Ideally the model will estimate Survival, Psi and the derived parameters Residency Time and Abundance all time-varying because we would like to monitor these parameters over time. I've tried several models and this one appears the best supported by the data, but as it has many poorly estimated parameters, I think the AIC may be incorrect because the inestimable parameters aren't counted. Can you suggest how to find AIC in this situation?
Once I have found the 'best' (lowest AIC/as close to the ideal as we can get/no estimation problems) I will use MCMC to get estimates robust to sampling variation.
I think that since the poorly estimated parameters are close to 0 or 1 this show problems with estimation near the boundary, and not confounding, which I think the constant Psi in 'nest to skip' has taken care of. Then finding the profile likelihood CI of the cloned data would be the next step.
This is the model specification:
- a. MSORD: multi-state open robust design. Two states, nest and skip.
a. S: 2 ageclass survival (transients & residents), time-varying.
b. Psi: time-varying 'nest to skip' transition probabilities but constant 'skip to nest' to avoid parameter confounding.
c. p, pent & phi probability of zero in the skipped state.
d. all other parameters time-varying.
In RMark:
- Code: Select all
tagging_test<-convert.inp("tagging.inp") # 15 years, 5 secondary occasions each
t.int<-c(rep(c(0,0,0,0,1),14),c(0,0,0,0))
ordms.process<-process.data(tagging_test,model="ORDMS",time.interval=t.int,begin.time=2005, strata.labels=c("1","2")) # 2 states; 1 nest; 2 skip
ordms.ddl=make.design.data(ordms.process)
# transient/resident effect on Survival
ordms.ddl=add.design.data(ordms.process,ordms.ddl,parameter="S",type="age",right=FALSE,bins=c(0,0.5,13),name="ageclass",replace=TRUE)
# parameter indexes for fixing values to 0.
up=as.numeric(row.names(ordms.ddl$p[ordms.ddl$p$stratum=="2",]))
upent=as.numeric(row.names(ordms.ddl$pent[ordms.ddl$pent$stratum=="2",]))
uphi=as.numeric(row.names(ordms.ddl$Phi[ordms.ddl$Phi$stratum=="2",]))
# Survival
S.a2.time=list(formula=~-1+ageclass:time) # time-varying 2 ageclass survival
# Transition probabilities
Psi.dot.time=list(formula=~-1+to1+to2:time)
p.time.time=list(formula=~-1+time:session:stratum,fixed=list(index=up,value=0))
pent.time.time=list(formula=~-1+time:session:stratum,fixed=list(index=upent,value=0))
Phi.time.time=list(formula=~-1+time:session:stratum,fixed=list(index=uphi,value=0))
These are the poorly estimated parameters:
95% Confidence Interval
[list=] Parameter Estimate Standard Error Lower Upper
-------------------------- -------------- -------------- -------------- --------------
11:S s1 g1 c2005 a10 t2 0.9996639 0.0053729 0.7291067E-10 1.0000000
13:S s1 g1 c2005 a12 t2 1.0000000 0.2552875E-06 0.9999995 1.0000005
27:Phi s1 g1 c1 a0 s200 1.0000000 0.1681379E-06 0.9999997 1.0000003
28:Phi s1 g1 c1 a0 s200 1.0000000 0.1443151E-04 0.1239199E-289 1.0000000
30:Phi s1 g1 c1 a0 s200 1.0000000 0.0000000 1.0000000 1.0000000
28:Phi s1 g1 c1 a0 s200 1.0000000 0.1443151E-04 0.1239199E-289 1.0000000
30:Phi s1 g1 c1 a0 s200 1.0000000 0.0000000 1.0000000 1.0000000
38:Phi s1 g1 c1 a0 s200 1.0000000 0.2656015E-05 0.9999948 1.0000052
47:Phi s1 g1 c1 a0 s201 1.0000000 0.0000000 1.0000000 1.0000000
54:Phi s1 g1 c1 a0 s201 1.0000000 0.4262330E-05 0.9999916 1.0000083
55:Phi s1 g1 c1 a0 s201 1.0000000 0.0000000 1.0000000 1.0000000
56:Phi s1 g1 c1 a0 s201 1.0000000 0.0000000 1.0000000 1.0000000
59:Phi s1 g1 c1 a0 s201 1.0000000 0.0000000 1.0000000 1.0000000
65:Phi s1 g1 c1 a0 s201 1.0000000 0.0000000 1.0000000 1.0000000
71:Phi s1 g1 c1 a0 s201 1.0000000 0.0000000 1.0000000 1.0000000
73:Phi s1 g1 c1 a0 s201 1.0000000 0.4715585E-06 0.9999991 1.0000009
78:Phi s1 g1 c1 a0 s201 0.9999999 0.4220431E-04 0.7254796E-301 1.0000000
79:Phi s1 g1 c1 a0 s201 0.9999709 0.0030372 0.5979220E-84 1.0000000
89:p s1 g1 s2006 t3 0.5214649 0.0000000 0.5214649 0.5214649
91:p s1 g1 s2006 t5 1.0000000 0.0000000 1.0000000 1.0000000
147:p s1 g1 s2018 t1 1.0000000 0.7081960E-05 0.3379634E-300 1.0000000
336:pent s1 g1 a0 s2005 0.5686495E-56 0.0000000 0.5686495E-56 0.5686495E-56
338:pent s1 g1 a0 s2005 0.4545653E-63 0.7364965E-60 -0.1443079E-59 0.1443988E-59
342:pent s1 g1 a0 s2006 0.4259980E-11 0.1122624E-08 -0.2196084E-08 0.2204604E-08
346:pent s1 g1 a0 s2007 0.1141971E-20 0.0000000 0.1141971E-20 0.1141971E-20
354:pent s1 g1 a0 s2009 0.1142761E-03 0.0000000 0.1142761E-03 0.1142761E-03
356:pent s1 g1 a0 s2010 0.3884196E-05 0.5456457E-03 0.1026143E-124 1.0000000
358:pent s1 g1 a0 s2010 0.1767426E-07 0.4032951E-05 0.1034506E-201 1.0000000
360:pent s1 g1 a0 s2011 0.7211397E-40 0.1853445E-36 -0.3632031E-36 0.3633474E-36
368:pent s1 g1 a0 s2013 0.6005180E-10 0.0000000 0.6005180E-10 0.6005180E-10 372:pent s1 g1 a0 s2014 0.2564095E-07 0.8951283E-05 0.1770696E-304 1.0000000
373:pent s1 g1 a0 s2014 0.5904186E-12 0.0000000 0.5904186E-12 0.5904186E-12
376:pent s1 g1 a0 s2015 0.3842264E-06 0.1344566E-03 0.5111796E-304 1.0000000
378:pent s1 g1 a0 s2015 0.5558775E-10 0.0000000 0.5558775E-10 0.5558775E-10
380:pent s1 g1 a0 s2016 0.1954978E-07 0.4965941E-05 0.1172356E-223 1.0000000
384:pent s1 g1 a0 s2017 0.1519375E-20 0.6520015E-18 -0.1276403E-17 0.1279442E-17
390:pent s1 g1 a0 s2018 0.6985258E-64 0.1156272E-60 -0.2265594E-60 0.2266991E-60
95% Confidence Interval
Grp. Str. Ses. N-hat Standard Error Lower Upper
---- ---- ---- -------------- -------------- -------------- --------------
1 1 2 1468.0061 0.0000000 1468.0061 1468.0061 [/list]
Many thanks!