Confidence interval conventions in tidycreel
Source:R/creel-confidence-intervals.R
creel_confidence_intervals.RdEstimators in this package do not all build confidence intervals the same way, because the quantities they estimate do not all live on the same scale or carry the same information about their own uncertainty. This topic states the two rules the package follows, so that a new estimator does not have to pick by coin flip.
Bounded quantities
Effort, catch, harvest, release, biomass, abundance and catch rates are all bounded below by zero, and exploitation rate is bounded on both sides. A symmetric Wald interval respects none of that: once the coefficient of variation exceeds roughly 0.51, the lower bound of a 95% interval falls below zero and the estimator reports a value outside the parameter space.
The package handles this in one of two ways, in this order of preference:
Transform, where a principled transform for the quantity exists.
estimate_exploitation_rate()builds its interval on the logit scale;estimate_angler_n()uses Sadinle's (2009) 0.5 transformed logit interval for Chapman and Petersen \(\hat{N}\); the product-total paths acceptci_type = "log". A transformed interval is right-skewed and cannot cross the boundary in the first place.Clamp at the feasible limit, where no transform is established for the estimator. This is
pmax(0, ...)applied to the lower bound, used by the product totals underci_type = "symmetric"and by every bus-route path.
Clamping is the weaker of the two and is deliberately not treated as equivalent. It keeps the symmetric width that produced the excursion and truncates the result at the boundary, so it stops the package reporting an impossible number but does not repair the skew that made the bound negative. A clamped lower bound of exactly zero should be read as a signal that the interval is wide relative to the estimate, not as a precise statement that the quantity could be zero.
Upper bounds are never clamped: none of these quantities has a finite upper limit that the package knows.
Two quantities are bounded below by something other than zero and are
therefore left alone: est_mean_length() and est_mean_age() are bounded by
the smallest occupied bin, so a clamp at zero would be the wrong repair.
Quantile choice
Where an estimator has a finite sample size of its own to appeal to, it uses
stats::qt() on an explicit degrees-of-freedom rule. The product-total paths
use total interviews minus the number of strata; the section paths use the
number of sections minus one; mark-recapture uses the number of occasions.
Six estimators use stats::qnorm() instead — est_biomass(),
est_mean_length(), est_compliance(), est_mean_age(), and since #310
est_length_distribution() and est_age_distribution() themselves. This is
deliberate, not an oversight.
The first four form a linear combination of the rows of a length or age
distribution, and their standard error is propagated from the per-bin
standard errors those rows already carry. The two distributions joined them
when their totals became two-phase: a bin total is no longer a quantity
svytotal() returns directly but a delta-method function of the measured
bins and the reported total, so its standard error is likewise propagated
rather than design-based. (The interval width is unchanged by that switch —
survey's confint() method for a svystat defaults to df = Inf, which
is the normal quantile.)
In every case there is no local sample size to key a t-quantile to:
The number of rows is the number of bins, which is a binning choice made by the caller. Keying degrees of freedom to it would make the interval narrow as the bins got finer, with no additional fish measured.
The row totals are expanded estimates, not counts of measured fish, so their sum is an estimated abundance rather than a sample size.
The honest degrees of freedom belong to the design that produced the upstream standard errors, and the large-sample argument is made there. These four estimators inherit that uncertainty rather than sampling afresh, so the normal quantile is the consistent choice at this level.
estimate_effort_aerial_glmm() is asymptotic by construction and has no
finite df to appeal to. The normal quantile inside Sadinle's logit interval
is part of the method, not a quantile choice.