This function fits detection functions to line or point transect data and
then (provided that survey information is supplied) calculates abundance and
density estimates. The examples below illustrate some basic types of
analysis using ds().
ds(
data,
truncation = ifelse(is.null(cutpoints), ifelse(is.null(data$distend),
max(data$distance), max(data$distend)), max(cutpoints)),
transect = "line",
formula = ~1,
key = c("hn", "hr", "unif"),
adjustment = c("cos", "herm", "poly"),
order = NULL,
scale = c("width", "scale"),
cutpoints = NULL,
dht.group = FALSE,
monotonicity = ifelse(formula == ~1, "strict", "none"),
region.table = NULL,
sample.table = NULL,
obs.table = NULL,
convert.units = 1,
er.var = ifelse(transect == "line", "R2", "P3"),
method = "nlminb",
quiet = FALSE,
debug.level = 0,
initial.values = NULL,
max.adjustments = 5,
er.method = 2,
dht.se = TRUE
)a data.frame containing at least a column called distance or
a numeric vector containing the distances. NOTE! If there is a column
called size in the data then it will be interpreted as group/cluster size,
see the section "Clusters/groups", below. One can supply data as a "flat
file" and not supply region.table, sample.table and obs.table, see
"Data format", below and flatfile.
either truncation distance (numeric, e.g. 5) or percentage
(as a string, e.g. "15%"). Can be supplied as a list with elements left
and right if left truncation is required (e.g. list(left=1,right=20) or
list(left="1%",right="15%") or even list(left="1",right="15%")). By
default for exact distances the maximum observed distance is used as the
right truncation. When the data is binned, the right truncation is the
largest bin end point. Default left truncation is set to zero.
indicates transect type "line" (default) or "point".
formula for the scale parameter. For a CDS analysis leave
this as its default ~1.
key function to use; "hn" gives half-normal (default), "hr"
gives hazard-rate and "unif" gives uniform. Note that if uniform key is
used, covariates cannot be included in the model.
adjustment terms to use; "cos" gives cosine (default),
"herm" gives Hermite polynomial and "poly" gives simple polynomial.
"cos" is recommended. A value of NULL indicates that no adjustments are
to be fitted.
orders of the adjustment terms to fit (as a vector/scalar), the
default value (NULL) will select via AIC up to max.adjustments
adjustments. If a single number is given, that number is expanded to be
seq(term.min, order, by=1) where term.min is the appropriate minimum
order for this type of adjustment. For cosine adjustments, valid orders are
integers greater than 2 (except when a uniform key is used, when the minimum
order is 1). For Hermite polynomials, even integers equal or greater than 2
are allowed and for simple polynomials even integers equal or greater than 2
are allowed (though note these will be multiplied by 2, see Buckland et al,
2001 for details on their specification).
the scale by which the distances in the adjustment terms are
divided. Defaults to "width", scaling by the truncation distance. If the
key is uniform only "width" will be used. The other option is "scale":
the scale parameter of the detection
if the data are binned, this vector gives the cutpoints of
the bins. Ensure that the first element is 0 (or the left truncation
distance) and the last is the distance to the end of the furthest bin.
(Default NULL, no binning.) Note that if data has columns distbegin
and distend then these will be used as bins if cutpoints is not
specified. If both are specified, cutpoints has precedence.
should density abundance estimates consider all groups to
be size 1 (abundance of groups) dht.group=TRUE or should the abundance of
individuals (group size is taken into account), dht.group=FALSE. Default
is FALSE (abundance of individuals is calculated).
should the detection function be constrained for
monotonicity weakly ("weak"), strictly ("strict") or not at all
("none" or FALSE). See Monotonicity, below. (Default "strict"). By
default it is on for models without covariates in the detection function,
off when covariates are present.
data.frame with two columns:
Region.Label label for the region
Area area of the region
region.table has one row for each stratum. If there is no
stratification then region.table has one entry with Area corresponding
to the total survey area. If Area is omitted density estimates only are
produced.
data.frame mapping the regions to the samples
(i.e. transects). There are three columns:
Sample.Label label for the sample
Region.Label label for the region that the sample belongs to.
Effort the effort expended in that sample (e.g. transect length).
data.frame mapping the individual observations
(objects) to regions and samples. There should be three columns:
object unique numeric identifier for the observation
Region.Label label for the region that the sample belongs to
Sample.Label label for the sample
conversion between units for abundance estimation, see "Units", below. (Defaults to 1, implying all of the units are "correct" already.)
encounter rate variance estimator to use when abundance
estimates are required. Defaults to "R2" for line transects and "P3" for
point transects. See dht2 for more information and if more
complex options are required.
suppress non-essential messages (useful for bootstraps etc).
Default value FALSE.
print debugging output. 0=none, 1-3 increasing levels
of debugging output.
a list of named starting values, see
mrds-opt. Only allowed when AIC term selection is not
used.
maximum number of adjustments to try (default 5) only
used when order=NULL.
encounter rate variance calculation: default = 2 gives the method of Innes et al, using expected counts in the encounter rate. Setting to 1 gives observed counts (which matches Distance for Windows) and 0 uses binomial variance (only useful in the rare situation where study area = surveyed area). See dht.se for more details.
should uncertainty be calculated when using dht? Safe to leave as TRUE, used in bootdht.
a list with elements:
ddf a detection function model object.
dht abundance/density information (if survey region data was supplied,
else NULL)
Note that if the data contains a column named size, cluster size will be
estimated and density/abundance will be based on a clustered analysis of
the data. Setting this column to be NULL will perform a non-clustered
analysis (for example if "size" means something else in your dataset).
The right truncation point is by default set to be largest observed distance or bin end point. This is a default will not be appropriate for all data and can often be the cause of model convergence failures. It is recommended that one plots a histogram of the observed distances prior to model fitting so as to get a feel for an appropriate truncation distance. (Similar arguments go for left truncation, if appropriate). Buckland et al (2001) provide guidelines on truncation.
When specified as a percentage, the largest right and smallest left
percent distances are discarded. Percentages cannot be supplied when using
binned data.
For left truncation, there are two options: (1) fit a detection function to
the truncated data as is (this is what happens when you set left). This
does not assume that g(x)=1 at the truncation point. (2) manually remove
data with distances less than the left truncation distance -- effectively
move the centre line out to be the truncation distance (this needs to be
done before calling ds). This then assumes that detection is certain at
the left truncation distance. The former strategy has a weaker assumption,
but will give higher variance as the detection function close to the line
has no data to tell it where to fit -- it will be relying on the data from
after the left truncation point and the assumed shape of the detection
function. The latter is most appropriate in the case of aerial surveys,
where some area under the plane is not visible to the observers, but their
probability of detection is certain at the smallest distance.
Note that binning is performed such that bin 1 is all distances greater or equal to cutpoint 1 (>=0 or left truncation distance) and less than cutpoint 2. Bin 2 is then distances greater or equal to cutpoint 2 and less than cutpoint 3 and so on.
When adjustment terms are used, it is possible for the detection function to not always decrease with increasing distance. This is unrealistic and can lead to bias. To avoid this, the detection function can be constrained for monotonicity (and is by default for detection functions without covariates).
Monotonicity constraints are supported in a similar way to that described
in Buckland et al (2001). 20 equally spaced points over the range of the
detection function (left to right truncation) are evaluated at each round
of the optimisation and the function is constrained to be either always
less than it's value at zero ("weak") or such that each value is
less than or equal to the previous point (monotonically decreasing;
"strict"). See also check.mono.
Even with no monotonicity constraints, checks are still made that the
detection function is monotonic, see check.mono.
In extrapolating to the entire survey region it is important that the unit
measurements be consistent or converted for consistency. A conversion
factor can be specified with the convert.units variable. The values of
Area in region.table, must be made consistent with the units for
Effort in sample.table and the units of distance in the data.frame
that was analyzed. It is easiest if the units of Area are the square of
the units of Effort and then it is only necessary to convert the units of
distance to the units of Effort. For example, if Effort was entered
in kilometres and Area in square kilometres and distance in metres then
using convert.units=0.001 would convert metres to kilometres, density
would be expressed in square kilometres which would then be consistent with
units for Area. However, they can all be in different units as long as
the appropriate composite value for convert.units is chosen. Abundance
for a survey region can be expressed as: A*N/a where A is Area for
the survey region, N is the abundance in the covered (sampled) region,
and a is the area of the sampled region and is in units of Effort * distance. The sampled region a is multiplied by convert.units, so it
should be chosen such that the result is in the same units as Area. For
example, if Effort was entered in kilometres, Area in hectares (100m x
100m) and distance in metres, then using convert.units=10 will convert
a to units of hectares (100 to convert metres to 100 metres for distance
and .1 to convert km to 100m units).
One can supply data only to simply fit a detection function. However, if
abundance/density estimates are necessary further information is required.
Either the region.table, sample.table and obs.table data.frames can
be supplied or all data can be supplied as a "flat file" in the data
argument. In this format each row in data has additional information that
would ordinarily be in the other tables. This usually means that there are
additional columns named: Sample.Label, Region.Label, Effort and
Area for each observation. See flatfile for an example.
If column Area is omitted, a density estimate is generated but note that
the degrees of freedom/standard errors/confidence intervals will not match
density estimates made with the Area column present.
If abundance estimates are required then the data.frames region.table
and sample.table must be supplied. If data does not contain the columns
Region.Label and Sample.Label then the data.frame obs.table must
also be supplied. Note that stratification only applies to abundance
estimates and not at the detection function level.
For more advanced abundance/density estimation please see the
dht and dht2 functions.
Examples of distance sampling analyses are available at http://examples.distancesampling.org/.
Hints and tips on fitting (particularly optimisation issues) are on the
mrds-opt manual page.
Buckland, S.T., Anderson, D.R., Burnham, K.P., Laake, J.L., Borchers, D.L., and Thomas, L. (2001). Distance Sampling. Oxford University Press. Oxford, UK.
Buckland, S.T., Anderson, D.R., Burnham, K.P., Laake, J.L., Borchers, D.L., and Thomas, L. (2004). Advanced Distance Sampling. Oxford University Press. Oxford, UK.
flatfile, AIC.ds, ds.gof,
p_dist_table, plot.ds,
add_df_covar_line
# NOT RUN {
# An example from mrds, the golf tee data.
library(Distance)
data(book.tee.data)
tee.data <- subset(book.tee.data$book.tee.dataframe, observer==1)
ds.model <- ds(tee.data, 4)
summary(ds.model)
plot(ds.model)
# }
# NOT RUN {
# same model, but calculating abundance
# need to supply the region, sample and observation tables
region <- book.tee.data$book.tee.region
samples <- book.tee.data$book.tee.samples
obs <- book.tee.data$book.tee.obs
ds.dht.model <- ds(tee.data, 4, region.table=region,
sample.table=samples, obs.table=obs)
summary(ds.dht.model)
# specify order 2 cosine adjustments
ds.model.cos2 <- ds(tee.data, 4, adjustment="cos", order=2)
summary(ds.model.cos2)
# specify order 2 and 3 cosine adjustments, turning monotonicity
# constraints off
ds.model.cos23 <- ds(tee.data, 4, adjustment="cos", order=c(2, 3),
monotonicity=FALSE)
# check for non-monotonicity -- actually no problems
check.mono(ds.model.cos23$ddf, plot=TRUE, n.pts=100)
# include both a covariate and adjustment terms in the model
ds.model.cos2.sex <- ds(tee.data, 4, adjustment="cos", order=2,
monotonicity=FALSE, formula=~as.factor(sex))
# check for non-monotonicity -- actually no problems
check.mono(ds.model.cos2.sex$ddf, plot=TRUE, n.pts=100)
# truncate the largest 10% of the data and fit only a hazard-rate
# detection function
ds.model.hr.trunc <- ds(tee.data, truncation="10%", key="hr",
adjustment=NULL)
summary(ds.model.hr.trunc)
# compare AICs between these models:
AIC(ds.model)
AIC(ds.model.cos2)
AIC(ds.model.cos23)
# }
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