Using time-covariates on age models

[scha]

Hi all,

I am currently running models with Rmark to investigate senescence on birds and more particulary effet of climat on bird aging.
I have 6 age groups ([0,1) [1,2) [2,3) [3,4) [4,28) [28,37];I start at age 0). I wish to test the effect of time covariates (Tmax for example) only on the two last age classes. To separately use each age class, I have created 6 age variables like that

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vaut.ddl.age$S$a0=0
vaut.ddl.age$S$a0[vaut.ddl.age$S$Age==0]=1
vaut.ddl.age$S$a1=0
vaut.ddl.age$S$a1[vaut.ddl.age$S$Age==1]=1
vaut.ddl.age$S$a2=0
vaut.ddl.age$S$a2[vaut.ddl.age$S$Age==2]=1
vaut.ddl.age$S$a3=0
vaut.ddl.age$S$a3[vaut.ddl.age$S$Age==3]=1
vaut.ddl.age$S$a4_28=0
vaut.ddl.age$S$a4_28[vaut.ddl.age$S$age_covar=="[4,28)"]=1
vaut.ddl.age$S$a28_37=0
vaut.ddl.age$S$a28_37[vaut.ddl.age$S$age_covar=="[28,37]"]=1

So I am able to build age model with this kind of function

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S.age=list(formula=~-1+a0+a1+a2+a3+a4_28+a28_37)

1) I want to know if there is a linear trend between survival of the last age class and a time covariate (Tmax) so I have done

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S.age1=list(formula=~-1+a0+a1+a2+a3+a4_28+a28_37:Tmax)

2) Same thing thes two last age class

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S.age2=list(formula=~-1+a0+a1+a2+a3+a4_28:Tmax+a28_37:Tmax)

My questions :
- Is it the correct to model the effect of covariate on age classes in this way? I think there is an intercept problem!!
- Is the model 2 correspond to an interaction model between Tmax and the two last age classes? I think that I also have an intercept problem (because I should estimate two intercepts and two slopes and I do not have parameter fot the intercepts).
- How can I test an additive effect of Tmax on the two last age classes (different intercept but one slope)

thanks and sorry in advance for my unclear English and my poor knowlegde of covariates models

Stephane

[jlaake]

My questions :
- Is it the correct to model the effect of covariate on age classes in this way? I think there is an intercept problem!!

The following model should be fine:

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S.age=list(formula=~-1+a0+a1+a2+a3+a4_28+a28_37)

but there is no reason for you to specify dummy values for age here and would be more concisely written as

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S.age=list(formula=~age_covar)

Note the subtle difference between the two models above. In the first, each age effect is independent of the other, whereas in the second, the first level (age 0) will be the intercept and the remaining betas are added to the intercept. You should get the same real parameters but the betas will differ.

- Is the model 2 correspond to an interaction model between Tmax and the two last age classes? I think that I also have an intercept problem (because I should estimate two intercepts and two slopes and I do not have parameter fot the intercepts).

Yes you do have an intercept problem here because you removed the overall intercept and then only specified a slope for Tmax for the last age class, so the last age class has no value at Tmax=0. The formula should be:

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S.age=list(formula=~age_covar+a28_37:Tmax)

and

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S.age=list(formula=~age_covar+a4_28:Tmax+a28_37:Tmax)

- How can I test an additive effect of Tmax on the two last age classes (different intercept but one slope)

It is easiest to do this by adding another level to the age variable which collapses the 2 age bins:

In your design data, add:

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vaut.ddl.age$S$a4_37=0
vaut.ddl.age$S$a4_37[vaut.ddl.age$S$age_covar=="[28,37]"|vaut.ddl.age$S$age_covar=="[4,28)"]=1


Then the following function will give you a single slope but different intercepts:

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S.age=list(formula=~age_covar+a4_37:Tmax)

Note that I have no easy way to test my code above so it could contain typos and I have used S.age throughout and you want to make those different. I highly recommend that you use model.matrix with the design data so you can see what DM the formula is creating and it will help you improve your knowledge in building these models.

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DM=model.matrix(~age_covar+a4_37:Tmax,vaut.ddl.age$S)


--jeff

[scha]

Hi Jeff

I am happy to know that I was wrong but that I was closed to the good formulation

Your reply are very clear and helpful, thank you so much

Stephane