Parameter estimates in Multi-seson model

[Niels Leuthold]

When fitting a multiseason model I am getting estimates of epsilon at certain sites that are 0, have an SE of 0, and have a confidence interval of 0 to 1. This only happened at sites between the 1st year and 2nd. In examining the data these sites are the larger sites (one of the covariates), and there were not local extinctions at the larger sites between the first and second year. Should I be concerned about the 0 estimate and the SE of 0? The estimate of 0 for the site makes sense to me, but I am concerned about the SE of 0.

[darryl]

Things can always be a bit ugly when you have estimates on the boundary of allowable values, but personally I don't get too concerned because if you think about the variance (SE^2) for Bernoulli or binomial random variables there's usually a term along the lines of p*(1-p), so if your estimate is either 1 or 0 this term becomes 0. I'd perhaps be less inclined to believe your CI though which is a result of the logit-link becoming very flat as it approaches 0 or 1. It sounds like you have covariates though so the main issue would be to check that everything looks ok for your beta parameters.
Darryl

[Niels Leuthold]

I am a bit concerned about the parameter for area in the extinction portion of the model. Between the 1st and 2nd season the parameter estimate is -19.0 (se 33.3), but between the 2nd and 3rd and 3rd and 4th the estimates are -0.24 (.24) and 0.014 (.30). The cause is clear, there were no extinctions in the larger sites between year 1 and 2, but there were in the following years. It seems I am getting an artificial importance of area due to this. While I suspect there may be some affect of area the values seem to be driven more by the lack of local extinctions rather than an effect of area.

Does it seem reasonable to exclude the area variable based on these grounds? If not are there any reasonable approaches for dealing with this? I have tried to fit a model that doesn't allow the effect of area to vary by year, and it gives a reasonable estimate, but I am worried that there is still an effect of the lack of extinction in the large sites between season 1 and 2. Thanks

[darryl]

I am a bit concerned about the parameter for area in the extinction portion of the model. Between the 1st and 2nd season the parameter estimate is -19.0 (se 33.3), but between the 2nd and 3rd and 3rd and 4th the estimates are -0.24 (.24) and 0.014 (.30). The cause is clear, there were no extinctions in the larger sites between year 1 and 2, but there were in the following years. It seems I am getting an artificial importance of area due to this. While I suspect there may be some affect of area the values seem to be driven more by the lack of local extinctions rather than an effect of area.

Does it seem reasonable to exclude the area variable based on these grounds? If not are there any reasonable approaches for dealing with this? I have tried to fit a model that doesn't allow the effect of area to vary by year, and it gives a reasonable estimate, but I am worried that there is still an effect of the lack of extinction in the large sites between season 1 and 2. Thanks

What models have you fit? How have you defined your design matrix for this model you're concerned about?

[Niels Leuthold]

For the local extinction portion of the model I am using year + year*treatment + year*area + year*dominate substrate as the full model and then fitting subsets of the model. In this study we have pre and post treatment data as well as control sites, so instead of year pre/post is also a variable of interest.

I am working with stream amphibians and to ensure site closure the 3 samples are done in a day and nets are used to ensure closure. This means that the survey covariates are the same for all the samples in a year, but can change between years. To save space I put the survey covariates as site covariates. So for year + year*treatment + year*area the DM looks like

eps covariates:

Matrix 3: rows=4, cols=10
-,c1,c2,c3,c4,c5,c6,c7,c8,c9,
eps1 1 0 0 South 0 0 area2005 0 0
eps2 0 1 0 0 South 0 0 area2006 0
eps3 0 0 1 0 0 South 0 0 area2007

For a model like 1 + treatment + area the DM looks like
eps1 1 South area2005
eps2 1 South area2006
eps3 1 South area2007

[darryl]

Hi Niels
Is it realistic to expect that the effect of area on extinction probability will be different in different years, or relatively consistent? The answer to this should guide you on which models to fit.

How are your area values distributed? There's no requirement for them to be normally distributed, but at the moment you're effectively trying to draw a straight line relationship between extinction and area. If you have a few sites with large areas, they could be having a big effect on your slope estimate so you might want to consider a transformation of area (like sqrt or log).

Darryl

[Niels Leuthold]

Hi Darryl,
I have actually been thinking about that over the last couple hours. My thought is that area effects shouldn't differ that much between years. I think it might change pre/post treatment in the treated areas, so that will be one of my tests but every year probably isn't realistic.

I will look at the area, but I don't think the range is all that big. There were a few large sites, but I don't think they were that much bigger. Thanks for your help on this!