Estimating SE for reconstituted psi values with >1 covari

[Abby]

I have been using the formulas given in the mark book (page 7-24) to reconstitute psi values from continuous habitat covariate betas. Some of the top models I am working with have multiple habitat covariates, and I am unsure how to handle that for the standard error estimates, because the example in the mark book only used one beta estimate in the calculation of SE.

What I am trying to do is construct plots of psi vs. each habitat covariate. For models with more than one habitat covariate, I am constructing individual graphs where I hold the other covariates constant (using the mean value from my sites) and vary only one covariate. For example, one model has two habitat covariates called tall emergents and interspersion- for the graph relating psi to tall emergents, I calculated psi values using a constant interspersion value and a range of tall emergent values. When I am calculating the SE around the psi estimates, do I incorporate only the beta estimate of interest (in the previous example, the beta for tall emergents), or all the beta estimates (intercept, tall, and interspersion), and if so how do I do that using the formula given on page 7-28? When I attempted to add them in my standard errors and confidence intervals where enormous.

[cooch]

I have been using the formulas given in the mark book (page 7-24) to reconstitute psi values from continuous habitat covariate betas. Some of the top models I am working with have multiple habitat covariates, and I am unsure how to handle that for the standard error estimates, because the example in the mark book only used one beta estimate in the calculation of SE.

What I am trying to do is construct plots of psi vs. each habitat covariate. For models with more than one habitat covariate, I am constructing individual graphs where I hold the other covariates constant (using the mean value from my sites) and vary only one covariate. For example, one model has two habitat covariates called tall emergents and interspersion- for the graph relating psi to tall emergents, I calculated psi values using a constant interspersion value and a range of tall emergent values. When I am calculating the SE around the psi estimates, do I incorporate only the beta estimate of interest (in the previous example, the beta for tall emergents), or all the beta estimates (intercept, tall, and interspersion), and if so how do I do that using the formula given on page 7-28? When I attempted to add them in my standard errors and confidence intervals where enormous.

The version of the book you're referring to is >1 year out of date - linear models are now covered in Chapter 6, not 7. Have a look at Chapter 6, find the appropriate equations/pages, and report back here.

Also, are you using MARK, or PRESENCE?

[cooch]

I have been using the formulas given in the mark book (page 7-24) to reconstitute psi values from continuous habitat covariate betas. Some of the top models I am working with have multiple habitat covariates, and I am unsure how to handle that for the standard error estimates, because the example in the mark book only used one beta estimate in the calculation of SE.

What I am trying to do is construct plots of psi vs. each habitat covariate. For models with more than one habitat covariate, I am constructing individual graphs where I hold the other covariates constant (using the mean value from my sites) and vary only one covariate. For example, one model has two habitat covariates called tall emergents and interspersion- for the graph relating psi to tall emergents, I calculated psi values using a constant interspersion value and a range of tall emergent values. When I am calculating the SE around the psi estimates, do I incorporate only the beta estimate of interest (in the previous example, the beta for tall emergents), or all the beta estimates (intercept, tall, and interspersion), and if so how do I do that using the formula given on page 7-28? When I attempted to add them in my standard errors and confidence intervals where enormous.

Also, you really should consult Appendix B - on the Delta method. Have a close look at Example 4, p. B-18.

[cooch]

Also, are you using MARK, or PRESENCE?

My mistake - I see now this was posted in the PRESENCE section of the forum.

[darryl]

Like Evan suggests you need to use the Delta Method as you need to account for the uncertainty in all your betas, and also how they covary. It's not as easy as just adding the beta SE's together. The delta method may sound hard, but you can actually set it up in a spreadsheet pretty easily.

Of course why do you want the SE? If you're really after confidence intervals for your lines you might be better to first calculate them on the logit-scale, then just transform the limits to the real (0-1) scale.

[cooch]

Like Evan suggests you need to use the Delta Method as you need to account for the uncertainty in all your betas, and also how they covary. It's not as easy as just adding the beta SE's together. The delta method may sound hard, but you can actually set it up in a spreadsheet pretty easily.

In fact it pretty trivial, in Excel, or R (after load/install of the right package).

Of course why do you want the SE? If you're really after confidence intervals for your lines you might be better to first calculate them on the logit-scale, then just transform the limits to the real (0-1) scale.

One reason might be to evaluate SE on the size of the effect of some 'treatment'. If we follow the paradigm espoused by B&A, we should focus on the size of the effect (and uncertainty thereto), and whether the CI bounds an effect we think is important in the 'biologically plausible' sense. This is discussed at some length in Chapter 4 and Chapter 6.