Large intercept

[Indermaur]

Hi folks,
I modeled site occupancy using single season models in presence, separately for 4 different species. To illustration psi-covariate relationships, i applied predictions for these species. Out of the four species, on had an intercept of -13.4 (SE 5.1) while the others are -1.6 (SE 0.54), -1.7 (SE 0.64), -0.57 (SE 0.66).

A consequence of the large intercept is that psi is zero over the range of predicted covariate values. when i divide the suspicious intercept by factor 10, what brings the intercept to the range of the intercepts of the other species, i see the expected relationship, i.e. psi decreases with increasing x. in fact, i should see a psi-covar relationship for the species with the high intercept too, as the beta-value for the specific covariate is significant (beta -1.66, SE 0.59).

any idea, why i got this large intercept and how it should be handled to show the psi-covar-predicitons?

I appreciate any hint.
Cheers,
Lukas

[jhines]

Lukas,

If the intercept is that large and all psi's are zero, then the covariate beta is meaningless. In fact, you should see an error message saying that the variance-covariance matrix could not be computed (due to the model being overparameterized).

I'd suggest trying to rerun the model for the species which had the large intercept with a better starting value. Sometimes the shape of the likelihood function will lead the optimization routine astray, and a better starting value will fix it. Try entering -1 or -1.5 as a starting value for the intercept beta, and zeros for the others to see if you get a better final log-likelihood value. If it doesn't, try entering all of the final betas from another species as starting values for that one.

Jim

[Indermaur]

Dear Jim,
Thanks for the feedback!

First, I got no warning regarding the construction of the VARCOV-matrix in presence. The model with the large intercept seems to have converged (no warning) and the VARCOV-matrix was constructed.

Starting values: i tried intercept values ranging from -1 to -1.5, fixing the other betas to zero. this did not not change the likelihood. hence, the intercept remained -13.4.

It seems that three covariates in the model exert a large impact on the intercept: A) competition of species 1(beta/SE: -31.5/19.6); B) competition of species 2 (-1.0/1.; C) predation risk (-5.8/6.7). these covariates are almost binomially distributed.

when I omit e.g. variable A, the intercept/SE changes from -13.4/5.1 to -6.4/1.0. omitting variables A and C gives again 6.4/1.0. and omitting variables A,B,C gives an intercept/SE of -5.2/0.8.

in summary: model convergence and the varcov-matrix seem OK, starting values don't change the likelihood but omitting covariates change the likelihood.

is my model overfitted or do i have problems with a particular distribution of my covarate values? if distribution is a problem, how can i find a way around this problem without kicking the covariate out of the model - it hurts kicking covariates out of the model that are biologically of uttermoust importance.

Thanks for any hint.
Lukas