# [R] plot of Bernoulli data

Frank E Harrell Jr fharrell at virginia.edu
Tue Oct 2 15:15:12 CEST 2001

```The loess smoother, with outlier detection turned off,
is an excellent way to estimate the relationship
between a continuous variable and the probability
of an event, based on a binary dependent variable.
Use lowess(x,y,iter=0).  I do wonder about the way in
which your data are generated, however.  You

p <- whatever  # and check that if you use pnorm the
# first arg to pnorm spans the right metric
y <- 1*(runif(n) <= p)  # n=100 in your example

Bill Simpson wrote:
>
> I have some Bernoulli data something like this:
>  x<-sort(runif(100,1,20))
>  p<-pnorm(x,10,3)
>  y<-as.numeric(runif(x)<p)
>  plot(x,y)
>  lines(x,p)
>
> This plot is not very satisfactory because the ogive does not visually
> fit the (0,1) points very well, and also because the points tend to fall
> on top of one another. The second problem can be eliminated by adding
> vertical jitter. However I was thinking about the following plot. Instead
> of plotting all the 0,1 points, instead divide the x axis into bins. In
> each bin, find the average y value. Then plot (x=average of x values in
> bin, y=average of 0,1 values in bin). So if I use 10 bins I have 10 points
> in the plot and now the y-values are proportions instead of 0/1.  Is this
> a plot that other people have used (refs appreciated)? If so maybe someone
> has code to do this. Otherwise, I am not sure of how to do this in R.
> Could someone help me?  Thanks very much.
>
> Bill
>
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--
Frank E Harrell Jr              Prof. of Biostatistics & Statistics
Div. of Biostatistics & Epidem. Dept. of Health Evaluation Sciences
U. Virginia School of Medicine  http://hesweb1.med.virginia.edu/biostat
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```