Is there a way to compute confidence intervals for regression estimates of simulated data?

Question

I've got a dataset where someone counted birds in the breeding season over 10 years. For each year (x site), we want to see how reduced sampling might affect our ability to detect a trend. So to that end, I have simulated various datasets from the original where we cut down sampling to once every 45 days (and 60, 90,120).

I fit the same negative binomial model to the original and each simulated dataset (5oo datasets for each of the different sampling intervals).

So now I have 500 regressions (and coefficients) for each dataset x location. Is there some way to throw a confidence band around these? Is it something very trivial, like computing CI around a mean?

Answer 1

Yes, you have repetitions of each scenario, so you can make a histogram of each coefficient values. Now treat it as a real distribution and just find a band that encloses this 99, 95 or whatever per cent of its area -- this will be the nonparametric approximation of CI.
The simpler way is to assume normality and just count standard deviation over repetitions; this is useful when the number of repetitions is low, but will obviously give bad results when the over-repetition distribution is far from normal.