ziphsmm (version 2.0.6)

hmmfit: Estimate the parameters of a general zero-inflated Poisson hidden Markov model by directly minimizing of the negative log-likelihood function using the gradient descent algorithm.

Description

Estimate the parameters of a general zero-inflated Poisson hidden Markov model by directly minimizing of the negative log-likelihood function using the gradient descent algorithm.

Usage

hmmfit(y, ntimes = NULL, M, prior_init, tpm_init, emit_init, zero_init,
  prior_x = NULL, tpm_x = NULL, emit_x = NULL, zeroinfl_x = NULL,
  method = "Nelder-Mead", hessian = FALSE, ...)

Arguments

y

observed time series values

ntimes

a vector specifying the lengths of individual, i.e. independent, time series. If not specified, the responses are assumed to form a single time series, i.e. ntimes=length(y)

M

number of latent states

prior_init

a vector of initial values for prior probability for each state

tpm_init

a matrix of initial values for transition probability matrix

emit_init

a vector of initial values for the means for each poisson distribution

zero_init

a vector of initial values for the structural zero proportions in each state

prior_x

matrix of covariates for generalized logit of prior probabilites (excluding the 1st probability). Default to NULL.

tpm_x

matrix of covariates for transition probability matrix (excluding the 1st column). Default to NULL.

emit_x

matrix of covariates for the log poisson means. Default to NULL.

zeroinfl_x

matrix of covariates for the nonzero structural zero proportions. Default to NULL.

method

method to be used for direct numeric optimization. See details in the help page for optim() function. Default to Nelder-Mead.

hessian

Logical. Should a numerically differentiated Hessian matrix be returned? Note that the hessian is for the working parameters, which are the generalized logit of prior probabilities (except for state 1), the generalized logit of the transition probability matrix(except 1st column), the logit of non-zero zero proportions, and the log of each state-dependent poisson means

...

Further arguments passed on to the optimization methods

Value

the maximum likelihood estimates of the zero-inflated hidden Markov model

References

Walter Zucchini, Iain L. MacDonald, Roland Langrock. Hidden Markov Models for Time Series: An Introduction Using R, Second Edition. Chapman & Hall/CRC

Examples

# NOT RUN {
prior_init <- c(0.5,0.2,0.3)
emit_init <- c(10,40,70)
zero_init <- c(0.5,0,0)
omega <- matrix(c(0.5,0.3,0.2,0.4,0.3,0.3,0.2,0.4,0.4),3,3,byrow=TRUE)
result <- hmmsim(n=1000,M=3,prior=prior_init, tpm_parm=omega,
         emit_parm=emit_init,zeroprop=zero_init)
y <- result$series
fit <- hmmfit(y=y,M=3,prior_init=prior_init,tpm_init=omega,
     emit_init=emit_init,zero_init=zero_init,
     method="Nelder-Mead",hessian=TRUE,control=list(maxit=500,trace=1))
str(fit)

#variances for the 12 working parameters, which are the logit of prior probabilities
#for state 2 and state 3, the generalized logit of the transition probability matrix
#(tpm[1,2],tpm[1,3],tpm[2,2],tpm[2,3],tpm[3,2],tpm[3,3]), the logit of structural zero
#proportions for state 1, and log of poisson means for state 1, 2, and 3
#logit of non-zero zero proportions, and the log of poisson means
variance <- diag(solve(fit$obsinfo))

#with covariates
data(CAT)
y <- CAT$activity
x <- data.matrix(CAT$night)
prior_init <- c(0.5,0.2,0.3)
emit_init <- c(10,50,100)
zero_init <- c(0.5,0,0)
omega <- matrix(c(0.5,0.3,0.2,0.4,0.3,0.3,0.2,0.4,0.4),3,3,byrow=TRUE)
fit2 <-  hmmfit(y,rep(1440,3),3,prior_init,omega,
     emit_init,zero_init, emit_x=x,zeroinfl_x=x,hessian=FALSE,
     method="Nelder-Mead", control=list(maxit=500,trace=1))
fit2
     
# }
# NOT RUN {
#two zero-inflated poissons
prior_init <- c(0.5,0.5)
emit_init <- c(10,50)
zero_init <- c(0.6,0.3)
omega <- matrix(c(0.9,0.1,0.2,0.8),2,2,byrow=TRUE)
result <- hmmsim(n=1000,M=2,prior=prior_init, tpm_parm=omega,
         emit_parm=emit_init,zeroprop=zero_init)
y <- result$series
fit <- hmmfit(y=y,M=2,prior_init=prior_init,tpm_init=omega,
     emit_init=emit_init,zero_init=zero_init,
     method="Nelder-Mead",hessian=FALSE,control=list(maxit=500,trace=1))
str(fit)

#four regular poissons
prior_init <- c(0.4,0.2,0.2,0.2)
emit_init <- c(10,40,70,100)
zero_init <- c(0,0,0,0)
omega <- matrix(c(0.3,0.3,0.2,0.2,0.4,0.2,0.3,0.1,
                  0.2,0.2,0.3,0.3,0.1,0.2,0.3,0.4),4,4,byrow=TRUE)
result <- hmmsim(n=1000,M=4,prior=prior_init, tpm_parm=omega,
         emit_parm=emit_init,zeroprop=zero_init)
y <- result$series
fit <- hmmfit(y=y,M=4,prior_init=prior_init,tpm_init=omega,
     emit_init=emit_init,zero_init=zero_init,
     method="Nelder-Mead",hessian=FALSE,control=list(maxit=500,trace=1))
str(fit)
# }