How to derive a encounter rate variance

[Takahashi Megumi]

Hi all,

I have been learning how to calculate the encounter rate variance of MCDS in dht().

Can I ask how to derive a variance-covariance matrix for the component of the encounter rate (dht_output$individuals$vc$er)?

According to the tutorial of the "mrds" package, the encounter rate variance can be computed by default using the encounter rate estimator Nhat/L (varflag=2).
I tried to calculate variance for each region mainly based on the following equation (Miller et al., 2019), but these are not consistent with the variance obtained from dht()

 ,

but these are not consistent with the variance obtained from dht().

The values of Nchat and Nchat_k were obtained from dht's output (dht_output$individuals$bysample %>% filter(region == "XXX")).

Also, the K (number of transects in a region) and L (total lengths of the K transects in a region = Effort) were obtained from dht's summary output (dht_output$individuals$summary).

Any guidance will be greatly appreciated.

Best,

Megumi

[Eric Rexstad]

Megumi

Thanks for your question and welcome to the list. I will investigate if you will provide some additional details.

Are you using MCDS or mrds to fit your detection function; you mention MCDS in the first line, but then make reference to the mrds​ package.

Are you calling ddf​ and then sending the resulting fitted model to dht​?

You are also using the default encounter rate estimator of Innes et al (2002) using Nhat/L as the estimate of encounter rate, correct?

Let me know a few more details, off-list if you wish, and I will examine further.

---

From: distance...@googlegroups.com <distance...@googlegroups.com> on behalf of Takahashi Megumi <margare...@gmail.com>
Sent: 29 May 2024 08:25
To: distance-sampling <distance...@googlegroups.com>
Subject: [distance-sampling] How to derive a encounter rate variance

 

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[Takahashi Megumi]

Dear Eric,

I appreciate your response and suggestion.

> Are you using MCDS or mrds to fit your detection function; you mention MCDS in the first line, but then make reference to the mrds package.

I‘m using MCDS to fit the detection function.

>Are you calling ddf and then sending the resulting fitted model to dht?

Yes, I am calling ddf and then sending the resulting fitted model to dht.

model1 <- ddf(method = ddf.method,
                     data = DDFdat,
                     dsmodel = ~ mcds(key = "hn", formula = ~schoolsize+beaufort),
                     meta.data = list(width=3))

>You are also using the default encounter rate estimator of Innes et al (2002) using Nhat/L as the estimate of encounter rate, correct?

Yes. I am using the default encounter rate in ddf and do not add any changes shown as below.

N_est <- dht(model1,
                   region.table = region.table1,
                   sample.table = sample.table1,
                   obs.table = obs.table1,
                   se=TRUE)

For a few more details, I would like to contact you off-list.

Thank you,

Megumi