View source: R/base_functions.R
LLO | R Documentation |
LLO-adjust predicted probabilities based on specified \delta
and
\gamma
.
LLO(x, delta, gamma)
x |
a numeric vector of predicted probabilities of an event. Must only contain values in [0,1]. |
delta |
numeric, must be > 0, parameter |
gamma |
numeric, parameter |
The Linear Log Odds (LLO) recalibration function can be written as
c(x_i;\delta, \gamma) = \frac{\delta x_i^\gamma}{\delta x_i^\gamma +
(1-x_i)^\gamma}
where x_i
is a predicted probability,
\delta > 0
and \gamma \in \mathbb{R}
. Then c(x_i;\delta,
\gamma)
is the corresponding LLO-adjusted probability that has been shifted
by \delta
and scaled by \gamma
on the log odds scale. When
\delta = \gamma = 1
, there is no shifting or scaling imposed on x
.
Vector of LLO-adjusted probabilities via specified \delta
and
\gamma
.
Turner, B., Steyvers, M., Merkle, E., Budescu, D., and Wallsten, T. (2014) Forecast aggregation via recalibration, Machine Learning 95, 261–289.
Gonzalez, R., and Wu, G. (1999), On the shape of probability weighting function, Cognitive Psychology 38, 129–66.
# Vector of probability predictions from 0 to 1
x1 <- seq(0, 1, by=0.1)
x1
# LLO-adjusted predictions via delta = 2, gamma = 3
x1_llo23 <- LLO(x1, 2, 3)
x1_llo23
# LLO-adjusted predictions via delta = 1, gamma = 1
x1_llo11 <- LLO(x1, 1, 1)
x1_llo11 # no change
# Create vector of 100 probability predictions
x2 <- runif(100)
# LLO-adjust via delta = 2, gamma = 3
x2_llo23 <- LLO(x2, 2, 3)
plot(x2, x2_llo23)
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