logit and inverse logit (expit) functions

Usage

logit(x, low = 0, high = 1)

expit(alpha, low = 0, high = 1)

logitNormInfo(mean = 0, sd = 1, low = 0, high = 1, abs.tol = 1e-06, ...)

probitNormInfo(mean = 0, sd = 1, low = 0, high = 1, abs.tol = 1e-06, ...)

Arguments

x: Input value(s) in range [low,high] to translate -Inf to Inf
low: Lowest value in the range
high: Highest value in the range
alpha: Infinite value(s) to translate to range of [low, high]
mean: logit-scale mean
sd: logit-scale standard deviation
abs.tol: absolute accuracy requested.
...: other parameters passed to integrate()

Value

values from logit and expit

Details

logit is given by:

logit(x, low, high) = log(x-low) - log(high-x)

which equals -log(1/p-1) with p = (x-low)/(high-low) but keeps precision near the bounds; it is -Inf at x = low, Inf at x = high (like qlogis()) and NaN outside [low, high].

expit is given by:

expit(p, low, high) = (high-low)/(1+exp(-alpha)) + low

so expit(-Inf) = low and expit(Inf) = high.

The logitNormInfo() gives the mean, variance and coefficient of variability on the untransformed scale.

Examples


logit(0.25)
#> [1] -1.098612

expit(-1.09)
#> [1] 0.2516183

logitNormInfo(logit(0.25), sd = 0.1)
#>         mean          var           cv 
#> 0.2504672899 0.0003515538 0.0748591440 

logitNormInfo(logit(1, 0, 10), sd = 1, low = 0, high = 10)
#>      mean       var        cv 
#> 1.3386966 1.2662276 0.8405697