Interpreting the eigen value of a population matrix (2nd try)

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Interpreting the eigen value of a population matrix (2nd try)

Anouk Simard
Thanks for telling me that you could not get my message, I hope this work
better...

so my question was:

I built a population matrix to which I applied the fonction eigen in order
to find the main parameters about my population. I know that the first
eigen value correspond to lambda or exponential growth rate of my
population. My problem is that I want to have the 95% confidence interval
of the specific lambda (1.056 in the case). Is there a way to do that? Are
the other eigen value shown in the output could help me doing it.
I would very appreciate any help.
Thanks for your time

$values
[1] 1.0561867+0.0000000i 0.0749653+0.5249157i 0.0749653-0.5249157i
[4] 0.4498348+0.0795373i 0.4498348-0.0795373i -0.3357868+0.0000000i
$vectors
[1,] -0.72849129+0i -0.11058308+0.3293511i -0.11058308-0.3293511i
0.00244042+0.03012017i 0.00244042-0.03012017i
[2,] -0.41384232+0i 0.35124594+0.1765638i 0.35124594-0.1765638i
0.01004458+0.03839895i 0.01004458-0.03839895i
[3,] -0.27427879+0i 0.29630718-0.4260863i 0.29630718+0.4260863i
0.02540181+0.05526223i 0.02540181-0.05526223i
[4,] -0.34274458+0i -0.62502691+0.0000000i -0.62502691+0.0000000i
0.55688585-0.17705587i 0.55688585+0.17705587i
[5,] -0.31754610+0i 0.19351247+0.1625154i 0.19351247-0.1625154i
-0.73460380+0.00000000i -0.73460380+0.00000000i
[6,] -0.06705781+0i -0.00340804-0.0295753i -0.00340804+0.0295753i
0.30711075+0.13557984i 0.30711075-0.13557984i

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Re: Interpreting the eigen value of a population matrix (2nd try)

Simon Blomberg-4
To get a confidence interval on lambda, you need to have measures of variability in the elements of the transition matrix. If you have that, you can use a parametric bootstrap to get approximate confidence intervals. I have done this, and it seems to work. Alternatively, you could calculate a Bayesian posterior density for lambda using the Bayesian melding methods developed by Adrian Raftery et al., and calculate an HPD interval from that. I've done that too. It's slightly more difficult, however.

Simon.

Simon Blomberg, BSc (Hons), PhD, MAppStat.
Lecturer and Consultant Statistician
Faculty of Biological and Chemical Sciences
The University of Queensland
St. Lucia Queensland 4072
Australia
T: +61 7 3365 2506
email: S.Blomberg1_at_uq.edu.au

Policies:
1.  I will NOT analyse your data for you.
2.  Your deadline is your problem.

The combination of some data and an aching desire for
an answer does not ensure that a reasonable answer can
be extracted from a given body of data. - John Tukey.



-----Original Message-----
From: [hidden email] on behalf of Anouk Simard
Sent: Wed 29/08/2007 1:17 AM
To: [hidden email]
Subject: [R] Interpreting the eigen value of a population matrix (2nd try)
 
Thanks for telling me that you could not get my message, I hope this work
better...

so my question was:

I built a population matrix to which I applied the fonction eigen in order
to find the main parameters about my population. I know that the first
eigen value correspond to lambda or exponential growth rate of my
population. My problem is that I want to have the 95% confidence interval
of the specific lambda (1.056 in the case). Is there a way to do that? Are
the other eigen value shown in the output could help me doing it.
I would very appreciate any help.
Thanks for your time

$values
[1] 1.0561867+0.0000000i 0.0749653+0.5249157i 0.0749653-0.5249157i
[4] 0.4498348+0.0795373i 0.4498348-0.0795373i -0.3357868+0.0000000i
$vectors
[1,] -0.72849129+0i -0.11058308+0.3293511i -0.11058308-0.3293511i
0.00244042+0.03012017i 0.00244042-0.03012017i
[2,] -0.41384232+0i 0.35124594+0.1765638i 0.35124594-0.1765638i
0.01004458+0.03839895i 0.01004458-0.03839895i
[3,] -0.27427879+0i 0.29630718-0.4260863i 0.29630718+0.4260863i
0.02540181+0.05526223i 0.02540181-0.05526223i
[4,] -0.34274458+0i -0.62502691+0.0000000i -0.62502691+0.0000000i
0.55688585-0.17705587i 0.55688585+0.17705587i
[5,] -0.31754610+0i 0.19351247+0.1625154i 0.19351247-0.1625154i
-0.73460380+0.00000000i -0.73460380+0.00000000i
[6,] -0.06705781+0i -0.00340804-0.0295753i -0.00340804+0.0295753i
0.30711075+0.13557984i 0.30711075-0.13557984i

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Re: Interpreting the eigen value of a population matrix (2nd try)

Ben Bolker
Simon Blomberg <s.blomberg1 <at> uq.edu.au> writes:

>
> To get a confidence interval on lambda, you need to have measures of
variability in the elements of the
> transition matrix. If you have that, you can use a parametric bootstrap to get
approximate confidence
> intervals. I have done this, and it seems to work. Alternatively, you could
calculate a Bayesian
> posterior density for lambda using the Bayesian melding methods developed by
Adrian Raftery et al., and
> calculate an HPD interval from that. I've done that too. It's slightly more
difficult, however.
>
> Simon.

   Or use the delta method:

Skalski, John R., Joshua J. Millspaugh, Peter Dillingham, and Rebecca A.
Buchanan. 2007. Calculating the variance of the finite rate of population change
from a matrix model in Mathematica. Environmental Modelling & Software 22, no. 3
(March): 359-364.
http://www.sciencedirect.com/science/article/B6VHC-4JMM5XY-1/2/a698149bc3798c273766cfacdf40bba5
(accessed August 29, 2007).

  I've written a little bit of generic delta-method code, but I don't
know if it's this generic.

  Ben Bolker

______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.