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Dear all,

I have already post my problem in another part of this forum, but my question is still without clear answer

My question could appear stupid but I do not succeed in finding any clear answer to this question neither on the mark book, nor on the forum, nor on the internet.

My question is quiet simple : Can I use environmental data (so shared by all individuals of a site) as an individual covariate?

My case :

On the one hand, we released 100 individually marked carabids on 5 sites and have done a survival analysis (CJS). Results give us a difference in survival among site (our prediction). For these analyses sites were treated as categorical variables.
On a second hand, some indices of fragmentation (numerical) were computed and we want to test if there is a correlation between these sites-level indices and survival. Is it possible to treat these indices as individual covariates? Is the pseudoreplication induce by this method make the slope estimation wrong?

The only answer I had (many thanks to him): "If you are interested in whether sites with similar fragmentation have similar survival, versus whether all sites, regardless of fragmentation levels have different survival you could simply use site as your “group” association and compare three models 1) All sites have equal survival. 2) All sites have different survival. 3) Sites with similar fragmentation metrics"

BUT : it seems to me that using fragmention as individual covariate do not answer to the same question (maybe I am wrong).
To be clear
The hypothesis tested with "group association" : Site with similar fragmentation have similar survival
The hypothesis tested with "environmental covariates" : A linear relation is existing between group survivals and fragmentation

Is it possible to use environmental covariates and answer to the second hypothesis? Could pseudoreplication be a problem to linear trend calculation and/or interpretation?

I pretty sure that my question is very stupid but could you confirm

many thanks in advance for the reply

stephane

Your question isn't stupid but it is not clearly stated. I believe what you are asking is the following:

Can I fit a model where the link function for survival is a linear function of fragmentation at the 5 sites?

Yes and that is different than fitting a ~group model or ~fragmentation where fragmentation is a factor variable. The ~group model would have 5 parameters and the ~fragmentation as a factor variable would have k parameters where k was the number of levels assigned to fragmentation. Now you can also fit a ~Fragmentation where Fragmentation is a numeric value and it will fit 2 parameters: an intercept at Fragmentation=0 and a slope for the link function. If you are using a logit link then survival will be

Phi=1/(1+exp(-a-b*Fragmentation))

where a is the intercept and b is the slope.

You are over-thinking this. There is no psuedo-replication issue. Imagine that your beetles were coin flips and the sites were different coins. Flipping the coin 100 times (beetles) provides the measure of the prob of heads or tails. The ~1 model would be all coins have the same probability, ~coin would be they all have a different probability and if the coins were weighted differently then ~Weight would say that the prob(heads) was a function of the Weight of the coin.

Now the only inferential issue you have is that you have very few sites and likely no replication at various fragmentation levels. Technically nothing wrong there but it just allows for the possibility that there is some other site level differences that are confounded with the fragmentation covariate. Also, if you think about regression, having an n=5 does not provide much ability to detect lack of fit to the linearity assumption.

Hope this clarification helps. --jeff

HI Jeff,

First, I am sorry if it was not clear at all but you succeed in understanding my question. Great job.

Second, yes your answer is very helpfull, thanks a lot

At last, I will copy and paste your answer in the other thread related to this subject

Stephane