Modeling covariates-- intercept or no intercept?

[Tamara Pandolfo]

Hi all,

I have a simple question--  maybe more stats related than unmarked.  I am working on a multiseason occupancy model with covariates.  Most of my covariates (e.g., species) are categorical-- but I also have one continuous variable (watershed area) and I have been omitting the intercept for all of them. I decided to do this after reading the part of the vignette about effects vs. means parameterization. 

e.g., (fm44 <- colext(~1, ~1, ~warea-1, ~spp-1, occ.umf))

This gives me results like this:

Extinction:
 Estimate      SE     z P(>|z|)
  -0.0133 0.00598 -2.22  0.0263

Detection:
          Estimate      SE       z P(>|z|)
sppAhet      1.581   1.196  1.3222 0.18609
sppAund     -1.454   0.490 -2.9677 0.00300
sppEfish     0.637   0.473  1.3467 0.17809

However, I realized that I did not know how to interpret the parameter value that I got for Extinction which used the continuous variable (without an intercept).  What does that estimate mean exactly? If I put in the intercept I understand the relationship. I played around with some predictions and realized the presence of the intercept changes the predictions-- so it made me wonder if I need to be including intercepts for ALL covariates? or just the continuous one?  or none?

Can someone give me some guidance on whether I should be leaving these intercepts in?  And if not, how do I interpret that parameter estimate in relation to the covariate?

Thanks for any help with this,
Tamara Pandolfo




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[Kery Marc]

Dear Tamara,

"subtracting the intercept" does not change your model when you do this with a factor (= categorical explanatory covariate), it produces a mere reparameterisation, which, in many cases and to many, is more easily interpretable in terms of the meaning of the params. BUT: subtracting the intercept in a model where you have only continuous explanatory variables DOES change the model and does not usually yield a sensible model. It enforces an intercept of 0, which does not normally make sense. So don't do it. And be sure to understand how to describe the linear models in all of this modeling (e.g., lm(), glm(), colext(), pcount() etc etc)

Kind regards  --  Marc

______________________________________________________________
 
Marc Kéry
Tel. ++41 41 462 97 93
marc...@vogelwarte.ch
www.vogelwarte.ch
 
Swiss Ornithological Institute | Seerose 1 | CH-6204 Sempach | Switzerland
______________________________________________________________
 
*** Introduction to Bayesian statistical modeling: Kéry (2010), Introduction to WinBUGS for Ecologists, Academic Press; see www.mbr-pwrc.usgs.gov/pubanalysis/kerybook 
*** Book on Bayesian statistical modeling: Kéry & Schaub (2012), Bayesian Population Analysis using WinBUGS, Academic Press; see www.vogelwarte.ch/bpa
*** Upcoming workshops: www.phidot.org/forum/viewforum.php?f=8

---

From: unma...@googlegroups.com [unma...@googlegroups.com] on behalf of Tamara Pandolfo [tjpa...@ncsu.edu]
Sent: 30 August 2013 21:50
To: unma...@googlegroups.com
Subject: [unmarked] Modeling covariates-- intercept or no intercept?

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[Tamara Pandolfo]

Thanks so much, Marc!  I will definitely review the stats behind these models.

Take care,
Tamara