hsmmfit: Estimate the parameters of a general zero-inflated Poisson...

In ziphsmm: Zero-Inflated Poisson Hidden (Semi-)Markov Models

Description

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

Usage

hsmmfit(y, ntimes = NULL, M, trunc, prior_init, dt_dist, dt_init, tpm_init,
  emit_init, zero_init, prior_x = NULL, dt_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(data)
M	number of hidden states
trunc	a vector specifying truncation at the maximum number of dwelling time in each state. The higher the truncation, the more accurate the approximation but also the more computationally expensive.
prior_init	a vector of initial value for prior probability for each state
dt_dist	dwell time distribution, can only be "log", "geometric", or "shiftedpoisson"
dt_init	a vector of initial value for the parameter in each dwell time distribution, which should be a vector of p's for dt_dist == "log" and a vector of theta's for dt_dist=="shiftpoisson"
tpm_init	a matrix of initial values for the transition probability matrix, whose diagonal elements should be zero's
emit_init	a vector initial value for the vector containing means for each poisson distribution
zero_init	a vector initial value for the vector containing structural zero proportions in each state
prior_x	matrix of covariates for generalized logit of prior probabilites (excluding the 1st probability). Default to NULL.
dt_x	matrix of covariates for the dwell time distribution parameters
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 logit of parameter p for each log-series dwell time distribution or the log of parameter theta for each shifted-poisson dwell time distribution, the generalized logit of prior probabilities (except for the 1st state),the logit of each nonzero structural zero proportions, the log of each state-dependent poisson means, and the generalized logit of the transition probability matrix(except 1st column and the diagonal elements)
...	Further arguments passed on to the optimization methods

Value

simulated series and corresponding states

References

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

Examples

#2 zero-inflated poissons
prior_init <- c(0.5,0.5)
emit_init <- c(10,30)
dt_init <- c(10,6)
trunc <- c(20,10)
zeroprop <- c(0.5,0.3)
omega <- matrix(c(0,1,1,0),2,2,byrow=TRUE)
sim2 <- hsmmsim(n=1000,M=2,prior=prior_init,dt_dist="shiftpoisson",
         dt_parm=dt_init, tpm_parm=omega,
         emit_parm=emit_init,zeroprop=zeroprop)
str(sim2)
y <- sim2$series
fit2 <- hsmmfit(y=y,M=2,trunc=trunc,prior_init=prior_init,dt_dist="shiftpoisson",
     dt_init=dt_init,
     tpm_init=omega,emit_init=emit_init,zero_init=zeroprop,
     method="Nelder-Mead",hessian=FALSE,control=list(maxit=500,trace=1))
str(fit2)


## Not run: 
#1 zero-inflated poisson and 3 regular poissons
prior_init <- c(0.5,0.2,0.2,0.1)
dt_init <- c(0.8,0.7,0.6,0.5)
emit_init <- c(10,30,70,130)
trunc <- c(10,10,10,10)
zeroprop <- c(0.6,0,0,0)  #only the 1st-state is zero-inflated
omega <- matrix(c(0,0.5,0.3,0.2,0.4,0,0.4,0.2,
                  0.2,0.6,0,0.2,0.1,0.1,0.8,0),4,4,byrow=TRUE)
sim1 <- hsmmsim(n=2000,M=4,prior=prior_init,dt_dist="log",
         dt_parm=dt_init, tpm_parm=omega,
         emit_parm=emit_init,zeroprop=zeroprop)
str(sim1)
y <- sim1$series
fit <- hsmmfit(y=y,M=4,trunc=trunc,prior_init=prior_init,dt_dist="log",dt_init=dt_init,
     tpm_init=omega,emit_init=emit_init,zero_init=zeroprop,
     method="Nelder-Mead",hessian=TRUE,control=list(maxit=500,trace=1))
str(fit)

#variances for the 20 working parameters, which are the logit of parameter p for 
#the 4 log-series dwell time distributions, the generalized logit of prior probabilities 
#for state 2,3,4, the logit of each nonzero structural zero proportions in state 1, 
#the log of 4 state-dependent poisson means, and the generalized logit of the 
#transition probability matrix(which are tpm[1,3],tpm[1,4], tpm[2,3],tpm[2,4],
#tpm[3,2],tpm[3,4],tpm[4,2],tpm[4,3])
variance <- diag(solve(fit$obsinfo)) 


#1 zero-inflated poisson and 2 poissons with covariates
data(CAT)
y <- CAT$activity
x <- data.matrix(CAT$night)
prior_init <- c(0.5,0.3,0.2)
dt_init <- c(0.9,0.6,0.3)
emit_init <- c(10,20,30)
zero_init <- c(0.5,0,0) #assuming only the 1st state has structural zero's
tpm_init <- matrix(c(0,0.3,0.7,0.4,0,0.6,0.5,0.5,0),3,3,byrow=TRUE)
trunc <- c(10,7,4)
fit2 <-  hsmmfit(y,rep(1440,3),3,trunc,prior_init,"log",dt_init,tpm_init,
     emit_init,zero_init,emit_x=x,zeroinfl_x=x,hessian=FALSE,
     method="Nelder-Mead", control=list(maxit=500,trace=1))
fit2

#another example with covariates for 2 zero-inflated poissons
data(CAT)
y <- CAT$activity
x <- data.matrix(CAT$night)
prior_init <- c(0.5,0.5)
dt_init <- c(10,5)
emit_init <- c(10, 30)
zero_init <- c(0.5,0.2)
tpm_init <- matrix(c(0,1,1,0),2,2,byrow=TRUE)
trunc <- c(10,5)
fit <-  hsmmfit(y,NULL,2,trunc,prior_init,"shiftpoisson",dt_init,tpm_init,
     emit_init,zero_init,dt_x=x,emit_x=x,zeroinfl_x=x,tpm_x=x,hessian=FALSE,
     method="Nelder-Mead", control=list(maxit=500,trace=1))
fit

## End(Not run)

ziphsmm documentation built on May 2, 2019, 6:10 a.m.