CDS/MCDS Distance Detection Function Fitting

Fits a conventional distance sampling (CDS) (likelihood eq 6.6 in Laake and Borchers 2004) or multi-covariate distance sampling (MCDS)(likelihood eq 6.14 in Laake and Borchers 2004) model for the detection function of observed distance data. It only uses key functions and does not incorporate adjustment functions as in CDS/MCDS analysis engines in DISTANCE (Marques and Buckland 2004). Distance can be grouped (binned), ungrouped (unbinned) or mixture of the two. This function is not called directly by the user and is called from ddf,ddf.io, or ddf.trial.

Usage

# S3 method for class 'ds'
ddf(
  dsmodel,
  mrmodel = NULL,
  data,
  method = "ds",
  meta.data = list(),
  control = list(),
  call
)

Arguments

dsmodel: model list with key function and scale formula if any
mrmodel: not used
data: data.frame; see ddf for details
method: analysis method; only needed if this function called from ddf.io or ddf.trial
meta.data: list containing settings controlling data structure
control: list containing settings controlling model fitting
call: original function call if this function not called directly from ddf (e.g., called via ddf.io)

Value

result: a ds model object

Details

For a complete description of each of the calling arguments, see ddf. The argument model in this function is the same as dsmodel in ddf. The argument dataname is the name of the dataframe specified by the argument data in ddf. The arguments control,meta.data,and method are defined the same as in ddf.

Note

If mixture of binned and unbinned distance, width must be set to be >= largest interval endpoint; this could be changed with a more complicated analysis; likewise, if all binned and bins overlap, the above must also hold; if bins don't overlap, width must be one of the interval endpoints; same holds for left truncation Although the mixture analysis works in principle it has not been tested via simulation.

References

Laake, J.L. and D.L. Borchers. 2004. Methods for incomplete detection at distance zero. In: Advanced Distance Sampling, eds. S.T. Buckland, D.R. Anderson, K.P. Burnham, J.L. Laake, D.L. Borchers, and L. Thomas. Oxford University Press.

Marques, F.F.C. and S.T. Buckland. 2004. Covariate models for the detection function. In: Advanced Distance Sampling, eds. S.T. Buckland, D.R. Anderson, K.P. Burnham, J.L. Laake, D.L. Borchers, and L. Thomas. Oxford University Press.

Author

Jeff Laake

Examples


# ddf.ds is called when ddf is called with method="ds"
# \donttest{
data(book.tee.data)
region <- book.tee.data$book.tee.region
egdata <- book.tee.data$book.tee.dataframe
samples <- book.tee.data$book.tee.samples
obs <- book.tee.data$book.tee.obs
result <- ddf(dsmodel = ~mcds(key = "hn", formula = ~1),
              data = egdata[egdata$observer==1, ], method = "ds",
              meta.data = list(width = 4))
summary(result,se=TRUE)
#> 
#> Summary for ds object
#> Number of observations :  124 
#> Distance range         :  0  -  4 
#> AIC                    :  311.1385 
#> Optimisation           :  mrds (nlminb) 
#> 
#> Detection function:
#>  Half-normal key function 
#> 
#> Detection function parameters 
#> Scale coefficient(s): 
#>              estimate         se
#> (Intercept) 0.6632435 0.09981249
#> 
#>                        Estimate          SE         CV
#> Average p             0.5842744  0.04637627 0.07937412
#> N in covered region 212.2290462 20.85130344 0.09824906
plot(result,main="cds - observer 1")

print(dht(result,region,samples,obs,options=list(varflag=0,group=TRUE),
          se=TRUE))
#> Abundance and density estimates from distance sampling
#> Variance       : R2, binomial 
#> 
#> Summary statistics
#> 
#>   Region Area CoveredArea Effort   n  k        ER      se.ER      cv.ER
#> 1      1 1040        1040    130  72  6 0.5538462 0.02926903 0.05284685
#> 2      2  640         640     80  52  5 0.6500000 0.08292740 0.12758061
#> 3  Total 1680        1680    210 124 11 0.5904762 0.03641856 0.06167659
#> 
#> Summary for clusters
#> 
#> Abundance:
#>   Region  Estimate       se         cv       lcl      ucl df
#> 1      1 123.22977 13.54083 0.10988275  99.41771 152.7452  0
#> 2      2  88.99928 10.64090 0.11956159  70.46547 112.4078  0
#> 3  Total 212.22905 20.85130 0.09824906 175.13617 257.1780  0
#> 
#> Density:
#>   Region  Estimate         se         cv        lcl       ucl df
#> 1      1 0.1184902 0.01302002 0.10988275 0.09559396 0.1468704  0
#> 2      2 0.1390614 0.01662640 0.11956159 0.11010230 0.1756372  0
#> 3  Total 0.1263268 0.01241149 0.09824906 0.10424772 0.1530821  0
#> 
#> Summary for individuals
#> 
#> Abundance:
#>   Region Estimate       se        cv      lcl      ucl df
#> 1      1 391.9391 46.10793 0.1176405 311.4775 493.1858  0
#> 2      2 260.1517 33.65581 0.1293699 202.0987 334.8806  0
#> 3  Total 652.0909 67.40510 0.1033677 532.7888 798.1070  0
#> 
#> Density:
#>   Region  Estimate         se        cv       lcl       ucl df
#> 1      1 0.3768645 0.04433455 0.1176405 0.2994976 0.4742171  0
#> 2      2 0.4064871 0.05258720 0.1293699 0.3157792 0.5232509  0
#> 3  Total 0.3881493 0.04012208 0.1033677 0.3171362 0.4750637  0
#> 
#> Expected cluster size
#>   Region Expected.S se.Expected.S cv.Expected.S
#> 1      1   3.180556    0.13362415    0.04201283
#> 2      2   2.923077    0.14443673    0.04941257
#> 3  Total   3.072581    0.09870565    0.03212467
print(ddf.gof(result))

#> 
#> Goodness of fit results for ddf object
#> 
#> Chi-square tests
#>           [0,0.364] (0.364,0.727] (0.727,1.09] (1.09,1.45] (1.45,1.82]
#> Observed     25.000        13.000       12.000      22.000      12.000
#> Expected     19.181        18.522       17.270      15.549      13.518
#> Chisquare     1.765         1.646        1.608       2.677       0.170
#>           (1.82,2.18] (2.18,2.55] (2.55,2.91] (2.91,3.27] (3.27,3.64] (3.64,4]
#> Observed        8.000      12.000       7.000       8.000       4.000    1.000
#> Expected       11.348       9.199       7.200       5.442       3.972    2.799
#> Chisquare       0.988       0.853       0.006       1.202       0.000    1.156
#>             Total
#> Observed  124.000
#> Expected  124.000
#> Chisquare  12.071
#> 
#> P = 0.20932 with 9 degrees of freedom
#> 
#> Distance sampling Cramer-von Mises test (unweighted)
#> Test statistic = 0.0655753 p-value = 0.77897
# }