Computes one of a series of possible variance estimates for the observed encounter rate for a set of sample measurements (e.g., line lengths) and number of observations per sample.
Details
The choice of type follows the notation of Fewster et al. (2009) in that there are 8 choices of encounter rate variance that can be computed for lines and one for points:
R2random line placement with unequal line lengths (design-assisted estimator)
R3random line placement, model-assisted estimator, based on true contagion process
R4random line placement, model-assisted estimator, based on apparent contagion process
S1systematic line placement, post-stratification with no strata overlap
S2systematic line placement, post-stratification with no strata overlap, variances weighted by line length per stratum
O1systematic line placement, post-stratification with overlapping strata (akin to S1)
O2systematic line placement, post-stratification with overlapping strata (weighted by line length per stratum, akin to S2)
O3systematic line placement, post-stratification with overlapping strata, model-assisted estimator with trend in encounter rate with line length
P2random point placement, potentially unequal number of visits per point, design-based estimator
P3random point placement, potentially unequal number of visits per point, model-based estimator
Default value is "R2", shown in Fewster et al. (2009) to have good
performance for completely random designs for lines. For systematic parallel
line transect designs, Fewster et al. recommend "O2". For point
transects the default is "P2" (but "P3" is also available).
For the systematic estimators, pairs are assigned in the order they are
given in the lengths and groups vectors.
Note
This function is also used with different calling arguments to compute Innes et al variance of the estimated abundances/length rather than observation encounter rate. The function covn is probably only valid for R3 and R2. Currently, the R2 form is used for all types other than R3.