Adjustment of SEs for overdispersion

[pld]

Hi,
This is my first post to this forum. I realise that this topic has been raised previously, but I cannot find an answer to my question. Where there is evidence of lack of model fit in occupancy models, the advice is to use c-hat to calculate QAIC, and to adjust SE of the parameter estimates. Can someome confirm that this adjustment is done by multiplying the variance-covariance matrix by c-hat? This seems to be the advice in Burnham and Anderson 2002 p 70, but I'd appreciate confirmation.
Thanks, Peter

[ferny]

I would also be interested in this. In addition to the Royle 2004 models I've posted about (for which I don't know how to do GOF/obtain c-hat: viewtopic.php?f=11&t=2802), I'm also running single-season single-species occupancy models (MacKenzie et al 2002). Having tested 'assess model fit' and got the GOF result I am over-dispersed with a c-hat value of 1.4. Accordingly I should use QAIC to select my top model and add 1 to the parameters for doing so (to account for estimating c-hat), which I have done using the Tools menu.

The next step would seem to be to make c-hat adjustments. One approach is mentioned in the excellent (exercise 4) of "Donovan, T. M. and J. Hines. 2007. Exercises in occupancy modeling and estimation"
http://www.uvm.edu/envnr/vtcfwru/spread ... upancy.htm

Here they state:

If c hat is larger than 1, (e.g., 2), it indicates a lack of fit and you should adjust your standard errors by multiplying the estimated standard errors by the square root of c hat.

In this tutorial no mention is made of the approach quoted above (in the OP) regarding Burnham and Anderson 2002 p70. Could I confirm that both the Donovan and Hines approach and the Burnham and Anderson approach are simply different ways of achieving the same end - and critically, that if you follow Donovan and Hines then you *do not need* to also follow Burnham and Anderson?

If this is the case then Donovan and Hines provide a quicker solution for Peter (given that PRESENCE already calculates SEs) and I needn't worry about making any fundamental changes to my VC structure!

Thanks,
Paul

[darryl]

The SE's come from the VC matrix (which PRESENCE can output as an option) where for a particular parameter SE = sqrt(Var), with the variances being the main diagonal terms of the VC matrix. Whether you multiply SE by sqrt(c-hat) or the VC matrix by c-hat (and then most likely sqrt to get SE's anyway) is essentially the same thing. You don't have to make any "fundamental changes to my VC structure". Just multiplying it by a constant.

Cheers
Darryl

[ferny]

Thanks Darryl - I'm glad my hunch was right and thank you for explaining the maths behind it - I always feel happier when I understand the answer!