Logistic and Inverse logistic functions

Description

Inverse-logit function, transforms continuous values to the range (0, 1)

Usage

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logit(x)
invlogit(x)

Arguments

x

A vector of continuous values

Details

The Inverse-logit function defined as: logit^-1(x) = e^x/(1+e^x) transforms continuous values to the range (0, 1), which is necessary, since probabilities must be between 0 and 1 and maps from the linear predictor to the probabilities

Value

A vector of estimated probabilities

Author(s)

Andrew Gelman gelman@stat.columbia.edu, M.Grazia Pittau grazia@stat.columbia.edu

References

Andrew Gelman and Jennifer Hill. (2006). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press.

Examples

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 data(frisk)
 n <- 100
 x1 <- rnorm (n)
 x2 <- rbinom (n, 1, .5)
 b0 <- 1
 b1 <- 1.5
 b2 <- 2
 Inv.logit <- invlogit(b0+b1*x1+b2*x2)
 plot(b0+b1*x1+b2*x2, Inv.logit)