# fit a hidden semi-Markov model Estimates parameters of a HSMM using the EM algorithm. ```r hsmmfit(x,model,mstep=NULL,M=NA,maxit=100, lock.transition=FALSE,lock.d=FALSE,graphical=FALSE) ``` ## Arguments - `x`: A hsmm.data object (see Details) - `model`: Starting parameters for the model (see `hsmmspec`) - `mstep`: Re-estimates the parameters of density function on each iteration - `maxit`: Maximum number of iterations - `M`: Maximum number of time spent in a state (truncates the waiting distribution) - `lock.transition`: If TRUE will not re-estimate the transition matrix - `lock.d`: If TRUE will not re-estimate the sojourn time density - `graphical`: If TRUE will plot the sojourn densities on each iteration ## Returns - **start**: A vector of the starting probabilities for each state - **a**: The transition matrix of the embedded Markov chain - **emission**: A list of the parameters of the emission distribution - **waiting**: A list of the parameters of the waiting distribution ## References Jared O'Connell, Soren Hojsgaard (2011). Hidden Semi Markov Models for Multiple Observation Sequences: The mhsmm Package for R., Journal of Statistical Software, 39(4), 1-22., URL http://www.jstatsoft.org/v39/i04/. Guedon, Y. (2003), Estimating hidden semi-Markov chains from discrete sequences, Journal of Computational and Graphical Statistics, Volume 12, Number 3, page 604-639 - 2003 ## Author(s) Jared O'Connell jaredoconnell@gmail.com ## See Also `hsmmspec`,`simulate.hsmmspec`,`predict.hsmm` ## Examples ```r J <- 3 init <- c(0,0,1) P <- matrix(c(0,.1,.4,.5,0,.6,.5,.9,0),nrow=J) B <- list(mu=c(10,15,20),sigma=c(2,1,1.5)) d <- list(lambda=c(10,30,60),shift=c(10,100,30),type='poisson') model <- hsmmspec(init,P,parms.emission=B,sojourn=d,dens.emission=dnorm.hsmm) train <- simulate(model,r=rnorm.hsmm,nsim=100,seed=123456) plot(train,xlim=c(0,400)) start.poisson <- hsmmspec(init=rep(1/J,J), transition=matrix(c(0,.5,.5,.5,0,.5,.5,.5,0),nrow=J), parms.emission=list(mu=c(4,12,23), sigma=c(1,1,1)), sojourn=list(lambda=c(9,25,40),shift=c(5,95,45),type='poisson'), dens.emission=dnorm.hsmm) M=500 # not run (takes some time) # h.poisson <- hsmmfit(train,start.poisson,mstep=mstep.norm,M=M) # plot(h.poisson$loglik,type='b',ylab='Log-likelihood',xlab='Iteration') ##has it converged? # summary(h.poisson) # predicted <- predict(h.poisson,train) # table(train$s,predicted$s) ##classification matrix # mean(predicted$s!=train$s) ##misclassification rate d <- cbind(dunif(1:M,0,50),dunif(1:M,100,175),dunif(1:M,50,130)) start.np <- hsmmspec(init=rep(1/J,J), transition=matrix(c(0,.5,.5,.5,0,.5,.5,.5,0),nrow=J), parms.emission=list(mu=c(4,12,23), sigma=c(1,1,1)), sojourn=list(d=d,type='nonparametric'), dens.emission=dnorm.hsmm) # not run (takes some time) # h.np <- hsmmfit(train,start.np,mstep=mstep.norm,M=M,graphical=TRUE) # mean(predicted$s!=train$s) ##misclassification rate #J <- 2 #init <- c(1, 0) #P <- matrix(c(0, 1, 1, 0), nrow = J) #B <- list(mu = list(c(2, 3), c(3, 4)), sigma = list(matrix(c(4, 2, 2, 3), ncol = 2), diag(2))) #d <- list(shape = c(10, 25), scale = c(2, 2), type = "gamma") #model <- hsmmspec(init, P, parms.emis = B, sojourn = d, dens.emis = dmvnorm.hsmm) #train <- simulate(model, c(1000,100), seed = 123, rand.emis = rmvnorm.hsmm) #yhat <- predict(model, train) #mean(predict(model,train)$s==train$s) ```

hsmmfit function