nLL: nLL - Negative log likelihood of distances

Description

Return the negative log likelihood of observed detection distances given a likelihood and the estimated parameters.

Usage

nLL(a, ml)

Value

A scalar, the negative of the log likelihood evaluated at parameters a.

Arguments

a: A vector of likelihood parameter values. Length and meaning depend on ml$series and ml$expansions. If no expansion terms were called for (i.e., ml$expansions = 0), the distance likelihood contain one or two canonical parameters (see Details). If one or more expansions are called for, coefficients for the expansion terms follow coefficients for the canonical parameters. i.e., length of this vector is (num Covars incl. intercept) + expansions + 1*(like %in% c("hazrate")).
ml: Either a Rdistance 'model frame' or an Rdistance 'fitted object'. Both are of class "dfunc". Rdistance 'model frames' are lists containing components necessary to estimate a distance function, but no estimates. Rdistance 'model frames' are typically produced by calls to parseModel. Rdistance 'fitted objects' are typically produced by calls to dfuncEstim. 'Fitted objects' are 'model frames' with additional components such as the parameters estimates, log likelihood value, convergence information, and the variance- covariance matrix of the parameters.

Details

Expansion Terms: If ml$expansions = k (k > 0), the expansion function specified by ml$series is called (see for example cosine.expansion). Assuming $h_{ij}(x)$ is the $j^{th}$ expansion term for the $i^{th}$ distance and that $c_1, c_2, \dots, c_k$ are (estimated) coefficients for the expansion terms, the likelihood contribution for the $i^{th}$ distance is, $$f(x|a,b,c_1,c_2,\dots,c_k) = f(x|a,b)(1 + \sum_{j=1}^{k} c_j h_{ij}(x)).$$

Examples

Run this code

set.seed(238642)

d <- rnorm(1000, mean = 0, sd = 40)
d <- units::set_units(d[0 <= d], "m")

# Min info in model list to compute likelihood
ml <- list(
    mf = model.frame(d ~ 1) 
  , likelihood = "halfnorm"
  , expansions = 0
  , w.lo = units::set_units(0, "m")
  , w.hi = units::set_units(125, "m")
  , outputUnits = units(units::set_units(1,"m"))
  , x.scl = units::set_units(0,"m")
  , g.x.scl = 1
  , data = 1
)
attr(ml$data, "transType") <- "line"
class(ml) <- "dfunc"
nLL(log(40), ml)

# Another way, b/c we have pnorm()
ones <- matrix(1, nrow = length(d), ncol = 1)
l <- halfnorm.like(log(40), d, ones)
scaler <-(pnorm(units::drop_units(ml$w.hi)
  , units::drop_units(ml$w.lo)
  , sd = l$params) - 0.5) * sqrt(2*pi) * l$params
-sum(log(l$L.unscaled/scaler))

# A third way, b/c we have pnorm() and dnorm(). 
l2 <- dnorm(units::drop_units(d), mean = 0, sd = 40)
scaler2 <- pnorm(125, mean = 0, sd = 40) - 0.5 
-sum(log(l2/scaler2))