I have a data set showing an (exponential) increase in the size of an animal population over time. I can fit an exponential model to these data and obtain an estimate of the population growth rate (under the assumption of unconstrained exponential growth).
However, I would like to get a handle on how variable this estimate is however. To do this, I have written an R script which conducts some Bootstrap resampling of the initial observations and harvests the value of the population growth rate for each Bootstrap resample. I am achieving this by fitting a lm of the form log(abundance)~Year.
While the initial exponential model was highly significant (p<<0.05), this is not necessarily the case in all Bootstrap resamples.
How can I construct reliable confidence intervals for the population growth rate, knowing that sometimes (in some runs) it is found to be non-significant at alpha=0.05?
I see 3 options here: 1) Generate a distribution of growth rate values based on all resamples, regardless of whether the regression was significant or not; 2) Only base the CI on the subset of resamples where the regression was significant; 3) Assign a value of zero to the regression coefficient whenever its associated p-value is larger than the chosen significance threshold, i.e. alpha=0.05.
I have only found one published paper that uses method 3) [Austin (2007). Using the bootstrap to improve estimation and confidence intervals for regression coefficients selected using backwards variable elimination. STATISTICS IN MEDICINE, 27, VOL. 17:3286-3300].
Is this a valid approach?