = "poisson" for Poisson sojourn distribution

  • a list containing the parameters shape and scale of the gamma distribution, for each semi-Markovian state, and type = "gamma" for gamma sojourn distribution

  • a list containing the parameters shape and scale of the Weibull distribution, for each semi-Markovian state, and type = "weibull" for Weibull sojourn distribution

  • a list containing the parameters meanlog and sdlog of the log-normal distribution, for each semi-Markovian state, and type = "lnorm" for log-normal sojourn distribution

dens.emission

the probability density function of the emission

remission

the random sample generation from the emission distribution

mstep

the M step function for the EM algorithm

semi

a logical vector of length nstate: the TRUE associated states are considered as semi-markov

Value

a model of class "hhsmmspec"

Author(s)

Morteza Amini, morteza.amini@ut.ac.ir, Afarin Bayat, aftbayat@gmail.com

Examples

init = c(1, 0)
transition = matrix(c(0, 1, 1, 0), 2, 2)
parms.emission = list(mix.p = list(c(0.5, 0.5), 1),
				mu = list(list(c(1, 2), c(5, 1)), c(2, 7)),
              sigma = list(list(diag(2), 2 * diag(2)), 0.5 * diag(2)))
sojourn = list(lambda = 1, shift = 5, type = "poisson")
dens.emission = dmixmvnorm
remission = rmixmvnorm
mstep = mixmvnorm_mstep
semi = rep(TRUE,2)
model = hhsmmspec(init, transition, parms.emission, sojourn, 
dens.emission, remission, mstep, semi)

Computing maximum homogeneity of two state sequences

Description

A function to compute the maximum homogeneity of two state sequences.

Usage

homogeneity(state.seq1, state.seq2)

Arguments

state.seq1

first state sequence

state.seq2

second state sequence

Value

a vector of a length equal to the maximum number of states giving the maximum homogeneity ratios

Author(s)

Morteza Amini, morteza.amini@ut.ac.ir

Examples

state.seq1 = c(3, 3, 3, 1, 1, 2, 2, 2, 2)
state.seq2 = c(2, 2, 2, 3, 3, 1, 1, 1, 1)
homogeneity(state.seq1, state.seq2)

initial clustering of the data set

Description

Provides an initial clustering for a data of class "hhsmmdata" which determines the initial states and mixture components (if necessary) to be used for initial parameter and model estimation

Usage

initial_cluster(
  train,
  nstate,
  nmix,
  ltr = FALSE,
  equispace = FALSE,
  final.absorb = FALSE,
  verbose = FALSE,
  regress = FALSE,
  resp.ind = 1
)

Arguments

train

the train data set of class "hhsmmdata", which can also contain missing data (NA or NaN)

nstate

number of states

nmix

number of mixture components which is of one of the following forms:

  • a vector of positive (non-zero) integers of length nstate

  • a positive (non-zero) integer

  • the text "auto": the number of mixture components will be determined automatically based on the within cluster sum of squares

  • NULL if no mixture distribution is not considered as the emission. This option is usefull for the nonparametric emission distribution (nonpar_mstep and dnonpar)

ltr

logical. if TRUE a left to right hidden hybrid Markov/semi-Markov model is assumed

equispace

logical. if TRUE the left to right clustering will be performed simply with equal time spaces. This option is suitable for speech recognition applications

final.absorb

logical. if TRUE the final state of the sequence is assumed to be the absorbance state

verbose

logical. if TRUE the outputs will be printed

regress

logical. if TRUE the linear regression clustering will be performed

resp.ind

the column indices of the response variables for the linear regression clustering approach. The default is 1, which means that the first column is the univariate response variable

Details

In reliability applications, the hhsmm models are often left-to-right and the modeling aims to predict the future states. In such cases, the ltr=TRUE and final.absorb=TRUE should be set.

Value

a list containing the following items:

Author(s)

Morteza Amini, morteza.amini@ut.ac.ir, Afarin Bayat, aftbayat@gmail.com

Examples

J <- 3
initial <- c(1, 0, 0)
semi <- c(FALSE, TRUE, FALSE)
P <- matrix(c(0.8, 0.1, 0.1, 0.5, 0, 0.5, 0.1, 0.2, 0.7), nrow = J, 
byrow = TRUE)
par <- list(mu = list(list(7, 8), list(10, 9, 11), list(12, 14)),
sigma = list(list(3.8, 4.9), list(4.3, 4.2, 5.4), list(4.5, 6.1)),
mix.p = list(c(0.3, 0.7), c(0.2, 0.3, 0.5), c(0.5, 0.5)))
sojourn <- list(shape = c(0, 3, 0), scale = c(0, 10, 0), type = "gamma")
model <- hhsmmspec(init = initial, transition = P, parms.emis = par,
dens.emis = dmixmvnorm, sojourn = sojourn, semi = semi)
train <- simulate(model, nsim = c(10, 8, 8, 18), seed = 1234, 
remission = rmixmvnorm)
clus = initial_cluster(train, nstate = 3, nmix = c(2 ,2, 2),ltr = FALSE,
final.absorb = FALSE, verbose = TRUE)

initial estimation of the model parameters for a specified emission distribution

Description

Provides the initial estimates of the model parameters of a specified emission distribution characterized by the mstep function, for an initial clustering obtained by initial_cluster

Usage

initial_estimate(clus, mstep = mixmvnorm_mstep, verbose = FALSE, ...)

Arguments

clus

an initial clustering obtained by initial_cluster

mstep

the mstep function of the EM algorithm with an style simillar to that of mixmvnorm_mstep

verbose

logical. if TRUE the outputs will be printed

...

additional parameters of the mstep function

Value

a list containing the following items:

Author(s)

Morteza Amini, morteza.amini@ut.ac.ir, Afarin Bayat, aftbayat@gmail.com

Examples

J <- 3
initial <- c(1, 0, 0)
semi <- c(FALSE, TRUE, FALSE)
P <- matrix(c(0.8, 0.1, 0.1, 0.5, 0, 0.5, 0.1, 0.2, 0.7), nrow = J, 
byrow = TRUE)
par <- list(mu = list(list(7, 8), list(10, 9, 11), list(12, 14)),
sigma = list(list(3.8, 4.9), list(4.3, 4.2, 5.4), list(4.5, 6.1)),
mix.p = list(c(0.3, 0.7), c(0.2, 0.3, 0.5), c(0.5, 0.5)))
sojourn <- list(shape = c(0, 3, 0), scale = c(0, 10, 0), type = "gamma")
model <- hhsmmspec(init = initial, transition = P, parms.emis = par,
dens.emis = dmixmvnorm, sojourn = sojourn, semi = semi)
train <- simulate(model, nsim = c(10, 8, 8, 18), seed = 1234, 
remission = rmixmvnorm)
clus = initial_cluster(train, nstate = 3, nmix = c(2 ,2, 2),ltr = FALSE,
final.absorb = FALSE, verbose = TRUE)
par = initial_estimate(clus, verbose = TRUE)

initialize the hhsmmspec model for a specified emission distribution

Description

Initialize the hhsmmspec model by using an initial clustering obtained by initial_cluster and the emission distribution characterized by mstep and dens.emission

Usage

initialize_model(
  clus,
  mstep = NULL,
  dens.emission = dmixmvnorm,
  sojourn = NULL,
  semi = NULL,
  M,
  verbose = FALSE,
  ...
)

Arguments

clus

initial clustering obtained by initial_cluster

mstep

the mstep function of the EM algorithm with an style simillar to that of mixmvnorm_mstep. If NULL, the mixmvnorm_mstep is considered for the complete data set and miss_mixmvnorm_mstep is considered for the data with missing values (NA or NaN)

dens.emission

the density of the emission distribution with an style simillar to that of dmixmvnorm

sojourn

one of the following cases:

  • "nonparametric" non-parametric sojourn distribution

  • "nbinom" negative binomial sojourn distribution

  • "logarithmic" logarithmic sojourn distribution

  • "poisson" poisson sojourn distribution

  • "gamma" gamma sojourn distribution

  • "weibull" weibull sojourn distribution

  • "lnorm" log-normal sojourn distribution

  • "auto" automatic determination of the sojourn distribution using the chi-square test

semi

logical and of one of the following forms:

  • a logical value: if TRUE all states are considered as semi-Markovian else Markovian

  • a logical vector of length nstate: the TRUE associated states are considered as semi-Markovian and FALSE associated states are considered as Markovian

  • NULL if ltr=TRUE then semi = c(rep(TRUE,nstate-1),FALSE), else semi = rep(TRUE,nstate)

M

maximum number of waiting times in each state

verbose

logical. if TRUE the outputs will be printed the normal distributions will be estimated

...

additional parameters of the mstep function

Value

a hhsmmspec model containing the following items:

Author(s)

Morteza Amini, morteza.amini@ut.ac.ir, Afarin Bayat, aftbayat@gmail.com

Examples

J <- 3
initial <- c(1, 0, 0)
semi <- c(FALSE, TRUE, FALSE)
P <- matrix(c(0.8, 0.1, 0.1, 0.5, 0, 0.5, 0.1, 0.2, 0.7), nrow = J, 
byrow = TRUE)
par <- list(mu = list(list(7, 8), list(10, 9, 11), list(12, 14)),
sigma = list(list(3.8, 4.9), list(4.3, 4.2, 5.4), list(4.5, 6.1)),
mix.p = list(c(0.3, 0.7), c(0.2, 0.3, 0.5), c(0.5, 0.5)))
sojourn <- list(shape = c(0, 3, 0), scale = c(0, 10, 0), type = "gamma")
model <- hhsmmspec(init = initial, transition = P, parms.emis = par,
dens.emis = dmixmvnorm, sojourn = sojourn, semi = semi)
train <- simulate(model, nsim = c(10, 8, 8, 18), seed = 1234, 
remission = rmixmvnorm)
clus = initial_cluster(train, nstate = 3, nmix = c(2 ,2, 2),ltr = FALSE,
final.absorb = FALSE, verbose = TRUE)
initmodel = initialize_model(clus = clus, sojourn = "gamma", 
M = max(train$N))

Create hhsmm data of lagged time series

Description

Creates a data of class hhsmmdata containing lagged time series which can be used for fitting auto-regressive hidden hybrid Makrov/semi-Markov model (AR-HHSMM)

Usage

lagdata(data, lags = 1)

Arguments

data

a data of class hhsmmdata containing a multivariate and multi-state time series

lags

a positive integer which is the number of lags to be calculated

Value

a data of class hhsmmdata containing lagged time series

Author(s)

Morteza Amini, morteza.amini@ut.ac.ir

Examples

J <- 3
initial <- c(1, 0, 0)
semi <- rep(FALSE, 3)
P <- matrix(c(0.5, 0.2, 0.3, 0.2, 0.5, 0.3, 0.1, 0.4, 0.5), nrow = J, 
byrow = TRUE)
par <- list(intercept = list(0.1, -0.1, 0.2),
coefficient = list(-0.6, 0.7, -0.5),
csigma = list(5.5, 4, 3.5), mix.p = list(1, 1, 1))
model <- hhsmmspec(init = initial, transition = P, parms.emis = par,
dens.emis = dmixlm, semi = semi)
train <- simulate(model, nsim = c(50, 60, 84, 100), seed = 1234, 
emission.control = list(autoregress = TRUE))
laggedtrain = lagdata(train)

left to right clustering

Description

A left to right initial clustering method using the mean differences and Hotelling's T-squared test

Usage

ltr_clus(Dat, k)

Arguments

Dat

a data matrix

k

number of clusters

Value

a (left to right) clustering vector

Author(s)

Morteza Amini, morteza.amini@ut.ac.ir, Afarin Bayat, aftbayat@gmail.com

Examples

data(CMAPSS)
clus = ltr_clus(CMAPSS$train$x[1:CMAPSS$train$N[1], ], 3)

left to right linear regression clustering

Description

A left to right initial linear regression clustering method using the coefficient differences and Hotelling's T-squared test

Usage

ltr_reg_clus(Dat, k, resp.ind = 1)

Arguments

Dat

a data matrix

k

number of clusters

resp.ind

the column indices of the response variables for the linear regression clustering approach. The default is 1, which means that the first column is the univariate response variable

Value

a (left to right) clustering vector

Author(s)

Morteza Amini, morteza.amini@ut.ac.ir

make a hhsmmspec model for a specified emission distribution

Description

Provides a hhsmmspec model by using the parameters obtained by initial_estimate for the emission distribution characterized by mstep and dens.emission

Usage

make_model(
  par,
  mstep = mixmvnorm_mstep,
  dens.emission = dmixmvnorm,
  semi = NULL,
  M,
  sojourn
)

Arguments

par

the parameters obtained by initial_estimate

mstep

the mstep function of the EM algorithm with an style simillar to that of mixmvnorm_mstep

dens.emission

the density of the emission distribution with an style simillar to that of dmixmvnorm

semi

logical and of one of the following forms:

  • a logical value: if TRUE all states are considered as semi-Markovian else Markovian

  • a logical vector of length nstate: the TRUE associated states are considered as semi-Markovian and FALSE associated states are considered as Markovian

  • NULL if ltr=TRUE then semi = c(rep(TRUE,nstate-1),FALSE), else semi = rep(TRUE,nstate)

M

maximum number of waiting times in each state

sojourn

the sojourn time distribution which is one of the following cases:

  • "nonparametric" non-parametric sojourn distribution

  • "nbinom" negative binomial sojourn distribution

  • "logarithmic" logarithmic sojourn distribution

  • "poisson" poisson sojourn distribution

  • "gamma" gamma sojourn distribution

  • "weibull" weibull sojourn distribution

  • "lnorm" log-normal sojourn distribution

  • "auto" automatic determination of the sojourn distribution using the chi-square test

Value

a hhsmmspec model containing the following items:

Author(s)

Morteza Amini, morteza.amini@ut.ac.ir, Afarin Bayat, aftbayat@gmail.com

Examples

J <- 3
initial <- c(1, 0, 0)
semi <- c(FALSE, TRUE, FALSE)
P <- matrix(c(0.8, 0.1, 0.1, 0.5, 0, 0.5, 0.1, 0.2, 0.7), nrow = J, 
byrow = TRUE)
par <- list(mu = list(list(7, 8), list(10, 9, 11), list(12, 14)),
sigma = list(list(3.8, 4.9), list(4.3, 4.2, 5.4), list(4.5, 6.1)),
mix.p = list(c(0.3, 0.7), c(0.2, 0.3, 0.5), c(0.5, 0.5)))
sojourn <- list(shape = c(0, 3, 0), scale = c(0, 10, 0), type = "gamma")
model <- hhsmmspec(init = initial, transition = P, parms.emis = par,
dens.emis = dmixmvnorm, sojourn = sojourn, semi = semi)
train <- simulate(model, nsim = c(10, 8, 8, 18), seed = 1234, remission = rmixmvnorm)
clus = initial_cluster(train, nstate = 3, nmix = c(2, 2, 2), ltr = FALSE,
final.absorb = FALSE, verbose = TRUE)
par = initial_estimate(clus, verbose = TRUE)
model = make_model(par, semi = NULL, M = max(train$N), sojourn = "gamma")

the M step function of the EM algorithm

Description

The M step function of the EM algorithm for the mixture of multivariate normals as the emission distribution with missing values using the observation matrix and the estimated weight vectors

Usage

miss_mixmvnorm_mstep(x, wt1, wt2, par)

Arguments

x

the observation matrix which can contain missing values (NA or NaN)

wt1

the state probabilities matrix (number of observations times number of states)

wt2

the mixture components probabilities list (of length nstate) of matrices (number of observations times number of mixture components)

par

the parameters of the model in the previous step of the EM algorithm. For initialization of the model when the data is initially imputed, par can be NULL

Value

list of emission (mixture multivariate normal) parameters: (mu, sigma and mix.p)

Author(s)

Morteza Amini, morteza.amini@ut.ac.ir

Examples

data(CMAPSS)
n = nrow(CMAPSS$train$x)
wt1 = matrix(runif(3*n),nrow=n,ncol=3)
wt2 = list()
for(j in 1:3) wt2[[j]] = matrix(runif(5*n),nrow=n,ncol=5)
emission = miss_mixmvnorm_mstep(CMAPSS$train$x, wt1, wt2, par=NULL)

the M step function of the EM algorithm

Description

The M step function of the EM algorithm for the mixture of multivariate normals with diagonal covariance matrix as the emission distribution using the observation matrix and the estimated weight vectors

Usage

mixdiagmvnorm_mstep(x, wt1, wt2)

Arguments

x

the observation matrix

wt1

the state probabilities matrix (number of observations times number of states)

wt2

the mixture components probabilities list (of length nstate) of matrices (number of observations times number of mixture components)

Value

list of emission (mixture multivariate normal) parameters: (mu, sigma and mix.p), where sigma is a diagonal matrix

Author(s)

Morteza Amini, morteza.amini@ut.ac.ir

Examples

data(CMAPSS)
n = nrow(CMAPSS$train$x)
wt1 <- matrix(runif(3 * n), nrow = n, ncol = 3)
wt2 <- list()
for(j in 1:3) wt2[[j]] <- matrix(runif(5 * n), nrow = n, ncol = 5)
emission <- mixdiagmvnorm_mstep(CMAPSS$train$x, wt1, wt2)

the M step function of the EM algorithm

Description

The M step function of the EM algorithm for the mixture of Gaussian linear (Markov-switching) regressions as the emission distribution using the responses and covariates matrices and the estimated weight vectors

Usage

mixlm_mstep(x, wt1, wt2, resp.ind = 1)

Arguments

x

the observation matrix including responses and covariates

wt1

the state probabilities matrix (number of observations times number of states)

wt2

the mixture components probabilities list (of length nstate) of matrices (number of observations times number of mixture components)

resp.ind

a vector of the column numbers of x which contain response variables. The default is 1, which means that the first column of x is the univariate response variable

Value

list of emission (mixture of Gaussian linear regression models) parameters: (intercept, coefficients, csigma (conditional covariance) and mix.p)

Author(s)

Morteza Amini, morteza.amini@ut.ac.ir

References

Kim, C. J., Piger, J. and Startz, R. (2008). Estimation of Markov regime-switching regression models with endogenous switching. Journal of Econometrics, 143(2), 263-273.

Examples

J <- 3
initial <- c(1, 0, 0)
semi <- rep(FALSE, 3)
P <- matrix(c(0.5, 0.2, 0.3, 0.2, 0.5, 0.3, 0.1, 0.4, 0.5), nrow = J, 
byrow = TRUE)
par <- list(intercept = list(3, list(-10, -1), 14),
coefficient = list(-1, list(1, 5), -7),
csigma = list(1.2, list(2.3, 3.4), 1.1),
mix.p = list(1, c(0.4, 0.6), 1))
model <- hhsmmspec(init = initial, transition = P, parms.emis = par,
dens.emis = dmixlm, semi = semi)
train <- simulate(model, nsim = c(20, 30, 42, 50), seed = 1234, 
remission = rmixlm, covar = list(mean = 0, cov = 1))
clus = initial_cluster(train = train, nstate = 3, nmix = c(1, 2, 1),
ltr = FALSE, final.absorb = FALSE, verbose = TRUE, regress = TRUE)
initmodel = initialize_model(clus = clus ,mstep = mixlm_mstep,
dens.emission = dmixlm, sojourn = NULL, semi = rep(FALSE, 3),
M = max(train$N),verbose = TRUE)
fit1 = hhsmmfit(x = train, model = initmodel, mstep = mixlm_mstep,
M = max(train$N))
plot(train$x[, 1] ~ train$x[, 2], col = train$s, pch = 16, 
xlab = "x", ylab = "y")
abline(fit1$model$parms.emission$intercept[[1]],
fit1$model$parms.emission$coefficient[[1]], col = 1)
abline(fit1$model$parms.emission$intercept[[2]][[1]],
fit1$model$parms.emission$coefficient[[2]][[1]], col = 2)
abline(fit1$model$parms.emission$intercept[[2]][[2]],
fit1$model$parms.emission$coefficient[[2]][[2]], col = 2)
abline(fit1$model$parms.emission$intercept[[3]],
fit1$model$parms.emission$coefficient[[3]], col = 3)

the M step function of the EM algorithm

Description

The M step function of the EM algorithm for the mixture of multivariate normals as the emission distribution using the observation matrix and the estimated weight vectors

Usage

mixmvnorm_mstep(x, wt1, wt2)

Arguments

x

the observation matrix

wt1

the state probabilities matrix (number of observations times number of states)

wt2

the mixture components probabilities list (of length nstate) of matrices (number of observations times number of mixture components)

Value

list of emission (mixture multivariate normal) parameters: (mu, sigma and mix.p)

Author(s)

Morteza Amini, morteza.amini@ut.ac.ir, Afarin Bayat, aftbayat@gmail.com

Examples

data(CMAPSS)
n = nrow(CMAPSS$train$x)
wt1 = matrix(runif(3*n),nrow=n,ncol=3)
wt2 = list()
for(j in 1:3) wt2[[j]] = matrix(runif(5*n),nrow=n,ncol=5)
emission = mixmvnorm_mstep(CMAPSS$train$x, wt1, wt2)

the M step function of the EM algorithm

Description

The M step function of the EM algorithm for estimation of the parameters of the multinomial emission distribution

Usage

mstep.multinomial(x, wt, n)

Arguments

x

the observation matrix

wt

the state probabilities matrix (number of observations times number of states)

n

the maximum possible level of the multinomial vector (i.e. from 1 to n)

Value

list of multinomial emission parameters: (prob)

Author(s)

Morteza Amini, morteza.amini@ut.ac.ir,

Examples

J <- 2
initial <- c(1, 0)
semi <- rep(TRUE, 2)
P <- matrix(c(0, 1, 1, 0), 
nrow = J, byrow = TRUE)
par <- list(prob = list(c(0.6,  0.2, 0.2),
                           c(0.2, 0.6,  0.2)))
sojourn <- list(shape = c(1, 3), scale = c(2, 10), type = "gamma")
model <- hhsmmspec(init = initial, transition = P, parms.emis = par,
dens.emis = dmultinomial.hhsmm, remission = rmultinomial.hhsmm,
 mstep = mstep.multinomial,sojourn = sojourn, semi = semi)
train <- simulate(model, nsim = c(20, 30, 42, 50), seed = 1234, 
remission = rmultinomial.hhsmm)
clus = initial_cluster(train = train, nstate = 2, nmix = NULL,
ltr = FALSE, final.absorb = FALSE, verbose = TRUE)
initmodel = initialize_model(clus = clus, mstep = mstep.multinomial, n = 3,
dens.emission = dmultinomial.hhsmm, sojourn = "gamma", semi = rep(TRUE, 2), 
M = max(train$N),verbose = TRUE)
fit1 = hhsmmfit(x = train, model = initmodel, mstep = mstep.multinomial, n = 3, 
M = max(train$N))
homogeneity(fit1$yhat,train$s)

the M step function of the EM algorithm

Description

The M step function of the EM algorithm for the mixture of splines nonparametric density estimator

Usage

nonpar_mstep(x, wt, control = list(K = 5, lambda0 = 0.5))

Arguments

x

the observation matrix

wt

the state probabilities matrix (number of observations times number of states)

control

the parameters to control the M-step function. The simillar name is chosen with that of dnonpar, to be used in ... argument of the hhsmmfit function. Here, it contains the following items:

  • K the degrees of freedom for the B-spline, default is K=5

  • lambda0 the initial value of the smoothing parameter, default is lambda0=0.5

Value

list of emission (nonparametric mixture of splines) parameters: (coef)

Author(s)

Morteza Amini, morteza.amini@ut.ac.ir, Reza Salehian, reza.salehian@ut.ac.ir

References

Langrock, R., Kneib, T., Sohn, A., & DeRuiter, S. L. (2015). Nonparametric inference in hidden Markov models using P-splines. Biometrics, 71(2), 520-528.

Examples

x <- rmvnorm(100, rep(0, 2), matrix(c(4, 2, 2, 3), 2, 2))
wt <- matrix(rep(1, 100), 100, 1)
emission = nonpar_mstep(x, wt)
coef <- emission$coef[[1]]
x_axis <- seq(min(x[, 1]), max(x[, 1]), length.out = 100)
y_axis <- seq(min(x[, 2]), max(x[, 2]), length.out = 100)
f1 <- function(x, y) { 
  data = matrix(c(x, y), ncol = 2)
  tmpmodel = list(parms.emission = emission)
	 dnonpar(data, 1, tmpmodel)
}
z1 <- outer(x_axis, y_axis, f1)
f2 <- function(x, y) { 
  data = matrix(c(x, y), ncol = 2)
  dmvnorm(data, rep(0, 2), matrix(c(4, 2, 2, 3), 2, 2))
}
z2 <- outer(x_axis, y_axis, f2)
par(mfrow = c(1, 2))
persp(x_axis, y_axis, z1, theta = -60, phi = 45, col = rainbow(50))
persp(x_axis, y_axis, z2, theta = -60, phi = 45, col = rainbow(50))

prediction of state sequence for hhsmm

Description

Predicts the state sequence of a fitted hidden hybrid Markov/semi-Markov model estimated by hhsmmfit for a new (test) data of class "hhsmmdata" with an optional prediction of the residual useful lifetime (RUL) for a left to right model

Usage

## S3 method for class 'hhsmm'
predict(
  object,
  newdata,
  ...,
  future = 0,
  method = "viterbi",
  RUL.estimate = FALSE,
  confidence = "max",
  conf.level = 0.95
)

Arguments

object

a fitted model of class "hhsmm" estimated by hhsmmfit

newdata

a new (test) data of class "hhsmmdata", which also can contain missing values (NA or NaN)

...

additional parameters for the dens.emission and mstep functions

future

number of future states to be predicted

method

the prediction method with two options:

  • "viterbi" (default) uses the Viterbi algorithm for prediction

  • "smoothing" uses the smoothing algorithm for prediction

RUL.estimate

logical. if TRUE the residual useful lifetime (RUL) of a left to right model, as well as the prediction interval will also be predicted (default is FALSE)

confidence

the method for obtaining the prediction interval of the RUL, with two cases:

  • "max" (default) the maximum probability as the point predict and the high probability critical values as the lower and upper bounds

  • "mean" the mean value as the point predict and the normal confidence lower and upper bounds as the prediction interval

conf.level

the confidence level of the prediction interval (default 0.95)

Value

a list containing the following items:

Author(s)

Morteza Amini, morteza.amini@ut.ac.ir, Afarin Bayat, aftbayat@gmail.com

References

Guedon, Y. (2005). Hidden hybrid Markov/semi-Markov chains. Computational statistics and Data analysis, 49(3), 663-688.

OConnell, J., & Hojsgaard, S. (2011). Hidden semi Markov models for multiple observation sequences: The mhsmm package for R. Journal of Statistical Software, 39(4), 1-22.

See Also

predict.hhsmmspec

Examples

J <- 3
initial <- c(1, 0, 0)
semi <- c(FALSE, TRUE, FALSE)
P <- matrix(c(0.8, 0.1, 0.1, 0.5, 0, 0.5, 0.1, 0.2, 0.7), nrow = J, 
byrow = TRUE)
par <- list(mu = list(list(7, 8), list(10, 9, 11), list(12, 14)),
sigma = list(list(3.8, 4.9), list(4.3, 4.2, 5.4), list(4.5, 6.1)),
mix.p = list(c(0.3, 0.7), c(0.2, 0.3, 0.5), c(0.5, 0.5)))
sojourn <- list(shape = c(0, 3, 0), scale = c(0, 10, 0), type = "gamma")
model <- hhsmmspec(init = initial, transition = P, parms.emis = par,
dens.emis = dmixmvnorm, sojourn = sojourn, semi = semi)
train <- simulate(model, nsim = c(10, 8, 8, 18), seed = 1234, remission = rmixmvnorm)
test <-  simulate(model, nsim = c(7, 3, 3, 8), seed = 1234, remission = rmixmvnorm)
clus = initial_cluster(train, nstate = 3, nmix = c(2, 2, 2),ltr = FALSE,
final.absorb = FALSE, verbose = TRUE)
semi <- c(FALSE, TRUE, FALSE)
initmodel1 = initialize_model(clus = clus,sojourn = "gamma",
M = max(train$N), semi = semi)
fit1 = hhsmmfit(x = train, model = initmodel1, M = max(train$N))
yhat1 <- predict(fit1, test)

prediction of state sequence for hhsmm

Description

Predicts the state sequence of a hidden hybrid Markov/semi-Markov model for a new (test) data of class "hhsmmdata" with an optional prediction of the residual useful lifetime (RUL) for a left to right model

Usage

## S3 method for class 'hhsmmspec'
predict(object, newdata, ..., method = "viterbi", M = NA)

Arguments

object

a hidden hybrid Markov/semi-Markov model

newdata

a new (test) data of class "hhsmmdata"

...

additional parameters of the function predict.hhsmm

method

the prediction method with two options:

  • "viterbi" (default) uses the Viterbi algorithm for prediction

  • "smoothing" uses the smoothing algorithm for prediction

M

maximum duration in states

Value

a list containing the following items:

Author(s)

Morteza Amini, morteza.amini@ut.ac.ir, Afarin Bayat, aftbayat@gmail.com

References

Guedon, Y. (2005). Hidden hybrid Markov/semi-Markov chains. Computational statistics and Data analysis, 49(3), 663-688.

OConnell, J., & Hojsgaard, S. (2011). Hidden semi Markov models for multiple observation sequences: The mhsmm package for R. Journal of Statistical Software, 39(4), 1-22.

See Also

predict.hhsmm

Examples

J <- 3
initial <- c(1, 0, 0)
semi <- c(FALSE, TRUE, FALSE)
P <- matrix(c(0.8, 0.1, 0.1, 0.5, 0, 0.5, 0.1, 0.2, 0.7), nrow = J, 
byrow = TRUE)
par <- list(mu = list(list(7, 8), list(10, 9, 11), list(12, 14)),
sigma = list(list(3.8, 4.9), list(4.3, 4.2, 5.4), list(4.5, 6.1)),
mix.p = list(c(0.3, 0.7), c(0.2, 0.3, 0.5), c(0.5, 0.5)))
sojourn <- list(shape = c(0, 3, 0), scale = c(0, 10, 0), type = "gamma")
model <- hhsmmspec(init = initial, transition = P, parms.emis = par,
dens.emis = dmixmvnorm, sojourn = sojourn, semi = semi)
train <- simulate(model, nsim = c(10, 8, 8, 18), seed = 1234, remission = rmixmvnorm)
test <-  simulate(model, nsim = c(5, 3, 3, 8), seed = 1234, remission = rmixmvnorm)
clus = initial_cluster(train, nstate = 3, nmix = c(2, 2, 2), ltr = FALSE,
final.absorb = FALSE, verbose = TRUE)
semi <- c(FALSE, TRUE, FALSE)
initmodel1 = initialize_model(clus = clus, sojourn = "gamma", M = max(train$N), semi = semi)
yhat1 <- predict(initmodel1, test)

Random data generation from the Gaussian additive (Markov-switching) model for hhsmm model

Description

Generates vectors of covariate and response observations from the Gaussian additive (Markov-switching) model, using B-Splines in a specified state and using the parameters of a specified model

Usage

raddreg(j, model, covar, ...)

Arguments

j

a specified state

model

a hhsmmspec model

covar

either a function which generates the covariate vector or a list containing the following items:

  • mean the mean vector of covariates (to be generated from multivariate normal distribution)

  • cov the variance-covariance matrix of covariates (to be generated from multivariate normal distribution)

...

additional arguments of the covar function

Value

a random matrix of observations from Gaussian additive (Markov-switching) model, in which the first columns are associated with the responses and the last columns are associated with the covariates

Author(s)

Morteza Amini, morteza.amini@ut.ac.ir

References

Langrock, R., Adam, T., Leos-Barajas, V., Mews, S., Miller, D. L., and Papastamatiou, Y. P. (2018). Spline-based nonparametric inference in general state-switching models. Statistica Neerlandica, 72(3), 179-200.

Examples

J <- 3
initial <- c(1, 0, 0)
semi <- rep(FALSE, 3)
P <- matrix(c(0.5, 0.2, 0.3, 0.2, 0.5, 0.3, 0.1, 0.4, 0.5), nrow = J, 
byrow = TRUE)
par <- list(intercept = list(-21, -83, 33),
coef = list(array(c(1, 8, 52, 27, 38), dim = c(5, 1, 1)),  
array(c(99, 87, 94, 77, 50), dim = c(5, 1, 1)), 
array(c(-1, -8, -40, -22, -28), dim = c(5, 1, 1))),
sigma = list(0.2, 0.4, 0.1))
model <- hhsmmspec(init = initial, transition = P, parms.emis = par,
dens.emis = dnorm_additive_reg, semi = semi)
train <- simulate(model, nsim = 70, seed = 1234, 
remission = raddreg, covar = list(mean = 0, cov = 1))
plot(train$x[, 1] ~ train$x[, 2], col = train$s, pch = 16, 
xlab = "x", ylab = "y")

Random data generation from the mixture of Gaussian linear (Markov-switching) autoregressive models for hhsmm model

Description

Generates vectors of observations from mixture of Gaussian linear (Markov-switching) autoregressive model in a specified state and using the parameters of a specified model

Usage

rmixar(j, model, x)

Arguments

j

a specified state

model

a hhsmmspec model

x

the previous x vector as the covariate of the autoregressive model

Value

a random matrix of observations from mixture of Gaussian linear (Markov-switching) autoregressive model

Author(s)

Morteza Amini, morteza.amini@ut.ac.ir

Random data generation from the mixture of Gaussian linear (Markov-switching) models for hhsmm model

Description

Generates vectors of covariate and response observations from mixture of Gaussian linear (Markov-switching) models in a specified state and using the parameters of a specified model

Usage

rmixlm(j, model, covar, ...)

Arguments

j

a specified state

model

a hhsmmspec model

covar

either a function which generates the covariate vector or a list containing the following items:

  • mean the mean vector of covariates (to be generated from multivariate normal distribution)

  • cov the variance-covariance matrix of covariates (to be generated from multivariate normal distribution)

...

additional arguments of the covar function

Value

a random matrix of observations from mixture of Gaussian linear (Markov-switching) models, in which the first columns are associated with the responses and the last columns are associated with the covariates

Author(s)

Morteza Amini, morteza.amini@ut.ac.ir

References

Kim, C. J., Piger, J. and Startz, R. (2008). Estimation of Markov regime-switching regression models with endogenous switching. Journal of Econometrics, 143(2), 263-273.

Examples

J <- 3
initial <- c(1, 0, 0)
semi <- rep(FALSE, 3)
P <- matrix(c(0.5, 0.2, 0.3, 0.2, 0.5, 0.3, 0.1, 0.4, 0.5), nrow = J, 
byrow = TRUE)
par <- list(intercept = list(3, list(-10, -1), 14),
coefficient = list(-1, list(1, 5), -7),
csigma = list(1.2, list(2.3, 3.4), 1.1),
mix.p = list(1, c(0.4, 0.6), 1))
model <- hhsmmspec(init = initial, transition = P, parms.emis = par,
dens.emis = dmixlm, semi = semi)

#use the covar as the list of mean and 
#variance of the normal distribution 

train1 <- simulate(model, nsim = c(20, 30, 42, 50), seed = 1234, 
remission = rmixlm, covar = list(mean = 0, cov = 1))
plot(train1$x[,1] ~ train1$x[,2], col = train1$s, pch = 16, 
xlab = "x", ylab = "y")

#use the covar as the runif function 
#to generate one covariate from standard uniform distribution 

train2 <- simulate(model, nsim = c(20, 30, 42, 50), seed = 1234, 
remission = rmixlm, covar = runif, 1)
plot(train2$x[,1] ~ train2$x[,2], col = train2$s, pch = 16, 
xlab = "x", ylab = "y")

Random data generation from the mixture of multivariate normals for hhsmm model

Description

Generates a vector of observations from mixture multivariate normal distribution in a specified state and using the parameters of a specified model

Usage

rmixmvnorm(j, model)

Arguments

j

a specified state

model

a hhsmmspec model

Value

a random vector of observations from mixture of multivariate normal distributions

Author(s)

Morteza Amini, morteza.amini@ut.ac.ir, Afarin Bayat, aftbayat@gmail.com

Examples

J <- 3
initial <- c(1, 0, 0)
semi <- c(FALSE, TRUE, FALSE)
P <- matrix(c(0.8, 0.1, 0.1, 0.5, 0, 0.5, 0.1, 0.2, 0.7), nrow = J, 
byrow = TRUE)
par <- list(mu = list(list(7, 8), list(10, 9, 11), list(12, 14)),
sigma = list(list(3.8, 4.9), list(4.3, 4.2, 5.4), list(4.5, 6.1)),
mix.p = list(c(0.3, 0.7), c(0.2, 0.3, 0.5), c(0.5, 0.5)))
sojourn <- list(shape = c(0, 3, 0), scale = c(0, 10, 0), type = "gamma")
model <- hhsmmspec(init = initial, transition = P, parms.emis = par,
dens.emis = dmixmvnorm, sojourn = sojourn, semi = semi)
x = rmixmvnorm(1, model)

Random data generation from the multinomial emission distribution for hhsmm model

Description

Generates a vector of observations from multinomial emission distribution in a specified state and using the parameters of a specified model

Usage

rmultinomial.hhsmm(j, model)

Arguments

j

a specified state

model

a hhsmmspec model

Value

a random vector of observations from multinomial emission distribution

Author(s)

Morteza Amini, morteza.amini@ut.ac.ir

Examples

J <- 2
initial <- c(1, 0)
semi <- rep(TRUE, 2)
P <- matrix(c(0, 1, 1, 0), 
nrow = J, byrow = TRUE)
par <- list(prob = list(c(0.6,  0.2, 0.2),
                           c(0.2, 0.6,  0.2)))
sojourn <- list(shape = c(1, 3), scale = c(2, 10), type = "gamma")
model <- hhsmmspec(init = initial, transition = P, parms.emis = par,
dens.emis = dmultinomial.hhsmm, remission = rmultinomial.hhsmm,
 mstep = mstep.multinomial,sojourn = sojourn, semi = semi)
train <- simulate(model, nsim = c(20, 30, 42, 50), seed = 1234, 
remission = rmultinomial.hhsmm)
plot(train)

the M step function of the EM algorithm

Description

The M step function of the EM algorithm for the robust emission proposed by Qin et al. (2024) using the observation matrix and the estimated weight vectors

Usage

robust_mstep(x, wt, control = list(k = 1.345))

Arguments

x

the observation matrix

wt

the state probabilities matrix (number of observations times number of states)

control

a list containing the control parameter k with the default value equal to 1.345

Value

list of emission parameters: (mu and sigma)

Author(s)

Morteza Amini, morteza.amini@ut.ac.ir

References

Qin, S., Tan, Z., & Wu, Y. (2024). On robust estimation of hidden semi-Markov regime-switching models. Annals of Operations Research, 1-33.

Examples

J <- 3
initial <- c(1, 0, 0)
semi <- c(FALSE, TRUE, FALSE)
P <- matrix(c(0.8, 0.1, 0.1, 0.5, 0, 0.5, 0.1, 0.2, 0.7), nrow = J, 
byrow = TRUE)
par <- list(mu = list(list(7, 8), list(10, 9, 11), list(12, 14)),
sigma = list(list(3.8, 4.9), list(4.3, 4.2, 5.4), list(4.5, 6.1)),
mix.p = list(c(0.3, 0.7), c(0.2, 0.3, 0.5), c(0.5, 0.5)))
sojourn <- list(shape = c(0, 3, 0), scale = c(0, 10, 0), type = "gamma")
model <- hhsmmspec(init = initial, transition = P, parms.emis = par,
dens.emis = dmixmvnorm, sojourn = sojourn, semi = semi)
train <- simulate(model, nsim = c(10, 8, 8, 18), seed = 1234, 
remission = rmixmvnorm)
clus = initial_cluster(train, nstate = 3, nmix = NULL ,ltr = FALSE,
final.absorb = FALSE, verbose = TRUE)
initmodel1 = initialize_model(clus = clus, sojourn = "gamma", 
M = max(train$N), semi = semi, dens.emission = drobust, mstep = robust_mstep)
# not test
# fit1 = hhsmmfit(x = train, model = initmodel1, M = max(train$N), 
# mstep = robust_mstep)

the score of new observations

Description

computes the score (log-likelihood) of new observations using a trained model

Usage

score(xnew, fit, ...)

Arguments

xnew

a new single observation, observation matrix or a list of the class hhsmmdata containing $x and $N elements

fit

a fitted model using the hhsmmfit function

...

additional parameters for the dens.emission and mstep functions

Value

the vector of scores (log-likelihood) of xnew

Author(s)

Morteza Amini, morteza.amini@ut.ac.ir

Examples

### first example
J <- 3
initial <- c(1, 0, 0)
semi <- c(FALSE, TRUE, FALSE)
P <- matrix(c(0.8, 0.1, 0.1, 0.5, 0, 0.5, 0.1, 0.2, 0.7), nrow = J, 
byrow = TRUE)
par <- list(mu = list(list(7, 8), list(10, 9, 11), list(12, 14)),
sigma = list(list(3.8, 4.9), list(4.3, 4.2, 5.4), list(4.5, 6.1)),
mix.p = list(c(0.3, 0.7), c(0.2, 0.3, 0.5), c(0.5, 0.5)))
sojourn <- list(shape = c(0, 3, 0), scale = c(0, 10, 0), type = "gamma")
model <- hhsmmspec(init = initial, transition = P, parms.emis = par,
dens.emis = dmixmvnorm, sojourn = sojourn, semi = semi)
train <- simulate(model, nsim = c(10, 8, 8, 18), seed = 1234, 
remission = rmixmvnorm)
test <- simulate(model, nsim = c(5, 4, 6, 7), seed = 1234, 
remission = rmixmvnorm)
clus = initial_cluster(train, nstate = 3, nmix = c(2, 2, 2), ltr = FALSE,
final.absorb = FALSE, verbose = TRUE)
semi <- c(FALSE, TRUE, FALSE)
initmodel1 = initialize_model(clus = clus, sojourn = "gamma",
M = max(train$N), semi = semi)
fit1 = hhsmmfit(x = train, model = initmodel1, M = max(train$N))
score(test, fit1)

### second example
num_states <- 3
semi <- rep(TRUE, num_states)
init_probs <- rep(1/num_states, num_states)
transition_matrix <- matrix(1/(num_states-1), nrow = num_states, ncol = num_states)
for (i in seq_along(semi)) {
  if (semi[i]) {
    transition_matrix[i, i] <- 0
  }
}
parms_emission <- list(prob = list(c(0.6, 0.2, 0.1, 0.1), 
c(0.2, 0.6, 0.1, 0.1), c(0.5, 0.3, 0.1, 0.1)))
sojourn <- list(shape = c(1, 3, 1), scale = c(3, 10, 4), type = "gamma")
dens_emission <- dmultinomial.hhsmm
initmodel <- hhsmmspec(
  init = init_probs,
  transition = transition_matrix,
  parms.emission = parms_emission,
  sojourn = sojourn,
  dens.emission = dens_emission,
  remission = rmultinomial.hhsmm, 
  mstep = mstep.multinomial, 
  semi = semi
)
prepared_data <- hhsmmdata(as.matrix(sample(1:4,100,replace=TRUE)))
fit1 <- hhsmmfit(x = prepared_data, model=initmodel, n=4, 
M=max(prepared_data$N))
score(xnew = prepared_data, fit = fit1, n=4)

Simulation of data from hhsmm model

Description

Simulates a data set of class "hhsmmdata" using a hhsmmspec model

Usage

## S3 method for class 'hhsmmspec'
simulate(
  object,
  nsim,
  seed = NULL,
  remission = rmixmvnorm,
  ...,
  emission.control = list(autoregress = FALSE, lags = 1, start = list(mean = NULL, cov =
    NULL))
)

Arguments

object

a hhsmmspec model

nsim

a vector of sequence lengths (might be of length 1)

seed

a random seed to be set

remission

a random emission generation function (default = rmixmvnorm)

...

additional parameters of the remission function

emission.control

a list of additional control parameters including the following items:

  • autoregress logical. if TRUE the auto-regressive data generation will be considered with rmixar function

  • lags a positive integer which is the number of lags to be considered for the auto-regressive sequence

  • start a list containing the items mean which is the mean vector and cov which is the covarince matrix for starting value of the auto-regressive sequence (if autoregress == TRUE). If start is not specified the zero mean vector and the identity matrix will be considered as mean and cov, respectively.

Value

a list of class "hsmm.data" containing the following items:

Author(s)

Morteza Amini, morteza.amini@ut.ac.ir, Afarin Bayat, aftbayat@gmail.com

Examples

J <- 3
initial <- c(1, 0, 0)
semi <- c(FALSE, TRUE, FALSE)
P <- matrix(c(0.8, 0.1, 0.1, 0.5, 0, 0.5, 0.1, 0.2, 0.7), nrow = J, 
byrow = TRUE)
par <- list(mu = list(list(7, 8), list(10, 9, 11), list(12, 14)),
sigma = list(list(3.8, 4.9), list(4.3, 4.2, 5.4), list(4.5, 6.1)),
mix.p = list(c(0.3, 0.7),c(0.2, 0.3, 0.5), c(0.5, 0.5)))
sojourn <- list(shape = c(0, 3, 0), scale = c(0, 8, 0), type = "gamma")
model <- hhsmmspec(init = initial, transition = P, parms.emis = par,
dens.emis = dmixmvnorm, sojourn = sojourn, semi = semi)
train <- simulate(model, nsim = c(8, 5, 5, 10), seed = 1234, 
remission = rmixmvnorm)

Splitting the data sets to train and test

Description

A function to split the train data of class "hhsmmdata" to train and test subsets with an option to right trim the sequences

Usage

train_test_split(train, train.ratio = 0.7, trim = FALSE, trim.ratio = NULL)

Arguments

train

the train data of class "hhsmmdata"

train.ratio

a number in (0,1] which determines the ratio of the train subset. It can be equal to 1, if we need the test set to be equal to the train set and we only need to right trim the sequences

trim

logical. if TRUE the sequences will be right trimmed with random lengths

trim.ratio

a vector of trim ratios with a length equal to that of train$N, or a single trim ratio for all sequences. If it is NULL, then random trim ratios will be used

Details

This function splits the sample to train and test samples and trims the test sample from right, in order to provide a sample for examination of the prediction tools. In reliability applications, the hhsmm models are often left-to-right and the modeling aims to predict the future states. In such cases, the test sets are right trimmed and the prediction aims to predict the residual useful lifetime (RUL) of a new sequence.

Value

a list containing:

Author(s)

Morteza Amini, morteza.amini@ut.ac.ir

Examples


data(CMAPSS)
tt = train_test_split(CMAPSS$train, train.ratio = 0.7, trim = TRUE)