LaMa (version 3.1.0)

statedens: State-dependent densities of one data stream

Description

Builds the matrix of state-dependent densities (or probabilities) of one data stream, as used in the allprobs matrix of forward. Several data streams that are conditionally independent given the state are combined by multiplying their matrices.

Usage

statedens(x, dens, ..., nStates = NULL, log = FALSE)

Value

matrix of dimension c(nObs, nStates)

Arguments

x

vector of observations of length nObs, possibly containing NAs

dens

density function, e.g. dnorm, dgamma2 or dvm, with the observations as first argument

...

parameters of dens, see ‘Details’

nStates

number of states. Only needed if all parameters are single values.

log

logical; if TRUE, log-densities are returned

Details

Each parameter in ... can be

• a single value, used for all states,

• a vector of length nStates, one value per state, or

• a matrix of dimension c(nObs, nStates), one value per observation and state, e.g. from a regression on covariates.

Missing observations contribute nothing to the likelihood, so their rows are 1 (0 with log = TRUE). As each data stream gets its own matrix, a missing value in one stream does not remove the observations of the others.

With log = TRUE, the log-densities are returned, to be added over data streams and used with forward(..., logspace = TRUE). They are computed by dens(..., log = TRUE) if dens has an argument log, otherwise as log(dens(...)) (e.g. for densities from zero_inflate).

In obj$simulate() of RTMB, x is registered as data and simulated by forward, see simulate.LaMaModel.

Writing the loop over states by hand is equally valid and gives the same result. statedens() is just a shortcut.

Examples

step <- trex$step[1:200]
angle <- trex$angle[1:200]
mu <- c(0.3, 2.5); sigma <- c(0.2, 1.5); kappa <- c(0.2, 1.5)

# one data stream
allprobs <- statedens(step, dgamma2, mu, sigma)

# the same by hand
allprobs2 <- matrix(1, length(step), 2)
ind <- which(!is.na(step))
for(j in 1:2) allprobs2[ind, j] <- dgamma2(step[ind], mu[j], sigma[j])
all.equal(allprobs, allprobs2)

# two data streams, mean of the turning angle the same in both states
allprobs <- statedens(step, dgamma2, mu, sigma) * statedens(angle, dvm, 0, kappa)

# on the log scale, for forward(..., logspace = TRUE)
logprobs <- statedens(step, dgamma2, mu, sigma, log = TRUE) +
  statedens(angle, dvm, 0, kappa, log = TRUE)