[R] Probit predictions outside (0,1) interval

[Arnab mukherji]

Hi!

I was trying to implement a probit model on a dichotomous outcome variable and found that the predictions were outside the (0,1) interval that one should get. I later tried it with some simulated data with a similar result. 

Here is a toy program I wrote and I cant figure why I should be getting such odd predictions.

x1<-rnorm(1000)
x2<-rnorm(1000)
x3<-rnorm(1000)
x4<-rnorm(1000)
x5<-rnorm(1000)
x6<-rnorm(1000)
e1<-rnorm(1000)/3
e2<-rnorm(1000)/3
e3<-rnorm(1000)/3
y<-1-(1-pnorm(-2+0.33*x1+0.66*x2+1*x3+e1)*1-(pnorm(1+1.5*x4-0.25*x5+e2)*pnorm(1+0.2*x6+e3)))
y <- y>runif(1000)
dat<-data.frame(y = y, x1 = x1, x2 = x2, x3 = x3)
g<-glm(y~., data = dat, family = binomial)
summary(g)
yhat<-predict(g, dat)


Call:
glm(formula = y ~ ., family = binomial, data = dat)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-1.8383  -1.3519   0.7638   0.9249   1.3698  

Coefficients:
            Estimate Std. Error z value Pr(>|z|)    
(Intercept)  0.71749    0.06901  10.397  < 2e-16 ***
x1           0.10211    0.07057   1.447  0.14791    
x2           0.21068    0.07177   2.936  0.00333 ** 
x3           0.35162    0.07070   4.974 6.57e-07 ***
---
Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 1275.3  on 999  degrees of freedom
Residual deviance: 1239.4  on 996  degrees of freedom
AIC: 1247.4

Number of Fisher Scoring iterations: 4

> yhat<-predict(g, dat)
> 
> range(yhat)
[1] -0.4416826  2.0056527
> range(y)
[1] 0 1

Any advice would be really helpful.

thanks
Arnab