View source: R/halfnorm.like.R
halfnorm.like  R Documentation 
This function computes the likelihood contributions for sighting distances, scaled appropriately, for use as a distance likelihood.
halfnorm.like(
a,
dist,
covars = NULL,
w.lo = units::set_units(0, "m"),
w.hi = max(dist),
series = "cosine",
expansions = 0,
scale = TRUE,
pointSurvey = FALSE
)
a 
A vector of likelihood parameter values. Length and
meaning depend on 
dist 
A numeric vector containing the observed distances. 
covars 
Data frame containing values of covariates at
each observation in 
w.lo 
Scalar value of the lowest observable distance.
This is the left truncation of sighting distances
in 
w.hi 
Scalar value of the largest observable distance.
This is the right truncation of sighting distances
in 
series 
A string specifying the type of expansion to use.
Currently, valid values are 'simple', 'hermite', and 'cosine'; but, see

expansions 
A scalar specifying the number of terms
in 
scale 
Logical scalar indicating whether or not to
scale the likelihood so it integrates to 1. This parameter is
used to stop recursion in other functions. If 
pointSurvey 
Boolean. TRUE if distances in 
The halfnormal likelihood is
f(xa) = \exp(x^2 / (2*a^2))
where a
is the parameter to be estimated.
Some halfnormal distance functions in the literature
do not use a "2" in the
denominator of the exponent. Rdistance
uses a
"2" in the denominator of the exponent to make quantiles of this
function agree with
the standard normal which means a can be interpreted as a
normal standard error. e.g., approximately 95% of all observations
will occur between 0 and 2a.
Expansion Terms: If expansions
= k (k > 0), the expansion function specified by 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(xa,b,c_1,c_2,\dots,c_k) = f(xa,b)(1 + \sum_{j=1}^{k} c_j h_{ij}(x)).
f(xa,b,c_1,c_2,...,c_k) = f(xa,b)(1 + c(1) h_i1(x) + c(2) h_i2(x) + ... + c(k) h_ik(x)).
A numeric vector the same length and order as dist
containing the
likelihood contribution for corresponding distances in dist
.
Assuming L
is the returned vector from one of these functions,
the negative log likelihood of all the data is sum(log(L), na.rm=T)
.
Note that the returned likelihood value for distances less
than w.lo
or greater than w.hi
is NA
,
hence na.rm=TRUE
in the sum.
If scale
= TRUE, the integral of the likelihood from
w.lo
to w.hi
is 1.0. If scale
= FALSE,
the integral of the likelihood is something else.
Values are always greater than or equal to zero.
dfuncEstim
,
hazrate.like
,
uniform.like
,
negexp.like
,
Gamma.like
## Not run:
set.seed(238642)
x < seq(0, 100, length=100)
# Plots showing effects of changes in parameter Sigma
plot(x, halfnorm.like(20, x), type="l", col="red")
plot(x, halfnorm.like(40, x), type="l", col="blue")
# Estimate 'halfnorm' distance function
a < 5
x < rnorm(1000, mean=0, sd=a)
x < x[x >= 0]
dfunc < dfuncEstim(x~1, likelihood="halfnorm")
plot(dfunc)
# evaluate the log Likelihood
L < halfnorm.like(dfunc$parameters, dfunc$detections$dist, covars=dfunc$covars,
w.lo=dfunc$w.lo, w.hi=dfunc$w.hi,
series=dfunc$series, expansions=dfunc$expansions,
scale=TRUE)
sum(log(L), na.rm=TRUE) # the negative log likelihood
## End(Not run)
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