Interpreting CT-DS results

[Verity Miles]

Hi,

I am looking for some advice on interpreting my results as I have had conflicting information from several sources and I want to make sure I am understanding this correctly.

I've used the distance package in R to estimate density, obtaining these results:

Density estimates from distance sampling Stratification : geographical Variance : P2, n/L Multipliers : creation Sample fraction : 0.1041667 Summary statistics: .Label Area CoveredArea Effort n k ER se.ER cv.ER Total 2.2967 2057.82 128331292 1034 147 0 0 0.201 Density estimates: .Label Estimate se cv LCI UCI df Total 2.4622 0.53 0.215 1.6176 3.7479 191.206 Component percentages of variance: .Label Detection ER Multipliers Total 7.12 87.34 5.54

I've then produced bootstrap estimates using bootdht, obtaining these results:

Bootstrap results Boostraps : 999 Successes : 999 Failures : 0 median mean se lcl ucl cv Dhat 4.23 4.37 1.22 2.62 6.79 0.29

Which density estimate and SE should I use - the boostrapped results (median) ?

Many thanks,

Verity 

[Eric Rexstad]

Morning Verity

My email client has made quite a mess of the dht2 output you cut and pasted, so it's a bit difficult to read. However, this addresses your specific questions:

• the bootstrap is used for measuring precision of your estimates. The measures of central tendency generated by bootdht​ aren't intended for inclusion in your report.  Hence, use the point estimate coming from dht2​ and the standard error and/or confidence interval produced by bootdht​.
  

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Sent: 15 October 2023 14:21
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Subject: [distance-sampling] Interpreting CT-DS results

 

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[Eric Howe]

Good day,

When the difference in point estimates from dht2 and bootdht are large as in Verity's case, the confidence interval reported by bootdht may not be useful because it's centered on the boostrap mean. Similarly, the magnitude of the bootdht SE is affected by the magnitude of the bootdht mean estimate. However, one can calculate a new symmetrical or (preferably) log-normal confidence interval from the dht2 point estimate and the CV reported by bootdht. The bootstrap CV (0.29) is larger than the analytic CV (0.215) so will inflate the confidence interval and avoid potential underestimation of variance by the analytical method (due to potentially severe overdispersion) as intended. 

Eric R, please correct me if this is wrong:

Calculate an SE around the dht2 point estimate as: 

dht2 Estimate * bootdht CV, so

2.466 * 0.29 = 0.714; this is larger than the analytic SE (avoids underestimation of variance) but smaller than the SE around the higher bootdht estimate (because it's scaled to the smaller dht2 point estimate).

Now you have an SE appropriate to your dht2 point estimate and your bootstrap precision, and you can calculate log-normal confidence limits following the Buckland et al. distance sampling books, e.g. Buckland et al. (2001) p. 77, or Buckland et al. (2015) p. 107

-e

[Verity Miles]

My query has been solved so I am posting the soltuion here in case it's of use to anyone. 

In this example, enquring about the appropriate results to report led to another question: why I have such different results from the point estimate producted by dht2 and the results of the bootstrap - specifically, the confidence interval bounds provided by the bootstrap did not include the point estimate produced by my actual analysis.  Furthermore, the median of the bootstrap replicate estimates (4.23) was nearly twice the estimate produced by the original analysis (2.46).

This was caused by a misunderstanding of how to include the activity parameter. When fitting the activity model, I limited the data to night time observations (for a nocurnal species). This meant I had only estimated the activity level at night, not over the whole period cameras were operational. For more info:

Cameras always operate 24 hours per day, but the time interval during which you estimate activity should match the daily survey duration used to define the survey duration component of effort (T sub k). The activity analysis was bounded (6 p.m. to 8 a.m.), so you estimated the proportion of the 14-hour nighttime that animals were active, which would be high, and not representative of the proportion of time they are active over a 24 hour day. You might have effectively told the software that animals were active for 50.4% of the entire 24-hour day, when really they're only active for 50.4% of your 14 hour interval.  This would cause overestimation of activity level/temporal effort (I think by a factor of 24/14 or 1.714), and proportional underestimation of density.

Removing the bounds and fitting the model to data from the 24h activity cycle fixed the issue. My results are now:

Results from dht2:

Estimate    se        cv       LCI       UCI        df

4.4396       0.739  0.166  3.2045  6.1509   187.619

Results from bootdht :

median  mean   se      lcl       ucl     cv

4.83       4.89     0.83   3.47   6.74   0.17

And it is now apropriate to report the precision estimates (CI, SE, CV) from `bootdht`.

Thanks to Eric R and Eric H for your help!