I am creating resource selection functions to examine habitat selection using radio telemetry data and 1:1 paired logistic regression models. Habitat features at each telemetry point are paired with a single measure of the availability of those features that is unique to a particular telemetry point. I first fit models using R's glm function by differencing the used and available points and fitting a no-intercept glm:
glm(point ~ -1 + diffx1 + diffx2 + diffx3 ... diffxn, data, family=binomial)
I have also fit the same model using the survival package's clogit/coxph functions. In this case, each 1:1 pair of used/available points is grouped into a stratum:
clogit(point ~ x1 + x2 + x3 ... xn + strata(pair), data)
I have 16 covariates and some of these are correlated. However, when I calculate pair-wise correlation coefficients and variance inflation factors I get different results depending on whether I use the differenced data used to fit the glm or the original data used to fit the clogit/coxph. Both glm and clogit/coxph give me identical results but the different degrees of collinearity have a strong influence on the resulting analyses.
Does anyone have a recommendation of which form the data (differenced or original) I should use for assessing collinearity.
Many thanks!
As I know, there is col-linearity if a variance inflation factor is >3. You can find it in the book 'Statistics for Biology and Health' co-authored by M. Gail, K. Krickeberg, J. M. Samet , A. Tsiatis and W. Wong, published in 2009.
Thanks for your reply Xiaoguang! I understand that you can use variance inflation factors (VIFs) to see if there is collinearity. My dilemma is that when I calculate VIFs for a conditional logistic regression model fit using glm and another fit using clogit/coxph, I get completely different VIFs, even though the model has the exact same covariates and returns the exact same beta estimates and standard errors. So which set of VIFs should I use?
Hey Javan,
My best guess is that you'd want to look at the differences, rather than the original data, since in the models you're really 'pairing' the data (subtracting use minus available), rather than looking at the data all together. It looks like that's what I did for the hognose data. I'm not sure if it is correct to examine correlations/VIFs with the original data, if the data is inherently paired.
I'm not that familiar with clogit. It looks like it pairs the use vs. available points with a True and False value? Are you able to get VIFs using the clogit function somehow?
If you wanted to get more complex, you could also try doing some sort of validation test (see Brad Timm's et al. 2014 spadefoot paper in J. of Herpetology), possibly this would get at how well the model is predicting with and without certain correlated variables. Collinearity might increase the standard errors of the Betas. You could try models with and without correlated variables, and see how much the SE of the Betas change. Lastly, when conducting model selection (i.e., with AIC), you can create models that don't have the correlated variables in the same model, and compare which one of those models has the best AIC value.
Hope this helps!
Mike
For the differenced data, what is the response variable? I can see taking the difference in relation to the used habitat, but then would it not be presence only data?
Please explain: ."...glm and clogit/coxph give me identical results but the different degrees of collinearity have a strong influence on the resulting analyses." In the meantime, see next lines.
For an idea how we dealt with collinearity across SDM algorithms (including GLM) by pair-wise comparison of independent variables (co-variates) and in step-wise removal of correlated co-variates see attached.
Article Where the bears roam in Majella National Park, Italy
Article Transferability of species distribution models: The case of ...
Hi Melanie and Hein,
Thanks for joining in on the discussion (and for the papers Hein, I look forward to reading them). Hopefully the following text answers both of your questions.
When we fit a conditional logistic regression using the glm, the response data are all 1's and the independent covariates are the differences between the used and available habitat values (i.e., within a 1:1 paired design). We remove the intercept to fit a no-intercept model which forces the relationship between relative probability of use and the independent variables to go through 0.50. The R syntax is:
glm(point ~ -1 + Difference1 + Difference2, data=data, family=binomial)
When I fit the same model using coxph, I do not difference the used and available data and the response variable is a an R object of class "Survival" (see the Survival package for details) of syntax:
Surv(time, point)
where time is always one (time-to-event = 1) and point is 0/1 indicating use/available. Additional, the strata argument must be used to identify matched (i.e., paired) points. The complete syntax for fitting a conditional logistic regression with coxph is:
coxph( Surv(time, point) ~ X1 + X2 + strata(pair), data=data)
These two formulas give identical beta estimates, AIC model rankings (but different absolute AIC values), standard errors, and p-values. I think this is because the syntax for coxph "tricks" the function into maximizing a likelihood that is identical to the likelihood function for a conditional logistic regression. I think that coxph differences observations within a pair "behind the scenes" but I am not positive.
Now regarding collinearity, if you calculate a correlation matrix for Difference1 and Difference 2 and then another matrix X1 and X2, you get different correlation coefficients. This makes sense because Difference1 = X1used - X1available and, in our study design, availability can vary widely from point to point even if used is fairly similar. These differences in collinearity means that different covariates are included in the final model set, depending on the cutoff for determining collinearity. Hence my original question, if these two different formulas which use different structures for the response variable give identical results, which data structure should be used to assess collinearity?
Hope this helps and thanks again for your questions,
Javan
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