Package 'moveHMM' reference manual

Title:	Animal Movement Modelling using Hidden Markov Models
Description:	Provides tools for animal movement modelling using hidden Markov models. These include processing of tracking data, fitting hidden Markov models to movement data, visualization of data and fitted model, decoding of the state process, etc. <doi:10.1111/2041-210X.12578>.
Authors:	Theo Michelot (aut, cre), Roland Langrock (aut, cre), Toby Patterson (aut, cre), Brett McClintock (ctb), Eric Rexstad (ctb)
Maintainer:	Theo Michelot <[email protected]>
License:	GPL-3
Version:	1.9
Built:	2024-11-21 06:54:32 UTC
Source:	CRAN

AIC

Description

Akaike information criterion of a moveHMM model.

Usage

## S3 method for class 'moveHMM'
AIC(object, ..., k = 2)
## S3 method for class 'moveHMM'
AIC(object, ..., k = 2)

Arguments

`object`	A `moveHMM` object.
`...`	Optional additional `moveHMM` objects, to compare AICs of the different models.
`k`	Penalty per parameter. Default: 2; for classical AIC.

Value

The AIC of the model(s) provided. If several models are provided, the AICs are output in ascending order.

Examples

# m is a moveHMM object (as returned by fitHMM), automatically loaded with the package
m <- example$m
AIC(m)

# m is a moveHMM object (as returned by fitHMM), automatically loaded with the package
m <- example$m
AIC(m)

Confidence intervals for angle parameters

Description

Simulation-based computation of confidence intervals for the parameters of the angle distribution. Used in CI.

Usage

angleCI(m, alpha, nbSims = 10^6)
angleCI(m, alpha, nbSims = 10^6)

Arguments

`m`	A `moveHMM` object
`alpha`	Range of the confidence intervals. Default: 0.95 (i.e. 95% CIs).
`nbSims`	Number of simulations. Default: 10^6.

Value

A list of the following objects:

`lower`	Lower bound of the confidence interval for the parameters of the angle distribution
`upper`	Upper bound of the confidence interval for the parameters of the angle distribution

Confidence intervals

Description

Computes the confidence intervals of the step length and turning angle parameters, as well as for the transition probabilities regression parameters.

Usage

CI(m, alpha = 0.95, nbSims = 10^6)
CI(m, alpha = 0.95, nbSims = 10^6)

Arguments

`m`	A `moveHMM` object
`alpha`	Range of the confidence intervals. Default: 0.95 (i.e. 95% CIs).
`nbSims`	Number of simulations in the computation of the CIs for the angle parameters. Default: 10^6.

Value

A list of the following objects:

`stepPar`	Confidence intervals for the parameters of the step lengths distribution
`anglePar`	Confidence intervals for the parameters of the turning angles distribution
`beta`	Confidence intervals for the regression coefficients of the transition probabilities.

Examples

# m is a moveHMM object (as returned by fitHMM), automatically loaded with the package
m <- example$m

CI(m)

# m is a moveHMM object (as returned by fitHMM), automatically loaded with the package
m <- example$m

CI(m)

Wrapped Cauchy density function

Description

Probability density function of the wrapped Cauchy distribution (written in C++)

Usage

dwrpcauchy_rcpp(x, mu, rho)
dwrpcauchy_rcpp(x, mu, rho)

Arguments

`x`	Vector of quantiles
`mu`	Mean
`rho`	Concentration

Value

Vector of densities

Elk data set from Morales et al. (2004, Ecology)

Description

It is a data frame with the following columns:

ID Track identifier
Easting Easting coordinate of locations
Northing Northing coordinate of locations
dist_water Distance of elk to water (in metres)

Usage

elk_data
elk_data

Example dataset

Description

This data is generated by the function exGen, and used in the examples and tests of other functions to keep them as short as possible.

Usage

example
example

Details

It is a list of the following objects:

data A moveData object
m A moveHMM object
simPar The parameters used to simulate data
par0 The initial parameters in the optimization to fit m

Example data simulation

Description

Generate the file data/example.RData, used in other functions' examples and unit tests.

Usage

exGen()
exGen()

Fit an HMM to the data

Description

Fit an hidden Markov model to the data provided, using numerical optimization of the log-likelihood function.

Usage

fitHMM(
  data,
  nbStates,
  stepPar0,
  anglePar0 = NULL,
  beta0 = NULL,
  delta0 = NULL,
  formula = ~1,
  stepDist = c("gamma", "weibull", "lnorm", "exp"),
  angleDist = c("vm", "wrpcauchy", "none"),
  angleMean = NULL,
  stationary = FALSE,
  knownStates = NULL,
  verbose = 0,
  nlmPar = NULL,
  fit = TRUE
)
fitHMM(
  data,
  nbStates,
  stepPar0,
  anglePar0 = NULL,
  beta0 = NULL,
  delta0 = NULL,
  formula = ~1,
  stepDist = c("gamma", "weibull", "lnorm", "exp"),
  angleDist = c("vm", "wrpcauchy", "none"),
  angleMean = NULL,
  stationary = FALSE,
  knownStates = NULL,
  verbose = 0,
  nlmPar = NULL,
  fit = TRUE
)

Arguments

`data`	An object `moveData`.
`nbStates`	Number of states of the HMM.
`stepPar0`	Vector of initial state-dependent step length distribution parameters. The parameters should be in the order expected by the pdf of `stepDist`, and the zero-mass parameter should be the last. Note that zero-mass parameters are mandatory if there are steps of length zero in the data. For example, for a 2-state model using the gamma distribution and including zero-inflation, the vector of initial parameters would be something like: `c(mu1,mu2,sigma1,sigma2,zeromass1,zeromass2)`.
`anglePar0`	Vector of initial state-dependent turning angle distribution parameters. The parameters should be in the order expected by the pdf of `angleDist`. For example, for a 2-state model using the Von Mises (vm) distribution, the vector of initial parameters would be something like: `c(mu1,mu2,kappa1,kappa2)`.
`beta0`	Initial matrix of regression coefficients for the transition probabilities (more information in "Details"). Default: `NULL`. If not specified, `beta0` is initialized such that the diagonal elements of the transition probability matrix are dominant.
`delta0`	Initial value for the initial distribution of the HMM. Default: `rep(1/nbStates,nbStates)`.
`formula`	Regression formula for the covariates. Default: `~1` (no covariate effect).
`stepDist`	Name of the distribution of the step lengths (as a character string). Supported distributions are: gamma, weibull, lnorm, exp. Default: gamma.
`angleDist`	Name of the distribution of the turning angles (as a character string). Supported distributions are: vm, wrpcauchy. Set to `"none"` if the angle distribution should not be estimated. Default: vm.
`angleMean`	Vector of means of turning angles if not estimated (one for each state). Default: `NULL` (the angle mean is estimated).
`stationary`	`FALSE` if there are covariates. If `TRUE`, the initial distribution is considered equal to the stationary distribution. Default: `FALSE`.
`knownStates`	Vector of values of the state process which are known prior to fitting the model (if any). Default: NULL (states are not known). This should be a vector with length the number of rows of 'data'; each element should either be an integer (the value of the known states) or NA if the state is not known.
`verbose`	Determines the print level of the optimizer. The default value of 0 means that no printing occurs, a value of 1 means that the first and last iterations of the optimization are detailed, and a value of 2 means that each iteration of the optimization is detailed.
`nlmPar`	List of parameters to pass to the optimization function `nlm` (which should be either '`gradtol`', '`stepmax`', '`steptol`', or '`iterlim`' – see `nlm`'s documentation for more detail)
`fit`	`TRUE` if an HMM should be fitted to the data, `FALSE` otherwise. If fit=`FALSE`, a model is returned with the MLE replaced by the initial parameters given in input. This option can be used to assess the initial parameters. Default: `TRUE`.

Details

The matrix beta of regression coefficients for the transition probabilities has one row for the intercept, plus one row for each covariate, and one column for each non-diagonal element of the transition probability matrix. For example, in a 3-state HMM with 2 covariates, the matrix beta has three rows (intercept + two covariates) and six columns (six non-diagonal elements in the 3x3 transition probability matrix - filled in row-wise). In a covariate-free model (default), beta has one row, for the intercept.
The choice of initial parameters is crucial to fit a model. The algorithm might not find the global optimum of the likelihood function if the initial parameters are poorly chosen.

Value

A moveHMM object, i.e. a list of:

`mle`	The maximum likelihood estimates of the parameters of the model (if the numerical algorithm has indeed identified the global maximum of the likelihood function), which is a list of: `stepPar` (step distribution parameters), `anglePar` (angle distribution parameters), `beta` (transition probabilities regression coefficients - more information in "Details"), and `delta` (initial distribution).
`data`	The movement data
`mod`	The object returned by the numerical optimizer `nlm`
`conditions`	A few conditions used to fit the model (`stepDist`, `angleDist`, `zeroInflation`, `estAngleMean`, `stationary`, and `formula`)
`rawCovs`	Raw covariate values, as found in the data (if any). Used in `plot.moveHMM`.
`knownStates`	Vector of states known a priori, as provided in input (if any, `NULL` otherwise). Used in `viterbi`,`logAlpha`, and `logBeta`
`nlmTime`	Computing time for optimisation, obtained with system.time

References

Patterson T.A., Basson M., Bravington M.V., Gunn J.S. 2009. Classifying movement behaviour in relation to environmental conditions using hidden Markov models. Journal of Animal Ecology, 78 (6), 1113-1123.

Langrock R., King R., Matthiopoulos J., Thomas L., Fortin D., Morales J.M. 2012. Flexible and practical modeling of animal telemetry data: hidden Markov models and extensions. Ecology, 93 (11), 2336-2342.

Examples

### 1. simulate data
# define all the arguments of simData
nbAnimals <- 2
nbStates <- 2
nbCovs <- 2
mu<-c(15,50)
sigma<-c(10,20)
angleMean <- c(pi,0)
kappa <- c(0.7,1.5)
stepPar <- c(mu,sigma)
anglePar <- c(angleMean,kappa)
stepDist <- "gamma"
angleDist <- "vm"
zeroInflation <- FALSE
obsPerAnimal <- c(50,100)

data <- simData(nbAnimals=nbAnimals,nbStates=nbStates,stepDist=stepDist,angleDist=angleDist,
                 stepPar=stepPar,anglePar=anglePar,nbCovs=nbCovs,zeroInflation=zeroInflation,
                 obsPerAnimal=obsPerAnimal)

### 2. fit the model to the simulated data
# define initial values for the parameters
mu0 <- c(20,70)
sigma0 <- c(10,30)
kappa0 <- c(1,1)
stepPar0 <- c(mu0,sigma0) # no zero-inflation, so no zero-mass included
anglePar0 <- kappa0 # the angle mean is not estimated, so only the concentration parameter is needed
formula <- ~cov1+cos(cov2)

m <- fitHMM(data=data,nbStates=nbStates,stepPar0=stepPar0,anglePar0=anglePar0,formula=formula,
              stepDist=stepDist,angleDist=angleDist,angleMean=angleMean)

print(m)

### 1. simulate data
# define all the arguments of simData
nbAnimals <- 2
nbStates <- 2
nbCovs <- 2
mu<-c(15,50)
sigma<-c(10,20)
angleMean <- c(pi,0)
kappa <- c(0.7,1.5)
stepPar <- c(mu,sigma)
anglePar <- c(angleMean,kappa)
stepDist <- "gamma"
angleDist <- "vm"
zeroInflation <- FALSE
obsPerAnimal <- c(50,100)

data <- simData(nbAnimals=nbAnimals,nbStates=nbStates,stepDist=stepDist,angleDist=angleDist,
                 stepPar=stepPar,anglePar=anglePar,nbCovs=nbCovs,zeroInflation=zeroInflation,
                 obsPerAnimal=obsPerAnimal)

### 2. fit the model to the simulated data
# define initial values for the parameters
mu0 <- c(20,70)
sigma0 <- c(10,30)
kappa0 <- c(1,1)
stepPar0 <- c(mu0,sigma0) # no zero-inflation, so no zero-mass included
anglePar0 <- kappa0 # the angle mean is not estimated, so only the concentration parameter is needed
formula <- ~cov1+cos(cov2)

m <- fitHMM(data=data,nbStates=nbStates,stepPar0=stepPar0,anglePar0=anglePar0,formula=formula,
              stepDist=stepDist,angleDist=angleDist,angleMean=angleMean)

print(m)

Discrete colour palette for states

Description

Discrete colour palette for states

Usage

getPalette(nbStates)
getPalette(nbStates)

Arguments

nbStates

Number of states

Value

Vector of colours, of length nbStates.

Data to produce plots of fitted model

Description

Data to produce plots of fitted model

Usage

getPlotData(m, type, format = "wide", alpha = 0.95)
getPlotData(m, type, format = "wide", alpha = 0.95)

Arguments

`m`	Fitted HMM object, as output by fitHMM.
`type`	Type of plot, one of: "dist", "tpm", "stat"
`format`	Format of data, either "wide" (for base graphics) or "long" (for ggplot)
`alpha`	Level of confidence intervals. Default: 0.95, i.e., 95% confidence intervals

Details

If type = "dist", the function evaluates each state-dependent distribution over the range of observed variable (step length or turning angle), and weighs them by the proportion of time spent in each state (obtained from Viterbi state sequence).
If type = "tpm", the function returns transition probabilities estimated over a range of covariate values. Other covariates are fixed to their mean values.

Value

Data frame (or list of data frames) containing data in a format that can easily be plotted. If type = "dist", the output is a list with two elements, "step" and "angle". If type = "tpm" or "stat", the output is a list with one element for each covariate. See details for more extensive description of output.

Wild haggis data set from Michelot et al. (2016, Methods Eco Evol)

Description

Data frame of the first three tracks from Michelot et al. (2016), with columns:

ID Track identifier
x Easting coordinate of locations
y Northing coordinate of locations
slope Terrain slope (in degrees)
temp Air temperature (in degrees Celsius)

Usage

haggis_data
haggis_data

Is moveData

Description

Check that an object is of class moveData. Used in fitHMM.

Usage

is.moveData(x)
is.moveData(x)

Arguments

`x`	An R object

Value

TRUE if x is of class moveData, FALSE otherwise.

Is moveHMM

Description

Check that an object is of class moveHMM. Used in CI, plotPR, plotStates, pseudoRes, stateProbs, and viterbi.

Usage

is.moveHMM(x)
is.moveHMM(x)

Arguments

`x`	An R object

Value

TRUE if x is of class moveHMM, FALSE otherwise.

Forward log-probabilities

Description

Used in stateProbs and pseudoRes.

Usage

logAlpha(m)
logAlpha(m)

Arguments

`m`	A `moveHMM` object.

Value

The matrix of forward log-probabilities.

Examples

## Not run: 
# m is a moveHMM object (as returned by fitHMM), automatically loaded with the package
m <- example$m

la <- logAlpha(m)

## End(Not run)
## Not run: 
# m is a moveHMM object (as returned by fitHMM), automatically loaded with the package
m <- example$m

la <- logAlpha(m)

## End(Not run)

Backward log-probabilities

Description

Used in stateProbs.

Usage

logBeta(m)
logBeta(m)

Arguments

`m`	A `moveHMM` object.

Value

The matrix of backward log-probabilities.

Examples

## Not run: 
# m is a moveHMM object (as returned by fitHMM), automatically loaded with the package
m <- example$m

lb <- logBeta(m)

## End(Not run)
## Not run: 
# m is a moveHMM object (as returned by fitHMM), automatically loaded with the package
m <- example$m

lb <- logBeta(m)

## End(Not run)

Constructor of `moveData` objects

Description

Constructor of moveData objects

Usage

moveData(data)
moveData(data)

Arguments

data

A dataframe containing: ID (the ID(s) of the observed animal(s)), step (the step lengths), angle (the turning angles, if any), x (either easting or longitude), y (either norting or latitude), and covariates, if any.

Value

An object moveData.

Constructor of `moveHMM` objects

Description

Constructor of moveHMM objects

Usage

moveHMM(m)
moveHMM(m)

Arguments

m

A list of attributes of the fitted model: mle (the maximum likelihood estimates of the parameters of the model), data (the movement data), mod (the object returned by the numerical optimizer nlm), conditions (a few conditions used to fit the model: stepDist, angleDist, zeroInflation, estAngleMean, stationary, and formula), rawCovs (optional – only if there are covariates in the data).

Value

An object moveHMM.

Scaling function: natural to working parameters.

Description

Scales each parameter from its natural interval to the set of real numbers, to allow for unconstrained optimization. Used during the optimization of the log-likelihood.

Usage

n2w(par, bounds, beta, delta = NULL, nbStates, estAngleMean)
n2w(par, bounds, beta, delta = NULL, nbStates, estAngleMean)

Arguments

`par`	Vector of state-dependent distributions parameters.
`bounds`	Matrix with 2 columns and as many rows as there are elements in `par`. Each row contains the lower and upper bound for the correponding parameter.
`beta`	Matrix of regression coefficients for the transition probabilities.
`delta`	Initial distribution. Default: `NULL` ; if the initial distribution is not estimated.
`nbStates`	The number of states of the HMM.
`estAngleMean`	`TRUE` if the angle mean is estimated, `FALSE` otherwise.

Value

A vector of unconstrained parameters.

Examples

## Not run: 
nbStates <- 3
par <- c(0.001,0.999,0.5,0.001,1500.3,7.1)
bounds <- matrix(c(0,1, # bounds for first parameter
                   0,1, # bounds for second parameter
                   0,1, # ...
                   0,Inf,
                   0,Inf,
                   0,Inf),
                 byrow=TRUE,ncol=2)
beta <- matrix(rnorm(18),ncol=6,nrow=3)
delta <- c(0.6,0.3,0.1)

# vector of working parameters
wpar <- n2w(par=par,bounds=bounds,beta=beta,delta=delta,nbStates=nbStates,
           estAngleMean=FALSE)

## End(Not run)

## Not run: 
nbStates <- 3
par <- c(0.001,0.999,0.5,0.001,1500.3,7.1)
bounds <- matrix(c(0,1, # bounds for first parameter
                   0,1, # bounds for second parameter
                   0,1, # ...
                   0,Inf,
                   0,Inf,
                   0,Inf),
                 byrow=TRUE,ncol=2)
beta <- matrix(rnorm(18),ncol=6,nrow=3)
delta <- c(0.6,0.3,0.1)

# vector of working parameters
wpar <- n2w(par=par,bounds=bounds,beta=beta,delta=delta,nbStates=nbStates,
           estAngleMean=FALSE)

## End(Not run)

Negative log-likelihood function

Description

Negative log-likelihood function

Usage

nLogLike(
  wpar,
  nbStates,
  bounds,
  parSize,
  data,
  stepDist = c("gamma", "weibull", "lnorm", "exp"),
  angleDist = c("vm", "wrpcauchy", "none"),
  angleMean = NULL,
  zeroInflation = FALSE,
  stationary = FALSE,
  knownStates = NULL
)
nLogLike(
  wpar,
  nbStates,
  bounds,
  parSize,
  data,
  stepDist = c("gamma", "weibull", "lnorm", "exp"),
  angleDist = c("vm", "wrpcauchy", "none"),
  angleMean = NULL,
  zeroInflation = FALSE,
  stationary = FALSE,
  knownStates = NULL
)

Arguments

`wpar`	Vector of working parameters.
`nbStates`	Number of states of the HMM.
`bounds`	Matrix with 2 columns and as many rows as there are elements in `wpar`. Each row contains the lower and upper bound for the correponding parameter.
`parSize`	Vector of two values: number of parameters of the step length distribution, number of parameters of the turning angle distribution.
`data`	An object `moveData`.
`stepDist`	Name of the distribution of the step lengths (as a character string). Supported distributions are: gamma, weibull, lnorm, exp. Default: gamma.
`angleDist`	Name of the distribution of the turning angles (as a character string). Supported distributions are: vm, wrpcauchy. Set to `"none"` if the angle distribution should not be estimated. Default: vm.
`angleMean`	Vector of means of turning angles if not estimated (one for each state). Default: `NULL` (the angle mean is estimated).
`zeroInflation`	`TRUE` if the step length distribution is inflated in zero. Default: `FALSE`. If `TRUE`, initial values for the zero-mass parameters should be included in `stepPar0`.
`stationary`	`FALSE` if there are covariates. If `TRUE`, the initial distribution is considered equal to the stationary distribution. Default: `FALSE`.
`knownStates`	Vector of values of the state process which are known prior to fitting the model (if any). Default: NULL (states are not known). This should be a vector with length the number of rows of 'data'; each element should either be an integer (the value of the known states) or NA if the state is not known.

Value

The negative log-likelihood of the parameters given the data.

Examples

## Not run: 
# data is a moveData object (as returned by prepData), automatically loaded with the package
data <- example$data
simPar <- example$simPar
par0 <- example$par0

estAngleMean <- is.null(simPar$angleMean)
bounds <- parDef(simPar$stepDist,simPar$angleDist,simPar$nbStates,
                 estAngleMean,simPar$zeroInflation)$bounds
parSize <- parDef(simPar$stepDist,simPar$angleDist,simPar$nbStates,
                  estAngleMean,simPar$zeroInflation)$parSize

par <- c(par0$stepPar0,par0$anglePar0)
wpar <- n2w(par,bounds,par0$beta0,par0$delta0,simPar$nbStates,FALSE)

l <- nLogLike(wpar=wpar,nbStates=simPar$nbStates,bounds=bounds,parSize=parSize,data=data,
             stepDist=simPar$stepDist,angleDist=simPar$angleDist,angleMean=simPar$angleMean,
             zeroInflation=simPar$zeroInflation)

## End(Not run)

## Not run: 
# data is a moveData object (as returned by prepData), automatically loaded with the package
data <- example$data
simPar <- example$simPar
par0 <- example$par0

estAngleMean <- is.null(simPar$angleMean)
bounds <- parDef(simPar$stepDist,simPar$angleDist,simPar$nbStates,
                 estAngleMean,simPar$zeroInflation)$bounds
parSize <- parDef(simPar$stepDist,simPar$angleDist,simPar$nbStates,
                  estAngleMean,simPar$zeroInflation)$parSize

par <- c(par0$stepPar0,par0$anglePar0)
wpar <- n2w(par,bounds,par0$beta0,par0$delta0,simPar$nbStates,FALSE)

l <- nLogLike(wpar=wpar,nbStates=simPar$nbStates,bounds=bounds,parSize=parSize,data=data,
             stepDist=simPar$stepDist,angleDist=simPar$angleDist,angleMean=simPar$angleMean,
             zeroInflation=simPar$zeroInflation)

## End(Not run)

Negative log-likelihood

Description

Computation of the negative log-likelihood (forward algorithm - written in C++)

Usage

nLogLike_rcpp(
  nbStates,
  beta,
  covs,
  data,
  stepDist,
  angleDist,
  stepPar,
  anglePar,
  delta,
  aInd,
  zeroInflation,
  stationary,
  knownStates
)
nLogLike_rcpp(
  nbStates,
  beta,
  covs,
  data,
  stepDist,
  angleDist,
  stepPar,
  anglePar,
  delta,
  aInd,
  zeroInflation,
  stationary,
  knownStates
)

Arguments

`nbStates`	Number of states
`beta`	Matrix of regression coefficients for the transition probabilities
`covs`	Covariates
`data`	A `moveData` object of the observations
`stepDist`	The name of the step length distribution
`angleDist`	The name of the turning angle distribution
`stepPar`	State-dependent parameters of the step length distribution
`anglePar`	State-dependent parameters of the turning angle distribution
`delta`	Stationary distribution
`aInd`	Vector of indices of the rows at which the data switches to another animal
`zeroInflation`	`true` if zero-inflation is included in the step length distribution, `false` otherwise.
`stationary`	`false` if there are covariates. If `true`, the initial distribution is considered equal to the stationary distribution.
`knownStates`	Vector of values of the state process which are known prior to fitting the model (if any). Default: NULL (states are not known). This should be a vector with length the number of rows of 'data'; each element should either be an integer (the value of the known states) or NA if the state is not known.

Value

Negative log-likelihood

Parameters definition

Description

Parameters definition

Usage

parDef(stepDist, angleDist, nbStates, estAngleMean, zeroInflation)
parDef(stepDist, angleDist, nbStates, estAngleMean, zeroInflation)

Arguments

`stepDist`	Name of the distribution of the step lengths.
`angleDist`	Name of the distribution of the turning angles. Set to `"none"` if the angle distribution should not be estimated.
`nbStates`	Number of states of the HMM.
`estAngleMean`	`TRUE` if the mean of the turning angles distribution is estimated, `FALSE` otherwise.
`zeroInflation`	`TRUE` if the step length distribution is inflated in zero.

Value

A list of:

`parSize`	Vector of two values: number of parameters of the step length distribution, number of parameters of the turning angle distribution
`bounds`	Matrix with 2 columns and `sum(parSize)` rows - each row contains the lower and upper bound for the correponding parameter)
`parNames`	Names of parameters of step distribution (the names of the parameters of the angle distribution are always the same).

Plot `moveData`

Description

Plot moveData

Usage

## S3 method for class 'moveData'
plot(x, animals = NULL, compact = FALSE, ask = TRUE, breaks = "Sturges", ...)
## S3 method for class 'moveData'
plot(x, animals = NULL, compact = FALSE, ask = TRUE, breaks = "Sturges", ...)

Arguments

`x`	An object `moveData`
`animals`	Vector of indices or IDs of animals for which information will be plotted. Default: `NULL` ; all animals are plotted.
`compact`	`TRUE` for a compact plot (all individuals at once), `FALSE` otherwise (default – one individual at a time).
`ask`	If `TRUE`, the execution pauses between each plot.
`breaks`	Histogram parameter. See `hist` documentation.
`...`	Currently unused. For compatibility with generic method.

Examples

# data is a moveData object (as returned by prepData), automatically loaded with the package
data <- example$data

plot(data,compact=TRUE,breaks=20,ask=FALSE)

# data is a moveData object (as returned by prepData), automatically loaded with the package
data <- example$data

plot(data,compact=TRUE,breaks=20,ask=FALSE)

Plot `moveHMM`

Description

Plot the fitted step and angle densities over histograms of the data, transition probabilities as functions of the covariates, and maps of the animals' tracks colored by the decoded states.

Usage

## S3 method for class 'moveHMM'
plot(
  x,
  animals = NULL,
  ask = TRUE,
  breaks = "Sturges",
  col = NULL,
  plotTracks = TRUE,
  plotCI = FALSE,
  alpha = 0.95,
  ...
)
## S3 method for class 'moveHMM'
plot(
  x,
  animals = NULL,
  ask = TRUE,
  breaks = "Sturges",
  col = NULL,
  plotTracks = TRUE,
  plotCI = FALSE,
  alpha = 0.95,
  ...
)

Arguments

`x`	Object `moveHMM`
`animals`	Vector of indices or IDs of animals for which information will be plotted. Default: `NULL`; all animals are plotted.
`ask`	If `TRUE`, the execution pauses between each plot.
`breaks`	Histogram parameter. See `hist` documentation. See `hist` documentation. Default: `NULL` ; the function sets default values.
`col`	Vector or colors for the states (one color per state).
`plotTracks`	If `TRUE`, the Viterbi-decoded tracks are plotted (default).
`plotCI`	If `TRUE`, confidence intervals are plotted on the transition probabilities (default: FALSE).
`alpha`	Significance level of the confidence intervals if plotCI=TRUE. Default: 0.95 (i.e. 95% CIs).
`...`	Currently unused. For compatibility with generic method.

Details

The state-dependent densities are weighted by the frequency of each state in the most probable state sequence (decoded with the function viterbi). For example, if the most probable state sequence indicates that one third of observations correspond to the first state, and two thirds to the second state, the plots of the densities in the first state are weighted by a factor 1/3, and in the second state by a factor 2/3.

Examples

# m is a moveHMM object (as returned by fitHMM), automatically loaded with the package
m <- example$m

plot(m,ask=TRUE,animals=1,breaks=20)

# m is a moveHMM object (as returned by fitHMM), automatically loaded with the package
m <- example$m

plot(m,ask=TRUE,animals=1,breaks=20)

Plot pseudo-residuals

Description

Plots time series, qq-plots (against the standard normal distribution), and sample ACF functions of the pseudo-residuals

Usage

plotPR(m)
plotPR(m)

Arguments

`m`	A `moveHMM` object

Details

If some turning angles in the data are equal to pi, the corresponding pseudo-residuals will not be included. Indeed, given that the turning angles are defined on (-pi,pi], an angle of pi results in a pseudo-residual of +Inf (check Section 6.2 of reference for more information on the computation of pseudo-residuals).
If some steps are of length zero (i.e. if there is zero-inflation), the corresponding pseudo- residuals are shown as segments, because pseudo-residuals for discrete data are defined as segments (see Zucchini and MacDonald, 2009, Section 6.2).

References

Zucchini, W. and MacDonald, I.L. 2009. Hidden Markov Models for Time Series: An Introduction Using R. Chapman & Hall (London).

Examples

# m is a moveHMM object (as returned by fitHMM), automatically loaded with the package
m <- example$m

plotPR(m)

# m is a moveHMM object (as returned by fitHMM), automatically loaded with the package
m <- example$m

plotPR(m)

Plot observations on satellite image

Description

Plot tracking data on a satellite map. This function only works with longitude and latitude values (not with UTM coordinates), and uses the package ggmap to fetch a satellite image from Google. An Internet connection is required to use this function.

Usage

plotSat(
  data,
  zoom = NULL,
  location = NULL,
  segments = TRUE,
  compact = TRUE,
  col = NULL,
  alpha = 1,
  size = 1,
  states = NULL,
  animals = NULL,
  ask = TRUE,
  return = FALSE
)
plotSat(
  data,
  zoom = NULL,
  location = NULL,
  segments = TRUE,
  compact = TRUE,
  col = NULL,
  alpha = 1,
  size = 1,
  states = NULL,
  animals = NULL,
  ask = TRUE,
  return = FALSE
)

Arguments

`data`	Data frame of the data, with necessary fields 'x' (longitude values) and 'y' (latitude values).
`zoom`	The zoom level, as defined for `get_map`. Integer value between 3 (continent) and 21 (building).
`location`	Location of the center of the map to be plotted.
`segments`	`TRUE` if segments should be plotted between the observations (default), `FALSE` otherwise.
`compact`	`FALSE` if tracks should be plotted separately, `TRUE` otherwise (default).
`col`	Palette of colours to use for the dots and segments. If not specified, uses default palette.
`alpha`	Transparency argument for `geom_point`.
`size`	Size argument for `geom_point`.
`states`	A sequence of integers, corresponding to the decoded states for these data (such that the observations are colored by states).
`animals`	Vector of indices or IDs of animals/tracks to be plotted. Default: `NULL`; all animals are plotted.
`ask`	If `TRUE`, the execution pauses between each plot.
`return`	If `TRUE`, the function returns a ggplot object (which can be edited and plotted manually). If `FALSE`, the function automatically plots the map (default).

Details

If the plot displays the message "Sorry, we have no imagery here", try a lower level of zoom.

References

D. Kahle and H. Wickham. ggmap: Spatial Visualization with ggplot2. The R Journal, 5(1), 144-161. URL: http://journal.r-project.org/archive/2013-1/kahle-wickham.pdf

Plot states

Description

Plot the states and states probabilities.

Usage

plotStates(m, animals = NULL, ask = TRUE)
plotStates(m, animals = NULL, ask = TRUE)

Arguments

`m`	A `moveHMM` object
`animals`	Vector of indices or IDs of animals for which states will be plotted.
`ask`	If `TRUE`, the execution pauses between each plot.

Examples

# m is a moveHMM object (as returned by fitHMM), automatically loaded with the package
m <- example$m

# plot states for first and second animals
plotStates(m,animals=c(1,2))

# m is a moveHMM object (as returned by fitHMM), automatically loaded with the package
m <- example$m

# plot states for first and second animals
plotStates(m,animals=c(1,2))

Plot stationary state probabilities

Description

Plot stationary state probabilities

Usage

plotStationary(m, col = NULL, plotCI = FALSE, alpha = 0.95)
plotStationary(m, col = NULL, plotCI = FALSE, alpha = 0.95)

Arguments

`m`	An object `moveHMM`
`col`	Vector or colors for the states (one color per state).
`plotCI`	Logical. Should 95% confidence intervals be plotted? (Default: FALSE)
`alpha`	Significance level of the confidence intervals if plotCI=TRUE. Default: 0.95 (i.e. 95% CIs).

Examples

# m is a moveHMM object (as returned by fitHMM), automatically loaded with the package
m <- example$m

plotStationary(m)

# m is a moveHMM object (as returned by fitHMM), automatically loaded with the package
m <- example$m

plotStationary(m)

Predict stationary state probabilities

Description

Predict stationary state probabilities

Usage

predictStationary(
  m,
  newData,
  beta = m$mle$beta,
  returnCI = FALSE,
  alpha = 0.95
)
predictStationary(
  m,
  newData,
  beta = m$mle$beta,
  returnCI = FALSE,
  alpha = 0.95
)

Arguments

`m`	Fitted moveHMM object, as returned by `fitHMM`
`newData`	Data frame with columns for the covariates
`beta`	Optional matrix of regression coefficients for the transition probability model. By default, uses estimates in `m`.
`returnCI`	Logical indicating whether confidence intervals should be returned. Default: FALSE.
`alpha`	Confidence level if returnCI = TRUE. Default: 0.95, i.e., 95% confidence intervals.

Value

List with elements 'mle', 'lci', and 'uci' (the last two only if returnCI = TRUE). Each element is a matrix of stationary state probabilities with one row for each row of newData and one column for each state.

Predict transition probabilities for new covariate values

Description

Predict transition probabilities for new covariate values

Usage

predictTPM(m, newData, beta = m$mle$beta, returnCI = FALSE, alpha = 0.95)
predictTPM(m, newData, beta = m$mle$beta, returnCI = FALSE, alpha = 0.95)

Arguments

`m`	Fitted moveHMM object, as returned by `fitHMM`
`newData`	Data frame with columns for the covariates
`beta`	Optional matrix of regression coefficients for the transition probability model. By default, uses estimates in `m`.
`returnCI`	Logical indicating whether confidence intervals should be returned. Default: FALSE.
`alpha`	Confidence level if returnCI = TRUE. Default: 0.95, i.e., 95% confidence intervals.

Value

List with elements 'mle', 'lci', and 'uci' (the last two only if returnCI = TRUE). Each element is an array, where each layer is a transition probability matrix corresponding to a row of newData.

Preprocessing of the tracking data

Description

Preprocessing of the tracking data

Usage

prepData(
  trackData,
  type = c("LL", "UTM"),
  coordNames = c("x", "y"),
  LLangle = NULL
)
prepData(
  trackData,
  type = c("LL", "UTM"),
  coordNames = c("x", "y"),
  LLangle = NULL
)

Arguments

`trackData`	A dataframe of the tracking data, including at least coordinates (either longitude/latitude values or cartesian coordinates), and optionnaly a field `ID` (identifiers for the observed individuals). Additionnal fields are considered as covariates. Note that, if the names of the coordinates are not "x" and "y", the `coordNames` argument should specified. Tracking data should be structured so that the rows for each track (or each animal) are grouped together, and ordered by date, in the data frame.
`type`	`'LL'` if longitude/latitude provided (default), `'UTM'` if easting/northing.
`coordNames`	Names of the columns of coordinates in the data frame. Default: `c("x","y")`.
`LLangle`	Logical. If TRUE, the turning angle is calculated with `geosphere::bearing` (default), else calculated with `atan2`.

Value

An object moveData, i.e. a dataframe of:

`ID`	The ID(s) of the observed animal(s)
`step`	The step lengths - in kilometers if longitude/latitude provided, and in the metrics of the data otherwise
`angle`	The turning angles (if any) - in radians
`x`	Either Easting or longitude (or e.g. depth for 1D data)
`y`	Either Northing or latitude (all zero if 1D data)
`...`	Covariates (if any)

Examples

coord1 <- c(1,2,3,4,5,6,7,8,9,10)
coord2 <- c(1,1,1,2,2,2,1,1,1,2)
trackData <- data.frame(coord1=coord1,coord2=coord2)
d <- prepData(trackData,type='UTM',coordNames=c("coord1","coord2"))

coord1 <- c(1,2,3,4,5,6,7,8,9,10)
coord2 <- c(1,1,1,2,2,2,1,1,1,2)
trackData <- data.frame(coord1=coord1,coord2=coord2)
d <- prepData(trackData,type='UTM',coordNames=c("coord1","coord2"))

Print `moveHMM`

Description

Print moveHMM

Usage

## S3 method for class 'moveHMM'
print(x, ...)
## S3 method for class 'moveHMM'
print(x, ...)

Arguments

`x`	A `moveHMM` object.
`...`	Currently unused. For compatibility with generic method.

Examples

# m is a moveHMM object (as returned by fitHMM), automatically loaded with the package
m <- example$m

print(m)

# m is a moveHMM object (as returned by fitHMM), automatically loaded with the package
m <- example$m

print(m)

Pseudo-residuals

Description

The pseudo-residuals of a moveHMM model, as described in Zucchini and McDonad (2009).

Usage

pseudoRes(m)
pseudoRes(m)

Arguments

`m`	A `moveHMM` object.

Details

If some turning angles in the data are equal to pi, the corresponding pseudo-residuals will not be included. Indeed, given that the turning angles are defined on (-pi,pi], an angle of pi results in a pseudo-residual of +Inf (check Section 6.2 of reference for more information on the computation of pseudo-residuals).

Value

A list of:

`stepRes`	The pseudo-residuals for the step lengths
`angleRes`	The pseudo-residuals for the turning angles

References

Zucchini, W. and MacDonald, I.L. 2009. Hidden Markov Models for Time Series: An Introduction Using R. Chapman & Hall (London).

Examples

# m is a moveHMM object (as returned by fitHMM), automatically loaded with the package
m <- example$m
res <- pseudoRes(m)
qqnorm(res$stepRes)
qqnorm(res$angleRes)

# m is a moveHMM object (as returned by fitHMM), automatically loaded with the package
m <- example$m
res <- pseudoRes(m)
qqnorm(res$stepRes)
qqnorm(res$angleRes)

Simulation tool

Description

Simulates movement data from an HMM.

Usage

simData(
  nbAnimals = 1,
  nbStates = 2,
  stepDist = c("gamma", "weibull", "lnorm", "exp"),
  angleDist = c("vm", "wrpcauchy", "none"),
  stepPar = NULL,
  anglePar = NULL,
  beta = NULL,
  covs = NULL,
  nbCovs = 0,
  zeroInflation = FALSE,
  obsPerAnimal = c(500, 1500),
  model = NULL,
  states = FALSE
)
simData(
  nbAnimals = 1,
  nbStates = 2,
  stepDist = c("gamma", "weibull", "lnorm", "exp"),
  angleDist = c("vm", "wrpcauchy", "none"),
  stepPar = NULL,
  anglePar = NULL,
  beta = NULL,
  covs = NULL,
  nbCovs = 0,
  zeroInflation = FALSE,
  obsPerAnimal = c(500, 1500),
  model = NULL,
  states = FALSE
)

Arguments

`nbAnimals`	Number of observed individuals to simulate.
`nbStates`	Number of behavioural states to simulate.
`stepDist`	Name of the distribution of the step lengths (as a character string). Supported distributions are: gamma, weibull, lnorm, exp. Default: gamma.
`angleDist`	Name of the distribution of the turning angles (as a character string). Supported distributions are: vm, wrpcauchy. Set to `"none"` if the angle distribution should not be estimated. Default: vm.
`stepPar`	Parameters of the step length distribution.
`anglePar`	Parameters of the turning angle distribution.
`beta`	Matrix of regression parameters for the transition probabilities (more information in "Details").
`covs`	Covariate values to include in the model, as a dataframe. Default: `NULL`. Covariates can also be simulated according to a standard normal distribution, by setting `covs` to `NULL`, and specifying `nbCovs>0`.
`nbCovs`	Number of covariates to simulate (0 by default). Does not need to be specified of `covs` is specified.
`zeroInflation`	`TRUE` if the step length distribution is inflated in zero. Default: `FALSE`. If `TRUE`, values for the zero-mass parameters should be included in `stepPar`.
`obsPerAnimal`	Either the number of the number of observations per animal (if single value), or the bounds of the number of observations per animal (if vector of two values). In the latter case, the numbers of obervations generated for each animal are uniformously picked from this interval. Default: `c(500,1500)`.
`model`	A moveHMM object. This option can be used to simulate from a fitted model. Default: NULL. Note that, if this argument is specified, most other arguments will be ignored – except for nbAnimals, obsPerAnimal, covs (if covariate values different from those in the data should be specified), and states.
`states`	`TRUE` if the simulated states should be returned, `FALSE` otherwise (default).

Details

The matrix beta of regression coefficients for the transition probabilities has one row for the intercept, plus one row for each covariate, and one column for each non-diagonal element of the transition probability matrix. For example, in a 3-state HMM with 2 covariates, the matrix beta has three rows (intercept + two covariates) and six columns (six non-diagonal elements in the 3x3 transition probability matrix - filled in row-wise). In a covariate-free model (default), beta has one row, for the intercept.
If the length of covariate values passed (either through 'covs', or 'model') is not the same as the number of observations suggested by 'nbAnimals' and 'obsPerAnimal', then the series of covariates is either shortened (removing last values - if too long) or extended (starting over from the first values - if too short).

Value

An object moveData, i.e. a dataframe of:

`ID`	The ID(s) of the observed animal(s)
`step`	The step lengths
`angle`	The turning angles (if any)
`x`	Either easting or longitude
`y`	Either northing or latitude
`...`	Covariates (if any)

Examples

# 1. Pass a fitted model to simulate from
# (m is a moveHMM object - as returned by fitHMM - automatically loaded with the package)
# We keep the default nbAnimals=1.
m <- example$m
obsPerAnimal=c(50,100)
data <- simData(model=m,obsPerAnimal=obsPerAnimal)

# 2. Pass the parameters of the model to simulate from
stepPar <- c(1,10,1,5,0.2,0.3) # mean1, mean2, sd1, sd2, z1, z2
anglePar <- c(pi,0,0.5,2) # mean1, mean2, k1, k2
stepDist <- "gamma"
angleDist <- "vm"
data <- simData(nbAnimals=5,nbStates=2,stepDist=stepDist,angleDist=angleDist,stepPar=stepPar,
               anglePar=anglePar,nbCovs=2,zeroInflation=TRUE,obsPerAnimal=obsPerAnimal)

stepPar <- c(1,10,1,5) # mean1, mean2, sd1, sd2
anglePar <- c(pi,0,0.5,0.7) # mean1, mean2, k1, k2
stepDist <- "weibull"
angleDist <- "wrpcauchy"
data <- simData(nbAnimals=5,nbStates=2,stepDist=stepDist,angleDist=angleDist,stepPar=stepPar,
               anglePar=anglePar,obsPerAnimal=obsPerAnimal)

# step length only and zero-inflation
stepPar <- c(1,10,1,5,0.2,0.3) # mean1, mean2, sd1, sd2, z1, z2
stepDist <- "gamma"
data <- simData(nbAnimals=5,nbStates=2,stepDist=stepDist,angleDist="none",stepPar=stepPar,
               nbCovs=2,zeroInflation=TRUE,obsPerAnimal=obsPerAnimal)

# include covariates
# (note that it is useless to specify "nbCovs", which is determined
# by the number of columns of "cov")
cov <- data.frame(temp=rnorm(500,20,5))
stepPar <- c(1,10,1,5) # mean1, mean2, sd1, sd2
anglePar <- c(pi,0,0.5,2) # mean1, mean2, k1, k2
stepDist <- "gamma"
angleDist <- "vm"
data <- simData(nbAnimals=5,nbStates=2,stepDist=stepDist,angleDist=angleDist,stepPar=stepPar,
                anglePar=anglePar,covs=cov)

# 1. Pass a fitted model to simulate from
# (m is a moveHMM object - as returned by fitHMM - automatically loaded with the package)
# We keep the default nbAnimals=1.
m <- example$m
obsPerAnimal=c(50,100)
data <- simData(model=m,obsPerAnimal=obsPerAnimal)

# 2. Pass the parameters of the model to simulate from
stepPar <- c(1,10,1,5,0.2,0.3) # mean1, mean2, sd1, sd2, z1, z2
anglePar <- c(pi,0,0.5,2) # mean1, mean2, k1, k2
stepDist <- "gamma"
angleDist <- "vm"
data <- simData(nbAnimals=5,nbStates=2,stepDist=stepDist,angleDist=angleDist,stepPar=stepPar,
               anglePar=anglePar,nbCovs=2,zeroInflation=TRUE,obsPerAnimal=obsPerAnimal)

stepPar <- c(1,10,1,5) # mean1, mean2, sd1, sd2
anglePar <- c(pi,0,0.5,0.7) # mean1, mean2, k1, k2
stepDist <- "weibull"
angleDist <- "wrpcauchy"
data <- simData(nbAnimals=5,nbStates=2,stepDist=stepDist,angleDist=angleDist,stepPar=stepPar,
               anglePar=anglePar,obsPerAnimal=obsPerAnimal)

# step length only and zero-inflation
stepPar <- c(1,10,1,5,0.2,0.3) # mean1, mean2, sd1, sd2, z1, z2
stepDist <- "gamma"
data <- simData(nbAnimals=5,nbStates=2,stepDist=stepDist,angleDist="none",stepPar=stepPar,
               nbCovs=2,zeroInflation=TRUE,obsPerAnimal=obsPerAnimal)

# include covariates
# (note that it is useless to specify "nbCovs", which is determined
# by the number of columns of "cov")
cov <- data.frame(temp=rnorm(500,20,5))
stepPar <- c(1,10,1,5) # mean1, mean2, sd1, sd2
anglePar <- c(pi,0,0.5,2) # mean1, mean2, k1, k2
stepDist <- "gamma"
angleDist <- "vm"
data <- simData(nbAnimals=5,nbStates=2,stepDist=stepDist,angleDist=angleDist,stepPar=stepPar,
                anglePar=anglePar,covs=cov)

State probabilities

Description

For a given model, computes the probability of the process being in the different states at each time point.

Usage

stateProbs(m)
stateProbs(m)

Arguments

`m`	A `moveHMM` object.

Value

The matrix of state probabilities, with element [i,j] the probability of being in state j in observation i.

References

Zucchini, W. and MacDonald, I.L. 2009. Hidden Markov Models for Time Series: An Introduction Using R. Chapman & Hall (London).

Examples

# m is a moveHMM object (as returned by fitHMM), automatically loaded with the package
m <- example$m

sp <- stateProbs(m)

# m is a moveHMM object (as returned by fitHMM), automatically loaded with the package
m <- example$m

sp <- stateProbs(m)

Stationary state probabilities

Description

Calculates the stationary probabilities of each state, for given covariate values.

Usage

stationary(m, covs, beta = m$mle$beta)
stationary(m, covs, beta = m$mle$beta)

Arguments

`m`	Fitted model (as output by `fitHMM`).
`covs`	Either a data frame or a design matrix of covariates.
`beta`	Optional matrix of regression coefficients for the transition probability model. By default, uses estimates in `m`.

Value

Matrix of stationary state probabilities. Each row corresponds to a row of covs, and each column corresponds to a state.

Examples

# m is a moveHMM object (as returned by fitHMM), automatically loaded with the package
m <- example$m

# data frame of covariates
stationary(m, covs = data.frame(cov1 = 0, cov2 = 0))

# design matrix (each column corresponds to row of m$mle$beta)
stationary(m, covs = matrix(c(1,0,cos(0)),1,3))

# m is a moveHMM object (as returned by fitHMM), automatically loaded with the package
m <- example$m

# data frame of covariates
stationary(m, covs = data.frame(cov1 = 0, cov2 = 0))

# design matrix (each column corresponds to row of m$mle$beta)
stationary(m, covs = matrix(c(1,0,cos(0)),1,3))

Summary `moveData`

Description

Summary moveData

Usage

## S3 method for class 'moveData'
summary(object, details = TRUE, ...)
## S3 method for class 'moveData'
summary(object, details = TRUE, ...)

Arguments

`object`	A `moveData` object.
`details`	`TRUE` if quantiles of the covariate values should be printed (default), `FALSE` otherwise.
`...`	Currently unused. For compatibility with generic method.

Examples

# m is a moveData object (as returned by prepData), automatically loaded with the package
data <- example$data

summary(data)

# m is a moveData object (as returned by prepData), automatically loaded with the package
data <- example$data

summary(data)

Transition probability matrix

Description

Computation of the transition probability matrix, as a function of the covariates and the regression parameters. Written in C++. Used in fitHMM, logAlpha, logBeta, plot.moveHMM, pseudoRes, and viterbi.

Usage

trMatrix_rcpp(nbStates, beta, covs)
trMatrix_rcpp(nbStates, beta, covs)

Arguments

`nbStates`	Number of states
`beta`	Matrix of regression parameters
`covs`	Matrix of covariate values

Value

Three dimensional array trMat, such that trMat[,,t] is the transition matrix at time t.

Turning angle

Description

Used in prepData.

Usage

turnAngle(x, y, z, LLangle)
turnAngle(x, y, z, LLangle)

Arguments

`x`	First point
`y`	Second point
`z`	Third point
`LLangle`	Logical. If TRUE, the turning angle is calculated with `geosphere::bearing`, else calculated with `atan2`.

Value

The angle between vectors (x,y) and (y,z)

Examples

## Not run: 
x <- c(0,0)
y <- c(4,6)
z <- c(10,7)
turnAngle(x,y,z,LLangle=FALSE)

## End(Not run)

## Not run: 
x <- c(0,0)
y <- c(4,6)
z <- c(10,7)
turnAngle(x,y,z,LLangle=FALSE)

## End(Not run)

Viterbi algorithm

Description

For a given model, reconstructs the most probable states sequence, using the Viterbi algorithm.

Usage

viterbi(m, newdata = NULL)
viterbi(m, newdata = NULL)

Arguments

`m`	An object `moveHMM`
`newdata`	An object `moveData` (optional)

Value

The sequence of most probable states.

References

Zucchini, W. and MacDonald, I.L. 2009. Hidden Markov Models for Time Series: An Introduction Using R. Chapman & Hall (London).

Examples

# m is a moveHMM object (as returned by fitHMM), automatically loaded with the package
m <- example$m

# reconstruction of states sequence
states <- viterbi(m)

# m is a moveHMM object (as returned by fitHMM), automatically loaded with the package
m <- example$m

# reconstruction of states sequence
states <- viterbi(m)

Scaling function: working to natural parameters

Description

Scales each parameter from the set of real numbers, back to its natural interval. Used during the optimization of the log-likelihood.

Usage

w2n(wpar, bounds, parSize, nbStates, nbCovs, estAngleMean, stationary)
w2n(wpar, bounds, parSize, nbStates, nbCovs, estAngleMean, stationary)

Arguments

`wpar`	Vector of state-dependent distributions unconstrained parameters.
`bounds`	Matrix with 2 columns and as many rows as there are elements in `wpar`. Each row contains the lower and upper bound for the correponding parameter.
`parSize`	Vector of two values: number of parameters of the step length distribution, number of parameters of the turning angle distribution.
`nbStates`	The number of states of the HMM.
`nbCovs`	The number of covariates.
`estAngleMean`	`TRUE` if the angle mean is estimated, `FALSE` otherwise.
`stationary`	`FALSE` if there are covariates. If TRUE, the initial distribution is considered equal to the stationary distribution. Default: `FALSE`.

Value

A list of:

`stepPar`	Matrix of natural parameters of the step length distribution
`anglePar`	Matrix of natural parameters of the turning angle distribution
`beta`	Matrix of regression coefficients of the transition probabilities
`delta`	Initial distribution

Examples

## Not run: 
nbStates <- 3
nbCovs <- 2
par <- c(0.001,0.999,0.5,0.001,1500.3,7.1)
parSize <- c(1,1)
bounds <- matrix(c(0,1,0,1,0,1,
                   0,Inf,0,Inf,0,Inf),
                 byrow=TRUE,ncol=2)
beta <- matrix(rnorm(18),ncol=6,nrow=3)
delta <- c(0.6,0.3,0.1)
wpar <- n2w(par,bounds,beta,delta,nbStates,FALSE)
print(w2n(wpar,bounds,parSize,nbStates,nbCovs,estAngleMean=FALSE,stationary=FALSE))

## End(Not run)


## Not run: 
nbStates <- 3
nbCovs <- 2
par <- c(0.001,0.999,0.5,0.001,1500.3,7.1)
parSize <- c(1,1)
bounds <- matrix(c(0,1,0,1,0,1,
                   0,Inf,0,Inf,0,Inf),
                 byrow=TRUE,ncol=2)
beta <- matrix(rnorm(18),ncol=6,nrow=3)
delta <- c(0.6,0.3,0.1)
wpar <- n2w(par,bounds,beta,delta,nbStates,FALSE)
print(w2n(wpar,bounds,parSize,nbStates,nbCovs,estAngleMean=FALSE,stationary=FALSE))

## End(Not run)

`x`	Vector of quantiles
`rate`	Rate
`foo`	Unused (for compatibility with template)

`x`	Vector of quantiles
`meanlog`	Mean of the distribution on the log-scale
`sdlog`	Standard deviation of the distribution on the log-scale

`x`	Vector of quantiles
`shape`	Shape
`scale`	Scale

Package 'moveHMM'

Help Index

AIC

Description

Usage

Arguments

Value

Examples

Confidence intervals for angle parameters

Description

Usage

Arguments

Value

Confidence intervals

Description

Usage

Arguments

Value

Examples

Exponential density function

Description

Usage

Arguments

Value

Gamma density function

Description

Usage

Arguments

Value

Log-normal density function

Description

Usage

Arguments

Value

Von Mises density function

Description

Usage

Arguments

Value

Weibull density function

Description

Usage

Arguments

Value

Wrapped Cauchy density function

Description

Usage

Arguments

Value

Elk data set from Morales et al. (2004, Ecology)

Description

Usage

Example dataset

Description

Usage

Details

Example data simulation

Description

Usage

Fit an HMM to the data

Description

Usage

Arguments

Details

Value

References

Examples

Discrete colour palette for states

Description

Usage

Arguments

Value

Data to produce plots of fitted model

Description

Usage

Arguments

Details

Value

Wild haggis data set from Michelot et al. (2016, Methods Eco Evol)

Description

Constructor of `moveData` objects

Constructor of `moveHMM` objects

Plot `moveData`

Plot `moveHMM`