In many circumstances political scientists study binary dependent variables that have been measured with bias. For example, in surveys the strategic interests of actors can lead them to misrepresent an attitude or behavior to the surveyor in a non-random fashion. Data on terror or torture that are coded using media reports likely suffer from a similar bias related to factors such as freedom of the press in a country.
To give you an idea of what this new model allows one to do, consider the issue of self-reported infidelity between romantic partners. Using survey data, the reported rate of infidelity is about 13% of the sample. Yet common sense would suggest that this rate be higher, at least due to social desirability bias that would lead respondents who did in fact cheat lie about it to avoid the negative stigma. The split population logit model allows us to separate respondents’ rates of honesty and infidelity separately, as shown in the table excerpt from our paper. It shows for example that 41% of the sample likely cheated on their partner, but also that around three-quarters chose to lie about it when surveyed. Quite a difference from the 13% reported in the observed data.
Here are replication files for the simulations we used to evaluate our estimator and replication files for the infidelity example. The simulations were run through Florida State University High Performance Computing.
Paper to follow in a few weeks.
Another set of notes from when I was TA for our Advanced Quantitative Methods course with Prof. Matt Golder in 2008. The notes for Programming MLE models in Stata (pdf) walk you through how to recreate your own logit regression command and ado files for Stata, as well as how to use simulations to check your model. Here are also the associated ado and do files.
The notes are closely based on Maximum Likelihood Estimation with Stata (2006, see full citation in the notes), which is definitely worth it if you are considering writing your own MLE commands in Stata.
A couple of lab notes from 2009, when I was TA for our Basic Quantitative Methods course: