How to compare process variance among age-classes?

[scha]

Dear all,

I have a statiscal question more than a modelling question.

Based on CMR model selection, I have strong evidence of senescence in my population of griffon vulture. So, I have split the age parameter in three age-classes -> young-adult-senescent.

According different evolutionary hypotheses, I would expect a higher temporal variance upon young and senescent age-classes than upon adult age class (long lived bird species).

I have used the process variance function implemented in Mark (I use RMArk) to achieve this analyse but I have a conceptual problem.
**Is it possible to compare variance among age classes?**
Indeed, although analyses gave the expected results (high variance for young and senescent age classes), I am not sure that these results are not biased by the fact that survival for young and senescent age-classes are lower.
The mean and the variance are mathematically linked and the variance of proportion data (as the survival estimates) is expected to be higher for value around 0.5.

So my question,
Is the analyse of variance process among age classes is not mathematically biaised?
Is Mark consider this mathematical link in the calculation of process variance?
If not, how can I consider this issue?

I have read and re-read the "variance component" part of the paper "ADVANCED FEATURES OF PROGRAM
MARK" but I am not sure to understand the calculation method in all his complexity.

Thank for the reply

Stephane

[cooch]

Dear all,

I have read and re-read the "variance component" part of the paper "ADVANCED FEATURES OF PROGRAM
MARK" but I am not sure to understand the calculation method in all his complexity.

Then I suggest reading/working through Appendix D of the 'MARK book', which is a significantly expanded version of what is presented in the paper you refer to:

http://www.phidot.org/software/mark/doc ... /app_4.pdf

[scha]

Thank for the reply and the link

Indeed, there is a lot of information in this appendix (I do not understand how I could miss it). However, I have not really found an answer to my previous question (which was poorly worded in the previous email I admit, the word bias was not used correctly).

I try again: To compare the variances calculated between different classes of ages (which differ in mean), do I need to scale the variances with the average?

For example to compare variance from several mixed models, the coefficient of variation can be calculated.
In MARK, Is there a way to compare variances that are calculated for survival with different mean ?

Until now, I calculated the variance processes in this way
1) I realize a model age-classes*time (Three age-classes)
2) I calculate the process variance by extracting the survival separately for each class of ages
 
Is there another (a better) method to calculate the variance process according to the ages-classes?

Thank in advance for the replies

Best
Stephane

[Rotella]

Morris & Doak (2004) discuss the use of relativized variances in the context of evaluating the demographic buffering hypothesis. Perhaps their ideas might be useful in your case. The paper's citation is:

Morris, W.F. & Doak, D.F. (2004) Buffering of life histories against environmental stochasticity: accounting for a spurious correlation between the variabilities of vital rates and their contributions to fitness. American Naturalist, 163, 579–590.

[cooch]

Thank for the reply and the link

Indeed, there is a lot of information in this appendix (I do not understand how I could miss it). However, I have not really found an answer to my previous question (which was poorly worded in the previous email I admit, the word bias was not used correctly).

No that you've found it, you now also need to read it - really read it. P. 35, middle paragraph:

Now let’s consider some random effects models. We’ll build 2 different models – one a simple
intercept only (mean)model,which would seem to be consistent with the strong support for the simple
time variation model {φt}, and one a model where survival is thought to vary randomly around a levels specific mean. In other words, we hypothesize μ(low)=μ(avg). We’ll assume, however, that σ2(low) = σ2(high). This is not directly testable using the moments-based variance components approach in MARK...

In other words, it is not currently possible to build a model using the moments approach where you test (by means of model selection) models with and without group effects. And age classes are, in fact, groups. So...

There are other conceptual challenges, and in theory, you could at least approach this using a Bayesian approach, but it would still be challenging.

[scha]

I have and especially this paragraphe .
Just, I was not sure to understand, it is not so simple when you are not an expert.

many thanks for your reply

Stephane