Fix parameters in single season heterogeneity

[kdennison]

I am attemping to use occupancy data collected from a camera trap array in order to estimate abundance of mountain lions. Running the abundance induced heterogeneity model produces extremely large estimates and confidence intervals for lambda and N. I believe this is due to a very low individual dectection probablility, resulting from few total observations. My question is: When is it appropriate to fix parameters, specifically "c"? I find that if I set "c" at the detection probability that is created from running other models (e.g. Single-season, 1 group, Constant P), then the model creates much more reasonable results.

Thank you for any help, or advice that you can provide. I'll post results from both tests below for reference.
~Katie

Total area of the study site is 342 square kilometers.

Running Model as is:
PRESENCE - Presence/Absence-Site Occupancy data analysis
Tue Jun 04 10:52:40 2013, Version 5.8_130315
- - - - - - - - - - - - - - - - - - - - - - - - - - - - -
==>i=groupedlocations_jantomarch.pao
==>l=pres_Abundance_Induced_Heterogeneity(Royle_Nichols_Het)_model.out
==>name=Abundance Induced Heterogeneity(Royle/Nichols Het) model
==>model=4100
==>j=f:\presence\groupedlocations_jantomarch_project\groupedlocations_jantomarch.dm
==>lmt=200
varcov: nsig=6 eps=1.000000e-002
model=4100 N,T-->12,18




********* Input Data summary *******
Number of sites = 12
Number of sampling occasions = 18
Number of missing observations = 0
Data checksum = 37141

NSiteCovs-->0
NSampCovs-->0
Primary periods=1 Secondary periods: 18
Naive occupancy estimate = 0.5000

- - - - - - - - - - - - - - - - - - - - - - - - - - - - -
groupedlocations jan-mar
- - - - - - - - - - - - - - - - - - - - - - - - - - - - -
N=12 T=18 Groups=1 bootstraps=0

-->1-18
Matrix 1: rows=2, cols=2
-,a1,
lambda 1
========================

Matrix 2: rows=19, cols=2
-,b1,
c(1) 1
c(2) 1
c(3) 1
c(4) 1
c(5) 1
c(6) 1
c(7) 1
c(8) 1
c(9) 1
c(10) 1
c(11) 1
c(12) 1
c(13) 1
c(14) 1
c(15) 1
c(16) 1
c(17) 1
c(18) 1
========================

Matrix 3: rows=0, cols=0
========================

Matrix 4: rows=0, cols=0
========================

Matrix 5: rows=0, cols=0
========================

Matrix 6: rows=0, cols=0
========================

modtype=4


Royle/Nichols Heterogeneity Model

Number of sites = 12
Number of sampling occasions = 18
Number of missing observations = 0

Number of parameters = 2


Number of parameters = 2
Number of function calls = 111
-2log(likelihood) = 61.7952
AIC = 65.7952
LikeNRSig=6 eps=0.01 ETA=1e-013

Untransformed Estimates of coefficients for covariates (Beta's)
======================================================================
estimate std.error
A1 lambda : 4.984163 7.839984
B1 c(1) : -8.396910 7.861688

============================================================

Individual Site estimates of <lambda>
Site estimate Std.err 95% conf. interval
lambda 1 site 1 :146.0812 1145.2744 0.0000 -688848493.1429

============================================================

Individual Site estimates of <c(1)>
Site estimate Std.err 95% conf. interval
c(1) 1 site 1 : 0.0002 0.0018 0.0000 - 0.9991
c(2) 1 site 1 : 0.0002 0.0018 0.0000 - 0.9991
c(3) 1 site 1 : 0.0002 0.0018 0.0000 - 0.9991
c(4) 1 site 1 : 0.0002 0.0018 0.0000 - 0.9991
c(5) 1 site 1 : 0.0002 0.0018 0.0000 - 0.9991
c(6) 1 site 1 : 0.0002 0.0018 0.0000 - 0.9991
c(7) 1 site 1 : 0.0002 0.0018 0.0000 - 0.9991
c(8) 1 site 1 : 0.0002 0.0018 0.0000 - 0.9991
c(9) 1 site 1 : 0.0002 0.0018 0.0000 - 0.9991
c(10) 1 site 1 : 0.0002 0.0018 0.0000 - 0.9991
c(11) 1 site 1 : 0.0002 0.0018 0.0000 - 0.9991
c(12) 1 site 1 : 0.0002 0.0018 0.0000 - 0.9991
c(13) 1 site 1 : 0.0002 0.0018 0.0000 - 0.9991
c(14) 1 site 1 : 0.0002 0.0018 0.0000 - 0.9991
c(15) 1 site 1 : 0.0002 0.0018 0.0000 - 0.9991
c(16) 1 site 1 : 0.0002 0.0018 0.0000 - 0.9991
c(17) 1 site 1 : 0.0002 0.0018 0.0000 - 0.9991
c(18) 1 site 1 : 0.0002 0.0018 0.0000 - 0.9991

============================================================

MODEL PARAMETERS:
Estimated parameter estimate std.err 95% confidence interval
-------------------------- -------- ------- ------------------------
Avg. abundance/sample unit(lambda) : 146.08 0.00 0.00 -688848493.14
Individual Detection prob c(1) : 0.0002 0.0018 -0.0032 - 0.0037
Individual Detection prob c(2) : 0.0002 0.0018 -0.0032 - 0.0037
Individual Detection prob c(3) : 0.0002 0.0018 -0.0032 - 0.0037
Individual Detection prob c(4) : 0.0002 0.0018 -0.0032 - 0.0037
Individual Detection prob c(5) : 0.0002 0.0018 -0.0032 - 0.0037
Individual Detection prob c(6) : 0.0002 0.0018 -0.0032 - 0.0037
Individual Detection prob c(7) : 0.0002 0.0018 -0.0032 - 0.0037
Individual Detection prob c(8) : 0.0002 0.0018 -0.0032 - 0.0037
Individual Detection prob c(9) : 0.0002 0.0018 -0.0032 - 0.0037
Individual Detection prob c(10) : 0.0002 0.0018 -0.0032 - 0.0037
Individual Detection prob c(11) : 0.0002 0.0018 -0.0032 - 0.0037
Individual Detection prob c(12) : 0.0002 0.0018 -0.0032 - 0.0037
Individual Detection prob c(13) : 0.0002 0.0018 -0.0032 - 0.0037
Individual Detection prob c(14) : 0.0002 0.0018 -0.0032 - 0.0037
Individual Detection prob c(15) : 0.0002 0.0018 -0.0032 - 0.0037
Individual Detection prob c(16) : 0.0002 0.0018 -0.0032 - 0.0037
Individual Detection prob c(17) : 0.0002 0.0018 -0.0032 - 0.0037
Individual Detection prob c(18) : 0.0002 0.0018 -0.0032 - 0.0037

Derived parameter estimate std.err 95% confidence interval
-------------------------- -------- ------- ------------------------
Occupancy (psi) : 1.0000 0.0000 0.0000 - 1.0000
Total Abundance (N) : 1752.97 13743.30 0.00 -8266181917.71
------------------------------------------------------
CPU time= 1.0 seconds

Running model with fixed c:
Number of missing observations = 0

Number of parameters = 2


Number of parameters = 2
Number of function calls = 31
-2log(likelihood) = 64.1597
AIC = 68.1597
LikeNRSig=6 eps=0.01 ETA=1e-013

Untransformed Estimates of coefficients for covariates (Beta's)
======================================================================
estimate std.error
A1 lambda : 0.189582 0.402697
B1 c(1) : 0.000000 10.000000

============================================================

Individual Site estimates of <lambda>
Site estimate Std.err 95% conf. interval
lambda 1 site 1 : 1.2087 0.4868 0.5490 - 2.6614

============================================================

Individual Site estimates of <c(1)>
Site estimate Std.err 95% conf. interval
c(1) : 0.0324 0.0000 0.0000 - 0.0000 fixed
c(2) : 0.0324 0.0000 0.0000 - 0.0000 fixed
c(3) : 0.0324 0.0000 0.0000 - 0.0000 fixed
c(4) : 0.0324 0.0000 0.0000 - 0.0000 fixed
c(5) : 0.0324 0.0000 0.0000 - 0.0000 fixed
c(6) : 0.0324 0.0000 0.0000 - 0.0000 fixed
c(7) : 0.0324 0.0000 0.0000 - 0.0000 fixed
c(8) : 0.0324 0.0000 0.0000 - 0.0000 fixed
c(9) : 0.0324 0.0000 0.0000 - 0.0000 fixed
c(10) : 0.0324 0.0000 0.0000 - 0.0000 fixed
c(11) : 0.0324 0.0000 0.0000 - 0.0000 fixed
c(12) : 0.0324 0.0000 0.0000 - 0.0000 fixed
c(13) : 0.0324 0.0000 0.0000 - 0.0000 fixed
c(14) : 0.0324 0.0000 0.0000 - 0.0000 fixed
c(15) : 0.0324 0.0000 0.0000 - 0.0000 fixed
c(16) : 0.0324 0.0000 0.0000 - 0.0000 fixed
c(17) : 0.0324 0.0000 0.0000 - 0.0000 fixed
c(18) : 0.0324 0.0000 0.0000 - 0.0000 fixed

============================================================

MODEL PARAMETERS:
Estimated parameter estimate std.err 95% confidence interval
-------------------------- -------- ------- ------------------------
Avg. abundance/sample unit(lambda) : 1.21 0.00 0.55 - 2.66
Individual Detection prob c(1) : 0.0324 0.0000 0.0324 - 0.0324
Individual Detection prob c(2) : 0.0324 0.0000 0.0324 - 0.0324
Individual Detection prob c(3) : 0.0324 0.0000 0.0324 - 0.0324
Individual Detection prob c(4) : 0.0324 0.0000 0.0324 - 0.0324
Individual Detection prob c(5) : 0.0324 0.0000 0.0324 - 0.0324
Individual Detection prob c(6) : 0.0324 0.0000 0.0324 - 0.0324
Individual Detection prob c(7) : 0.0324 0.0000 0.0324 - 0.0324
Individual Detection prob c(8) : 0.0324 0.0000 0.0324 - 0.0324
Individual Detection prob c(9) : 0.0324 0.0000 0.0324 - 0.0324
Individual Detection prob c(10) : 0.0324 0.0000 0.0324 - 0.0324
Individual Detection prob c(11) : 0.0324 0.0000 0.0324 - 0.0324
Individual Detection prob c(12) : 0.0324 0.0000 0.0324 - 0.0324
Individual Detection prob c(13) : 0.0324 0.0000 0.0324 - 0.0324
Individual Detection prob c(14) : 0.0324 0.0000 0.0324 - 0.0324
Individual Detection prob c(15) : 0.0324 0.0000 0.0324 - 0.0324
Individual Detection prob c(16) : 0.0324 0.0000 0.0324 - 0.0324
Individual Detection prob c(17) : 0.0324 0.0000 0.0324 - 0.0324
Individual Detection prob c(18) : 0.0324 0.0000 0.0324 - 0.0324

Derived parameter estimate std.err 95% confidence interval
-------------------------- -------- ------- ------------------------
Occupancy (psi) : 0.7014 0.1453 0.4225 - 0.9302
Total Abundance (N) : 14.50 5.84 6.59 - 31.94
------------------------------------------------------
CPU time= 1.0 seconds

[darryl]

It's not a good idea to be doing that as the detection probabilities have different defintions, one's for individuals while that other is for the species.

With a species specific detection rate that low am guessing that your psi estimate from the basic single season model is near 1? If so, then it may be that your data is too sparse to do much of a meaningful analysis on (sorry).

Cheers
Darryl