Exploratory data analysis for discrete data

I am using a probit and a logit model for obtaining the choice probabilities of some data. What kind of plots can be useful to conduct a exploratory data analysis for these data?

Here is the simulated data:

set.seed(1)
x.first <- rbinom(1000,1,0.5)
x.second <- rbinom(1000,1,0.5)
y <- rbinom(1000,1,0.5)
delta.x <- x.first-x.second


and my models are

 logit(p) <- delta.x beta

phi^{-1}(p) <- delta.x beta


where phi^{-1} is the inverse of the standard normal distribution cdfand beta is the regression coefficients.

I am not quite sure why your independent variable is the difference between two binomials, but your delta.x takes three values: -1, 0 and 1. Thus, both your DV and your IV are categorical.

One good graphic for such data is the mosaic plot. One implementation is in the vcd package. Add to your code, e.g.,

library(vcd)
mosaic(y~delta.x)


for a very basic version.

• There are two options for people to choose from: first and second which are represented by x.first and x.second. What I am interested in is that I want to obtain the probability of choosing the first over second. Therefore, I use the difference matrix. What would you suggest in my situation? – Günal Jan 22 '13 at 7:18
• I don't know exactly what you mean by "first over second" but there isn't anything wrong with your dependent variable, I just wasn't sure why you had picked it. – Peter Flom Jan 22 '13 at 11:07
• The interest here is to estimate the choice probabilities by using either a logit or probit model. People are given two options and they choose one. So, the aim is to estimate the probability that the first option is chosen. – Günal Jan 22 '13 at 12:59