How to enter data for spatial correlation model

[sprihharsh]

I am trying to use Hines 2010 model for doing analysis of my data on tiger presence. The data has been arranged in 10 replicates for each 180 sites.
Now i have to do the analysis but I am struggling in entering data and how to design matrix for this model.
What if I want to use certain site covariates like habitat type?

Please help me out.

Thanks,
Sprih

[jhines]

Hi Sprih,

The help file (under the 'Help/Overview' menu gives instructions on how to get your input data into PRESENCE. Assuming you have your detection data and habitat covariate in a spreadsheet, you just select the detection data, copy to the clipboard, then paste into the data input form in PRESENCE. How to enter the habitat covariate depends on whether this covariate is a 'categorical' or 'continuous' covariate. If it is 'continuous', then just select that covariate and copy it to the clipboard. In PRESENCE, change the number of site covariates (box in top row) to 1, then click the 'site covar' tab, then click in the first row/col. Go to the 'Edit' menu and select 'paste'. If habitat is categorical, then you might need to convert the values into indicator variables (0 or 1 to indicate occurrence of each particular habitat type). Then paste these covariates into PRESENCE.

There is an example in the overview of how to build a model where an estimate is a function of a covariate. If your habitat covariate is 'continuous' and you want occupancy to be a function of habitat, your design matrix for psi would be:

a1 a2
psi 1 habitat

If your covariate is categorical, then the design matrix for psi would be:

a1 a2 a3 a4
psi 1 hab1 hab2 hab3 ... hab(N-1)

where N is the number of habitat categories.

There are a few tutorials which explain model building and data entry in the Help menu.

Jim

[sprihharsh]

Thanks Jim for the prompt reply. But I guess I wasn't clear in asking my question.

Let me explain my problem in detail again.

I have 180 sites and for each of these sites I have 10 replicates of 1 km each which are arranged in columns. So the data looks like this:
Site Column1 Column2 Column3... Column10 (10 replicates)
A 0 1 1 .....0
B
...
180 1 0 1 ....0
Now I want to run single season analysis and Hines 2010 model for spatial correlation, which I believe comes under Analysis->Single Season->Correlated detections. Once I do this, I get model as psi,th0(),th1(),p(),th0pi(). Now in design matrix, I have 6 tabs- Occupancy/use, __, __, Detection, th0pi,__
In first tab i.e. Occupancy/use tab, we have rows like
a1 a2 a3
psi 1 0 0
th0(1-1) 0 1 0
th0(1-10)0 1 0
th1(1-1) 0 0 1
th1(1-10) 0 0 1
Now if I want to use habitat as site covariates, do this design matrix look like this?
a1 a2 a3 a4
psi 1 0 0 Habitat1
th0(1-1) 0 1 0 0
th0(1-10)0 1 0 0
th1(1-1) 0 0 1 0
th1(1-10) 0 0 1 0

Is this correct? And what about other tabs? Do I have to do something with them? And if not now, then when they have to be changed?

Now when I run this model putting habitat as covarite in psi, in my result I get 180 psi values for each of the site. Is this correct? and the beta value for psi is greater than 1. What if I want to get a single value of psi instead of 180 values for each of the site.

I am really confused in interpreting the result.

Please help me out and thank you again for your time.

Regards,
Sprih

[jhines]

Hi Sprih,

You can model any of the parameters in the spatial correlation model as a function of your habitat covariate. In your design matrix, you are modeling occupancy (psi) as a function of habitat. That means that occupancy is (potentially) different for each site, since habitat is different for each site. That is why you get 180 values of occupancy estimates. You would use the 'detection' tab if you wanted to run a model where detection (p) is a function of habitat. Although it's possible to model the mixture parameter (th0pi) as a function of habitat using the last tab, I can't think of a valid reason to do so.

The untransformed parameter estimates (beta's) are not bound to the interval (0-1). This allows the program to model the 'real' estimate (psi) as a linear function (on the logit scale) of habitat. This linear function has a slope and intercept. We wouldn't want the slope or intercept to be restricted to values between 0 and 1. The reason we can't model the real parameter as a linear function of habitat is that it would be possible for some values of the covariate to give negative values of psi, or values of psi which are greater than 1. So, those beta estimates are transformed using a logit link function to get the 'real' values of psi. The first beta in your output is the intercept, which is equal to the logit of psi when the habitat covariate is zero. The other psi beta, labelled 'psi.habitat1', is the slope, or effect of habitat on (the logit of) occupancy. If psi.habitat is positive, there is a positive relationship between habitat and occupancy (ie., as habitat increases, occupancy increases).

If you want a single estimate of occupancy, you can take the average of the 180 estimates, or just run the model without any covariates.

Jim