Basic design matrix question, and Q about initial values

[Daisy]

Hello,

I'm somewhat new to using PRESENCE. My question is: when using covariates (whether site-specific or survey-specific), do you always use an intercept term in the design matrix? Is there a situation where you wouldn't?

In other words, if you are using covariates, will there always be an a1 or b1 value in the design matrix which is 1, then the second column (a2 or b2) will be the covariate? I've thought it through and I believe this to be correct because (at least in my thinking) there should be an intercept (even if it turned out to be zero) for the basic occupancy or detection probability, then the covariate adds an additional effect to the value.

[edit for clarification: I'm asking about if there can be cases where there is just one column (a1 or b1). So if for example, detection varies with temperature, should the design matrix always be: b1=1, b2=temp, or could the design matrix just be b1=temp?)]

My second question is, when supplying initial values for a model that didn't converge, are they just supplied in the order of the design matrix? So first a1, then b1, b2, b3, etc...?

Thank you for taking the time to read this!

Daisy

[jhines]

The design matrix specifies equations for each parameter. So, if the 1st row of the design matrix has:

psi 1 elevation

then that means that

logit(psi) = 1*a1 + elevation*a2

or

psi = 1 / (1 + exp[ (1*a1 + elevation*a2)]

So, if you omit the '1' (intercept), then

logit(psi) = elevation*a2

If elevation is zero, then logit(psi)=0 and psi=0.5. So, you're forcing occupancy to be near 0.5 for sites with small elevation values. That, in turn will effect the effect of the covariate. Since you're building the model to reflect reality, it probably isn't the case where occupancy has to be a specific known value (0.5) when the covariate is zero. So, it makes sense to estimate the value of psi when the covariate is zero (intercept) and the rate of increase/decrease (effect) in psi as the covariate increases.

2nd question: yes, initial values are specified in the order: a1,a2,a3,...b1,b2,b3...c1,c2,c3,...

[Daisy]

Hi,

Thank you for the response. I can see now that although I had the right idea of using the intercept, my reasoning wasn't correct because I was forgetting about the logit part of the equation. I really appreciate your response and clear explanation!

Daisy