## AICc and effective sample size

questions concerning analysis/theory using programs M-SURGE, E-SURGE and U-CARE

### AICc and effective sample size

Hello,

I have a question about AICc and effective sample size in E-surge.

If I am not mistaken, AICc = AIC + 2k(k+1)/(n-k-1)
with k = number of parameters and n = effective sample size.

I read in a previous post (http://www.phidot.org/forum/viewtopic.php?f=5&t=1597&p=4636&hilit=sample+size#p4636) that the effective sample size is: total number of capture - number of animals retired.

But it does not seem to be the case.
If I use a dataset with no individuals retired, I manage to calculate the AICc and I find the same value as in the E-surge output.
But if some individuals are retired (RC=-1) then:
the values are different if I use n = total captures - number of individuals retired,
but the values are similar with n = total captures + number of individuals retired.

Could you confirm that the effective sample size used in E-surge is total number of captures + number of individuals retired? Or am I using a wrong formula?

Thank you,
Josefa
jbleu

Posts: 8
Joined: Tue Feb 19, 2013 10:20 am

### Re: AICc and effective sample size

Hello Josefa,
You are right. E-SURGE didn't show the AICc with removed individuals as AICc = AIC + 2k(k+1)/(n-k-1)
with n = total captures - number of individuals retired, due to a bug.
It will be corrected in the next version of E-SURGE.
Thank you very much and sorry for this disturbance.
Rémi
CHOQUET

Posts: 211
Joined: Thu Nov 24, 2005 4:58 am
Location: CEFE, Montpellier, FRANCE.

### Re: AICc and effective sample size

Hello,
No problem and thank you for your answer.
Josefa
jbleu

Posts: 8
Joined: Tue Feb 19, 2013 10:20 am

### Re: AICc and effective sample size

Could anyone clarify what the "number of animals retired" is?

I am trying to reach the same AICc values calculated by E-SURGE, but I have not succeeded. I am guessing we are calculating the effective sample size differently. I did not find the effective sample size in any outputs from E-SURGE to check if this is really the case.

Thank you!
wisc88

Posts: 9
Joined: Mon Nov 06, 2017 11:35 am

### Re: AICc and effective sample size

Hi,

I am pretty sure this problem does not apply to the current version of E-SURGE (2.1.2).
Regarding your question about the number of retired animals (look for "removed" in the E-SURGE manual), these are individuals that at a certain capture session are removed from the population. This is a relatively frequent situation, for instance when the population of study is used to repopulate others (e.g. think of rabbits). In that case, for the line of the removed individual you will have a -1 in the "RC:" column if you are using the Headed Format or in at the end of your line if you are using the inp format (e.g. "1010 -1;" means that the individual was first captured in the first occasion, recaptured and removed in the third).
simone77

Posts: 148
Joined: Mon Aug 10, 2009 2:52 pm

### Re: AICc and effective sample size

Hello,
I am probably missing something stupid.
My dataset has 942 marked individuals, 341 individuals of which were recaptured. Zero individuals were removed.
I ran a model with 10 mathematical parameters (estimated rank =10). E-SURGE gave me an AIC value of 5065.9012 and AICc of 5066.0302.

When I replace the values in the AICc formula, I don't reach the same result as E-SURGE.
AICc = AIC + 2k(k+1)/(n-k-1)
AICc = 5065.9012 + 20*11 / 931
AICc = 5066.1375

By the way, my version of E-surge is even more recent 2.1.4.
wisc88

Posts: 9
Joined: Mon Nov 06, 2017 11:35 am

### Re: AICc and effective sample size

wisc88 wrote:Hello,
I am probably missing something stupid.
My dataset has 942 marked individuals, 341 individuals of which were recaptured. Zero individuals were removed.
I ran a model with 10 mathematical parameters (estimated rank =10). E-SURGE gave me an AIC value of 5065.9012 and AICc of 5066.0302.

When I replace the values in the AICc formula, I don't reach the same result as E-SURGE.
AICc = AIC + 2k(k+1)/(n-k-1)
AICc = 5065.9012 + 20*11 / 931
AICc = 5066.1375

By the way, my version of E-surge is even more recent 2.1.4.

Try working backwards. Take the AICc that E-SURGE reports, and figure out what the effective sample size must have been used in those calculations. My guess is that is where the difference arises. What is the correct 'effective sample' size is a matter of some debate -- it could be total number of individuals, or, number of Bernouli trials, or some hybrid. For example, for CJS models, program MARK uses the number
of animals released and re-released as the effective sample size, because these releases form Bernoulli trials. Similarly for dead recoveries and known fate data types. Difficulties arise for models that have different types of parameters – what constitutes the ‘effective sample size’ for these data types is an open question. For example, consider patch occupancy models – ψ (the overall proportion of patches occupied) has a different sample size than the encounter probability, p: ψ is based on the number of patches, whereas p is based on the number of visits to patches.

I'm not sure what approach E-SURGE uses but you could at least get some insight(s), based on working backwards, as suggested.
cooch

Posts: 1356
Joined: Thu May 15, 2003 4:11 pm
Location: Cornell University

### Re: AICc and effective sample size

Hi Cooch, thank you for the idea!
I have done that. The sample size I estimated while working backwards from the provided AICc is higher than mine! This even allowing for the fact that E-SURGE gives QAICc, which should add one parameter to the total.
So, with the same values as before:
5066.0302 = 5065.9012 + (2*(10+1))*((10+1)+1)/(n - (10+1)-1)
0.129 = 21*12 / (n-10)
(n-10) = 252 / 0.129
n = 1953.488 +10
n = 1963.488

or (not adding 1 parameter due to c-hat correction):
5066.0302 = 5065.9012 + 20*11/(n - 11)
n = 1716.426

For now, I will rely on my hand calculations with the effective sample size equal to total sample size, but it would be nice if someone could still clarify this.
wisc88

Posts: 9
Joined: Mon Nov 06, 2017 11:35 am

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