Distance sampling: Advanced topics

David L Miller

Recap

Line transects - general idea

  • Calculate average detection probability
    • using detection function (\( g(x) \))
  • \( \hat{p} = \int_0^w \frac{1}{w} g(x; \hat{\theta}) dx \)
  • \( \frac{1}{w} \) tells us about assumed density wrt line
    • uniform from the line (out to \( w \))

plot of chunk pi-y

Line transects - distances

  • Model drop-off using a detection function
  • Use extra information estimate \( \hat{N} \)
  • How should we adjust \( n \)? (inflate by \( n/\hat{p}) \))

Fitting detection functions

  • Using the package Distance
  • Need to have data setup a certain way
    • At least columns called object, distance
library(Distance)
df_hn <- ds(distdata, truncation=6000, adjustment = NULL)

Model summary

summary(df_hn)

Summary for distance analysis 
Number of observations :  132 
Distance range         :  0  -  6000 

Model : Half-normal key function 
AIC   : 2252.06 

Detection function parameters
Scale Coefficients:  
            estimate         se
(Intercept) 7.900732 0.07884776

                       Estimate          SE         CV
Average p             0.5490484  0.03662569 0.06670757
N in covered region 240.4159539 21.32287580 0.08869160

Plotting models

plot of chunk unnamed-chunk-2

plot(df_hn)

New stuff

Overview

Here we'll look at:

  • Model checking and selection
  • What else affects detection?
  • Estimating abundance and uncertainty
  • More R!

Why check models?

  • AIC best model can still be a terrible model
  • AIC only measures relative fit
  • Don't know if the model gives “sensible” answers

What to check?

  • Convergence
    • Fitting ended, but our model is not good
  • Monotonicity
    • Our model is “lumpy”
  • “Goodness of fit”
    • Our model sucks statistically
  • (Other sampling assumptions are also important!)

Convergence

Distance will warn you about this:

** Warning: Problems with fitting model. Did not converge**
Error in detfct.fit.opt(ddfobj, optim.options, bounds, misc.options) :
  No convergence.

This can be complicated, see ?"mrds-opt" for info.

Monotonicity

  • Only a problem with adjustments
  • check.mono can help
check.mono(df_hr$ddf)
[1] TRUE

Monotonicity (when it goes wrong)

plot of chunk checkmonobad

Goodness of fit