real parameter estimates
Posted: Sat Mar 21, 2020 2:44 pmI have been reviewing documentation on marked and something that is not well documented and should be is that the real parameter estimates computed from compute.real and predict.crm are not adjusted for time interval length. This is only relevant to survival which is the only parameter that is scaled on time. Thus the survival estimates are always on the unit interval (eg annual if the unit is 1 year). Hopefully, this was obvious if you looked at beta estimates and computed the real values as a check. If it was not obvious, my sinceres apologies for any problems this may have caused. Below is an example that demonstrates the point. I am going to add an option to compute using time interval value.
- Code: Select all
data(dipper)
> dipper.proc=process.data(dipper,model="cjs",begin.time=1)
255 capture histories collapsed into 53
> dipper.ddl=make.design.data(dipper.proc)
> mod.Phit.p=crm(dipper.proc,dipper.ddl,
+ model.parameters=list(Phi=list(formula=~time),p=list(formula=~1)))
Computing initial parameter estimates
Starting optimization for 7 parameters...
Number of evaluations: 400 -2lnl: 660.2026972
Elapsed time in minutes: 0.0045
> mod.Phit.p
crm Model Summary
Npar : 7
-2lnL: 659.7301
AIC : 673.7301
Beta
Estimate
Phi.(Intercept) 0.514389842
Phi.time2 -0.698144440
Phi.time3 -0.600934471
Phi.time4 -0.006102359
Phi.time5 -0.075710457
Phi.time6 -0.178061661
p.(Intercept) 2.220394714
> predict(mod.Phit.p)
$Phi
time occ estimate
1 6 6 0.5832983
2 5 5 0.6079443
3 4 4 0.6244049
4 3 3 0.4783773
5 2 2 0.4541902
6 1 1 0.6258350
$p
occ estimate
1 7 0.9020661
>
> dipper.proc=process.data(dipper,model="cjs",begin.time=1,time.intervals=rep(.5,6))
255 capture histories collapsed into 53
> dipper.ddl=make.design.data(dipper.proc)
> mod.Phit.p=crm(dipper.proc,dipper.ddl,
+ model.parameters=list(Phi=list(formula=~time),p=list(formula=~1)))
Computing initial parameter estimates
Starting optimization for 7 parameters...
Number of evaluations: 400 -2lnl: 659.7391348
Elapsed time in minutes: 0.0038
> mod.Phit.p
crm Model Summary
Npar : 7
-2lnL: 659.7301
AIC : 673.7301
Beta
Estimate
Phi.(Intercept) -0.440804390
Phi.time1.5 -0.906580318
Phi.time2 -0.774014992
Phi.time2.5 -0.006985002
Phi.time3 -0.093134136
Phi.time3.5 -0.221426050
p.(Intercept) 2.220420652
> predict(mod.Phit.p)
$Phi
time occ estimate
1 3.5 6 0.3402388
2 3 5 0.3695988
3 2.5 4 0.3898865
4 2 3 0.2288494
5 1.5 2 0.2062983
6 1 1 0.3915493
$p
occ estimate
1 7 0.9020684
> 0.3402388^.5
[1] 0.5832999