LLO {BRcal}

Linear Log Odds (LLO) Recalibration Function

Description

LLO-adjust predicted probabilities based on specified \delta and \gamma.

Usage

LLO(x, delta, gamma)

Arguments

x

a numeric vector of predicted probabilities of an event. Must only contain values in [0,1].

delta

numeric, must be > 0, parameter \delta in LLO recalibration function.

gamma

numeric, parameter \gamma in LLO recalibration function.

Details

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.

Value

Vector of LLO-adjusted probabilities via specified \delta and \gamma.

References

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.

Examples

# 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)