# vignettes/examples/groupExample.R In momentuHMM: Maximum Likelihood Analysis of Animal Movement Behavior Using Multivariate Hidden Markov Models

```##This example is based on simulation Scenario A for the group dynamic model of Langrock et al (2014; Methods in Ecology and Evolution 5: 190-199)
library(momentuHMM)

oldRNG<-setRNG::setRNG()

setRNG::setRNG(kind="Mersenne-Twister",normal.kind="Inversion",seed=4)

#########################################################################
## Simulate group centroid path as BCRW relative to origin ##############
#########################################################################
dist <- list(step="gamma", angle="vm")
nbObs <- 250

Parc <- list(step=c(15,10), angle = c(0.15,log(1)))
DMc <- list(angle=list(mean=~center1.angle,concentration=~1))

centroidData <- simData(nbStates=1,dist=dist,Par=Parc,DM=DMc,circularAngleMean=list(angle=TRUE),centers=matrix(0,1,2),obsPerAnimal = nbObs)
centroidData\$ID <- "centroid"
#########################################################################

#########################################################################
## Simulate individual paths with state 1 as BRW relative to centroid ###
#########################################################################
nbAnimals <- 20
nbStates<-2
stateNames <- c("group","solitary")

Par <- list(step=c(30,50,15,25), angle = c(1,log(2.5),log(5)))
DM <- list(angle=list(mean=~state1(centroid.angle),concentration=~1))

beta <- matrix(c(-2.944439,-1.734601),1,nbStates)

# calculate stationary distribution
gamma <- diag(nbStates)
gamma[!gamma] <- exp(beta)
gamma <- t(gamma)
gamma <- gamma/apply(gamma,1,sum)
delta <- solve(diag(nbStates) - t(gamma) + 1, rep(1, nbStates))

# draw random initial locations for each individual
initialPositions <- vector("list")
for (i in 1:nbAnimals) {
initialPositions[[i]] <- runif(2, -10, 10)
}

groupData <- simData(nbAnimals=nbAnimals,nbStates=nbStates,dist=dist,Par=Par,beta=beta,delta=delta,DM=DM,circularAngleMean=list(angle=0),centroids=list(centroid=data.frame(x=centroidData\$x,y=centroidData\$y)),obsPerAnimal=nbObs,initialPosition=initialPositions,states=TRUE,stateNames=stateNames)
#########################################################################

#########################################################################
## Fit group dynamic model to simulated paths ###########################
Par0 <- list(step=c(30,50,15,25), angle = c(1,log(2.5),log(5)))
fixPar <- list(angle=c(1,NA,NA))
groupFit <- fitHMM(groupData,nbStates=nbStates,dist=dist,Par=Par0,DM=DM,stationary=TRUE,estAngleMean=list(angle=TRUE),circularAngleMean=list(angle=0),fixPar=fixPar,stateNames=stateNames)