I have a continuous independent variable, X, and two binary dependent variables, Y and Z. I'm trying to run a binary logistic regression that models the correlation between Y and Z. X = age, while Y and Z are two pass/fail tasks. I want to determine the probability of an individual passing a given task at a given age, but I also want to test whether individuals who pass one task tend to also pass the other.
How should I go about doing this? I've tried the following in R:
glm(cbind(Z,Y)~X, family="binomial", data= my_data)
This gives me a coefficient of -0.02335 for X. However, when I reverse the order of (Z,Y) in the formula above, the X coefficient becomes positive. Why is that?
Does anyone know how to run a binary logistic regression in R with correlated dependent variables?