dsdive.obstxmat.cov: Compute probability transition matrix for partially observed...
In jmhewitt/dsdive: Discrete Space Models for Dive Trajectories of Animals

Given model parameters, this function will compute the probability transition matrix for a Continuous time Markov chain (CTMC) that is observed once, and then again at a time of tstep units of time later. If include.raw==TRUE, then raw components of the probability transition matrix will be returned so that the transition matrix can be computed for arbitrary timesteps.

dsdive.obstxmat.cov(
  pi.designs,
  lambda.designs,
  beta1,
  beta2,
  alpha1,
  alpha2,
  alpha3,
  s0,
  ind,
  tstep,
  include.raw,
  depth.bins,
  delta
)

`pi.designs`	list of design matrices for the diving preference parameters by stage.
`lambda.designs`	list of design matrices for the diving speed parameters by stage.
`beta1`	coefficient values for linear model for logit(pi^(1)).
`beta2`	coefficient values for linear model for logit(pi^(3)).
`alpha1`	coefficient values for linear model for log(lambda^(1)).
`alpha2`	coefficient values for linear model for log(lambda^(2)).
`alpha3`	coefficient values for linear model for log(lambda^(3)).
`s0`	stage for which the transition matrix should be computed
`ind`	transition matrix is unique for each dive. The parameter `ind` specifies that the transition matrix should be computed for the dive associated with the covariates in row `ind` in the design matrices (see `pi.designs`, `lambda.designs`).
`tstep`	Time between observations of the CTMC
`include.raw`	`TRUE` to include raw components of the probability transition matrix so that the matrix can be computed for arbitrary timesteps
`depth.bins`	n x 2 Matrix that defines the depth bins. The first column defines the depth at the center of each depth bin, and the second column defines the half-width of each bin.
`delta`	If `delta>0`, then the observation matrix and raw components computed will be for a transition matrix whose generator is perturbed to allow much faster computation.

data('dive.sim')
attach(dive.sim)
attach(dive.sim$params)

beta1 = c(0, 0)
beta2 = c(0, 0)
alpha1 = c(0, 0)
alpha2 = c(0, 0)
alpha3 = c(0, 0)

covs = data.frame(x1 = c(.5, 1), x2 = c(0, .3))

pi.formula = ~x1
lambda.formula = ~x1:x2


#
# expand covariate design matrices
#

if(!inherits(pi.formula, 'list')) {
  pi.formula = list(pi.formula, pi.formula)
}

if(!inherits(lambda.formula, 'list')) {
  lambda.formula = list(lambda.formula, lambda.formula, lambda.formula)
}

pi.designs = lapply(pi.formula, function(f) model.matrix(f, covs))
lambda.designs = lapply(lambda.formula, function(f) model.matrix(f, covs))


#
# build transition matrix
#

m = dsdive.obstxmat.cov(
  pi.designs = pi.designs, lambda.designs = lambda.designs, beta1 = beta1, 
  beta2 = beta2, alpha1 = alpha1, alpha2 = alpha2, alpha3 = alpha3, s0 = 1, 
  ind = 1, tstep = 300, include.raw = TRUE, depth.bins = depth.bins, 
  delta = 1e-10)

detach(dive.sim$params)
detach(dive.sim)