Nest Survival + 1 continuous covariate (HELP!)

[alex_martorano]

Greetings to anyone who might help me! :P

I'm using the Nest Survival model in Program MARK associated with only one continuous covariate (distance from nests to highway). I've been following the 'gentle introduction' manual, but I'm having some difficulties with the model specifications.

After loading my INP file and opening the Parameter Index Matrix, I set all the values in the PIM to 1, so as to consider a constant Daily Survival Rate. Then I opened the reduced Design Matrix (as the manual instructs to do, if I've interpreted it correctly), which was when my first doubt arose. Considering I only have one covariate, I'm tempted to enter '1' as the number of covariates in the design matrix. However, based on the screencaps in the manual, it seems I should consider my data as having two covariates, so that the design matrix will have two columns. In this case, the first column (B1) contains the value '1', and the third column (B2) contains the name of my covariate ('Road', in this case).

Is this really the way it should be done? If so, what does the value '1' stand for in the B1 column? In fact, what do the B1 and B2 columns represent?

Despite my reservations, I ran this model and it presented a lower AICc (145,0260) than the model in which no covariates are considered (150,3574). Does this mean this model receives less support? If so, should I stick with the no-covariate model?

Out of curiosity, I ran the model considering only one covariate (i.e., one column with the name of my covariate). This one presented a hight AICc than the previous ones (167,9168). But is it incorrect, though?

One last thing, when I view estimates of real parameters I find the following message at the top:

Following estimates based on unstandardized individual covariate values:
Variable Value
--------- -------------
ROAD 233.50000

The value makes sense as one of the distances in the input file, but what does it mean?

I apologize for the long post and possibly 'noob' questions, but I admit I'm having a hard time with the program.

Thanks so much!
Alex

[birdman]

Alex,

There are several things you should do, if you haven't. I would encourage you to read not only the chapter on the nest survival module, but also, at the very least, the first six chapters of the Gentle Intro. In particular, you'll want to spend some time in chapter 6 on MARK and linear models to help you understand what those B1 and B2 columns are. They represent the beta terms in the linear model, and if you aren't familiar with that, you should do some reading on linear models in a good statistics text.

That said, you can, as you've done, set all PIMs to 1, then run a design matrix (DM) model with two columns, one with a "1", and one with the covariate. You are basically constraining daily survival rate (DSR) to be constant with a simple additive effect of the covariate. The 1 codes an intercept term (in the linear model) and the B2 column allows survival to vary by distance from highway.

Out of curiosity, I ran the model considering only one covariate (i.e., one column with the name of my covariate). This one presented a hight AICc than the previous ones (167,9168). But is it incorrect, though?

This is incorrect. Again, need to review linear models. Although it will give you an answer, what is your covariate additive to, in this model? Nothing since there's no intercept.

And lastly,

One last thing, when I view estimates of real parameters I find the following message at the top:
Following estimates based on unstandardized individual covariate values:
Variable Value
--------- -------------
ROAD 233.50000

The value makes sense as one of the distances in the input file, but what does it mean?

The estimates of DSR that MARK gives you must be based on some value of your parameters of interest. So, if it said that DSR was 0.94 in your best model, and the Variable Value at the top of the results says, "ROAD 233.50", That is the value used to genterate your estimates, and represents the mean value across all of your nests. If you rerun the model, just like you did before, but click the "User-specified Covariate Values" radio button in the lower right box of the Model run set-up dialogue box (just before you run the model), you'll get a second screen asking you to set the covariate value. So you could set it at 10, and the estimates you get would be based on nests 10 (meters?) from the road. Run again with the value set at 100, or 250... whatever values fall within the range of your data, and you'd get estimates of DSR at that distance. If you do this, remember that you need to delete all but a single model for your AIC table to make sense.

I hope this helps to get you grounded, but you definitely need to do some more reading, but in the Gentle Intro, and it sounds like in a stats book too.

Cheers,
b

[alex_martorano]

Birdman,

Thank you so much for your reply! It has really helped me understand what I've done, although I admit I really do need to do some reading in statistics.

One more question though.

So you could set it at 10, and the estimates you get would be based on nests 10 (meters?) from the road. Run again with the value set at 100, or 250... whatever values fall within the range of your data, and you'd get estimates of DSR at that distance. If you do this, remember that you need to delete all but a single model for your AIC table to make sense.

What do you mean by needing to delete all but a single model? Are you referring to the Results Browser?

I reran the model setting my own covariate values (100, 150,...,350m) and got results with equal AICc (which is to be expected, I imagine) and spacial variation in DSR fitting to my hipotheses! Hooray!

Thank you so much for the tremendous help!

[birdman]

Yes, sorry. If you run the same model multiple times to obtain estimates at multiple levels you'll see those models stacked in the results browser with the same AIC values, but the weight of support will be split between the identical models. Just delete all duplicate models to obtain the correct results table output.

[alex_martorano]

Ok, got it. Thanks again!

[alex_martorano]

Hey,

I did a bit more reading, but I'm still insecure about the Delta AICc and AICc weight. From what I understood, the Delta AICc just informs me if my models are significantly different (similar to a Chi-square test) while the AICc weight tells me how much more support the better model has received (like saying one model is X times better than the other). Am I on the right track?


And now that I've calculated the DSRs for different distances from the nests the road (100 m, 150 m,...), is there a way to compare them in MARK to see if they're significantly different? I've only been able to compare different models, but not different values within a model (due to different user-specified covariate values).

Thanks again!

[bacollier]

I did a bit more reading, but I'm still insecure about the Delta AICc and AICc weight. From what I understood, the Delta AICc just informs me if my models are significantly different (similar to a Chi-square test) while the AICc weight tells me how much more support the better model has received (like saying one model is X times better than the other). Am I on the right track?

Alex, you probably need to read, in detail, Chapter 2 of Burnham and Anderson 2002 (or the 1998 version), paying special attention to sections 2.2, 2.5, 2.6, 2.8 and 2.9. A model cannot be 'significantly different' (although some may argue), rather, it can fit the data as good, better or not as good as a competing model. Read those sections, it should clarify things for you.

And now that I've calculated the DSRs for different distances from the nests the road (100 m, 150 m,...), is there a way to compare them in MARK to see if they're significantly different? I've only been able to compare different models, but not different values within a model (due to different user-specified covariate values).

There is no internal test statistic in MARK for what you are asking, nor is it a good idea as you have a continuous (relatively) covariate (distance) so you want to know the predicted value of the DSR relative to the distance from the road. Since you are using user-defined covariate and rerunning the same model over and over, you might, as an alternative, get the beta parameter estimates from the 'best' model and put them into whatever computing program you are comfortable with (R, MatLab, S, that abomination Excel) and then predict the DSR for the range of distance values and the associated CI bounds for that line. There are several examples of how to do this out and about on the list and you can do this in MARK as well I think.

As an aside, all the questions you have been asking are detailed in the MARK manual, on Gary's MARK website, and in a litany of course notes by a variety of folks who teach this stuff, and in hundreds of places in the literature, so a little extra background research on your end might be a useful exercise if you plan to continue this type of work in the future.

Bret