Abstract from BTO Research Report No 377:

Noble, D.G., Newson, S.E. & Joys, A.C. (2004, published 2005)

Investigation of methods for producing joint CBC – BBS trends.

1. In the production of joint CBC/BBS indices, inclusion of weightings in the SAS GENMOD analyses for the BBS data (to account for differences in survey coverage among regions) requires that some weighting for the CBC is also used.

2. Although the coverage of the CBC is mainly restricted to Southern Britain and is not randomly based, regional weighting has not been previously used in the production of trends based solely on the CBC. Given that the CBC ended in 2000 anyway, we did not want to expend effort on introducing regional weighting in the CBC at this stage that would retrospectively change all previously reported changes. This means that we needed to assign an arbitrary and equal weighting across all CBC sites.

3. Standard BBS and CBC analyses (on their own) correct for over-dispersion in the data using scaling (pscale or dscale commands), so it makes sense to continue to do this. In the presence of scaling, an increase in the absolute weighting values does not influence the estimated parameters. However, CBC or BBS weights should be adjusted so that they are comparable (i.e. either adjust up CBC weights, giving all CBC sites the mean BBS weight across sites/years, or adjust down the BBS to have a mean weight of 1 and give CBC sites a weight of one). Both methods give the same estimates and standard errors, so the choice of these is analytically irrelevant. We decided to keep the BBS weightings the same as in previous BBS analyses and scale up the CBC weights.

4. A problem, however, is that by scaling, one is assuming that over-dispersion is the same in both CBC and BBS surveys. The results here suggest that this assumption is basically true for non-flocking species, with the over-dispersion likely to be relatively similar between surveys. However for flocking species, where the over-dispersion is likely to differ between surveys, the standard errors of the resulting joint estimates may not represent the combined situation particularly well. This is especially apparent in the Wood Pigeon when joint CBC/BBS trends are presented for the period 1965 to 2000, with BBS trends from 1994 to 2000. Ideally each survey should be scaled separately, although there is no obvious way to do this in SAS and further work would be needed to examine this problem further.

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