Predict method for rc_powerlaw objects

Usage

# S3 method for class 'rc_powerlaw'
predict(object, ..., new_stage = NULL, conflev = NULL, predlev = NULL)

Arguments

object: An rc_powerlaw object.
...: Must be empty. Present so that every argument after it has to be named in full; a misspelt or unsupported argument is an error, not silently ignored.
new_stage: Stages at which to predict discharge. If NULL, a grid of 1000 equally spaced stages spanning the observed range is used.
conflev: The confidence level for the confidence limits; if NULL, no confidence limits are returned.
predlev: The prediction level for the prediction limits; if NULL, no prediction limits are returned.

Value

A tibble with the stages (stage), the predicted discharges (fit) and, if requested, the lower and upper confidence limits (ci_lwr, ci_upr) and prediction limits (pi_lwr, pi_upr).

What the limits assume

The limits use the t distribution, so they assume the scatter of the gaugings about the curve is normal (on the log scale, for rc_powerlaw_log()), with the spread the weighting scheme describes. Confidence limits depend on this only mildly, because estimates average over many gaugings. Prediction limits depend on it directly: if the scatter is skewed or has heavy tails, they can miss, especially at high levels such as 0.99. Check the residuals before relying on them.

Even when the scatter is normal, most limits are approximations: a 95% interval covers the truth roughly, not exactly, 95% of the time. That is because the curve is nonlinear in its parameters and is approximated by a straight line about the estimates (the delta method), because the weights are themselves estimated from the fit (under var_prop() and var_power()), or, for rc_loess(), because of the smoother's approximations. The approximation is good with plenty of gaugings, and poorer with few, or beyond the range of the gaugings. The limits are exact only for fits that are linear in their parameters with weights fixed in advance: rc_poly() with var_none() or var_spec(), and rc_powerlaw_log() with offset given.