To finish off our “toy” example of using Discrete Dependent Variables analysis, following on from the discussion of our data, we will use the probit link function and the NY Times data to test each of our variables for inclusing in a model forecasting the probability to a Republican President. The predictors are:

• height difference (Republican candidate height in feet minus Democrat candidate height in feet);
• weight difference (Republican candidate weight in pounds minus Democrate candidate weight in pounds);
• incumbency i.e. the prior value of the Presidential Party state variable; and,
• change i.e. the value of the Presidential Party state variable at two lags.

I am going to perform this analysis in RATS, but to continue from the prior post I will also illustrate the command used in R to fit such models.

summary(glm(PRES ~ HEIGHT + WEIGHT + INCUMBENCY + CHANGE,
    family=binomial(link="probit"), data=presdata))

The results are:

This analysis performed on all data up to and including 2004 — replicating the original out-of-sample nature of the 2008 election. With over 98% confidence we reject the null hypothesis and add the HEIGHT variable to the model. We then test the remaining variables and will over 97% confidence add CHANGE to the model including HEIGHT. 

The above chart illustrates the implied probabilities extracted from the estimated model. (The shading illustrates the actual party selection.) Out of sample, this exhibits a very strong prediction that President Barack Obama would have been elected and, given the unknown stature of his coming opponent, a marginal probability favouring his relection. Finally, after entertaining ourselves with this “toy” model, we will return to applying this methodology to market data in a coming post.