Indicator variable in nest survival

[EricM]

Thank to some help from this board, I was able to get my woodcock nest survival model working. Since then I have been playing with my data to see if there is a better way to test it.

Previously, I had set my variables in my encounter history which looked like this.

/* Eric Miller data for woodcock nests
in xxxxxx State Park, Pennsylvania,
Occasions=49 (march 15 thru May 2),
Covariates are
1) shrub_Height in meters,
2) Stem_density (# of woody stems per measurement area),
3) indicator variable for cover type (0 if native, 1 if invasive),
4) indicator variable for soil moisture (0 if dry, 1 if moist, 2 if wet) */

nest survival group=1;
/* 1 */ 25 27 40 0 1 12.5 20 1 1 ;
/* 3 */ 27 29 40 0 1 8.0 15 1 0 ;
/* 4 */ 14 27 40 0 1 5.0 17 1 0 ;
/* 5 */ 20 27 40 1 1 6.0 15 1 0 ;
/* 6 */ 28 28 40 0 1 15.0 15 1 0 ;
/* 7 */ 30 33 40 1 1 5.0 15 1 0 ;
/* 8 */ 32 34 40 0 1 13.0 13 1 1 ;
/* 9 */ 33 37 40 0 1 13.0 17 1 1 ;
/* 10 */ 34 37 40 0 1 6.0 9 1 1 ;

The model turned out ok and produced the following graph:



But after reading chapter 17 again, I am wondering if I should reassign my cover variable as 2 seperate indicator variables similiar to the mallard example. My confusion is due to the fact that the model only indentified cover as an important factor, not specifically native or invasive cover which is needed to test my hypothesis that female woodcock will successfully nest in invasive cover. Also, the text "Proportion of Native Cover" under the x axis should read "Cover type" since the model didn't seem to express which cover was favored.

Thanks for your help.

Eric

homiller@state.pa.us

[jlaake]

I'm a bit confused by your post because you showed cover as an indicator variable of 0/1 but then your plot showed proportion of native cover. Were the proportions just 0 and 100% or was it coded as 0 if there was any invasive plants?

If it was a 0/1 variable as shown in your data then you have a factor variable with 2 levels but typically for any factor variable with k levels you use k-1 dummy variables (0/1) to represent the effect of the factor variable relative to an intercept. However, you can represent the design as 2 separate levels but then you can't have an intercept and that gets more difficult when you use more than one covariate and you need an additive model. I think you need to go back and read more about DMs and what they represent. For example if your model was ~cover then
with the first row for invasive and the second for native, you can represent that with a DM of
Int Native
1 0
1 1

Int Invasive
1 1
1 0

Invasive Native
1 0
0 1

In the first model the intercept represents Invasive and the second is how much native differs from Invasive. For the second, the opposite is true with the intercept being for native and the second for the amount invasive differs from intercept. In the last the first is for invasive and the second for native but they are separate and not expressed relative to each other and could be expressed using a PIM with an identity matrix. All of these will produce the same model but the betas will differ because they represent different quantities. There are other constrasts that could be used as well in the DM but the above are the most common and usually the easiest to understand.

Now consider a model ~cover+rain. You could represent that as

Int Native Rain
1 0 0
1 1 0
1 0 1
1 1 1

Int Invasive Rain
1 1 0
1 0 0
1 1 1
1 0 1

Inv Native Rain
1 0 0
0 1 0
1 0 1
0 1 1


However, you can't have a PIM representation for an additive model. But if you were to fit ~cover*rain the inteaction model then you could represent as:

Invasive/NR Native/NR Inv/Rain Nat/Rain
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1

Typically it is advantageous to use the additive DM because it represents the difference between the intercept and the other levels and you can get any comparison by simply changing the factor level which is used for the intercept. In your case with invasive being the 1, the beta for cover represents the change in survival (on the logit scale) for invasive relative to native.

Hope this helps. --jeff

[EricM]

Jeff, are you available to discuss over the phone? It may speed up my explanation.

Thanks.

Eric

[jlaake]

I am but don't want to post my number. If you don't have it send me an email to jeff.laake@noaa.gov