Simulating Data for Logistic Regression

Some data

set.seed(123)

x <- rnorm(100,0,5)

z <- 5 + 5*x - 0.5*x^2

pr <- exp(z) / ( 1 + exp(z))   ## inverse-logit

y <- rbinom(100, 1, pr)

df <- data.frame(y=y, x=x)

Logistic Regression

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## 
## Call:
## glm(formula = y ~ poly(x, degree = 2, raw = TRUE), family = binomial, 
##     data = df)
## 
## Deviance Residuals: 
##      Min        1Q    Median        3Q       Max  
## -1.31828  -0.00093   0.00093   0.00639   1.95644  
## 
## Coefficients:
##                                  Estimate Std. Error z value Pr(>|z|)  
## (Intercept)                        4.8998     2.3243   2.108   0.0350 *
## poly(x, degree = 2, raw = TRUE)1   4.0819     1.7397   2.346   0.0190 *
## poly(x, degree = 2, raw = TRUE)2  -0.4153     0.1796  -2.313   0.0207 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 135.372  on 99  degrees of freedom
## Residual deviance:  16.619  on 97  degrees of freedom
## AIC: 22.619
## 
## Number of Fisher Scoring iterations: 10

Sensitivity Plots

library(plotmo)

## Loading required package: plotrix

## Loading required package: TeachingDemos

plotmo(quad.logit, type="response")  #prob

plotmo(quad.logit, type="link")      #log-odds