Very cool model! Quite impressive work.
A couple thoughts/ideas:
- Do you think it's worth adding in a covariate for Class (i.e., Class I, Class II, Class III) races? For example, this year's races are predominantly in R-leaning states, which may confound your measurement of national environment. So, it seems a little difficult to compare national environment in, e.g., 2018 with 2016 because the races are taking places in different states and have different voter pools.
- I know you're dealing with limited sample sizes here, but it seems like it would be helpful for the model to include covariates for which party is controlling the white house (or I guess in your dataset, whether a candidate is in the same party as the President) and whether or not it's a midterm race. If you looked at an interaction of these two you'd probably get an estimate of how much we can expect the national environment to turn against incumbent Presidents in midterms.
- When plotting the response curves of the win probabilities against PVI for each year, it's a little difficult to pick out a trend. It may be more helpful if you use a continuous color scale instead of the color key you're using (e.g., ranging from light to dark red; it looks like you're using R, you can probably get these colors using the rainbow() function). I guess you don't really need to do this because you already have a time series pot of the incumbent advantage, but it may make those response curves easier to digest.
- Kind of a weird question... your model is logistic, so for each race, you'll get a probability of winning for each candidate. Is there any trend over time in how certain these victories are? (e.g., is there a trend where 20 years ago your model had 51% Dem. win probabilities, which is still a highly competitive race, but something like an 80% Dem. win probability in later years, which is a less competitive race?) Sorry this is kind of a weird question and I'm probably not asking it well, so feel free to ask me for clarification.
I told y'all that if you crunch the numbers, Arizona and Florida should be much safer for the Democrats than they currently are.
I take slight issue with North Dakota and West Virginia. I do not think we can obtain meaningful predictions regarding these races, unless there is historical precedent in your model for incumbents in states won by the opposite party President by >35 points running for re-election?
The problem might be that, by its very nature, the model assumes a linear effect of PVI. That is to say, moving a State's PVI from Even to R+10 shifts the odds by the same amount (in the logit scale) as moving it from R+30 to R+40. There's good reason to believe that that's not the case, and that there's really not much difference between an R+30 State and an R+40 one. I could test for that by adding a PVI-squared variable, but I doubt it improves the model all that much. I can still try it if anyone's curious.
I'm curious and definitely think this is worthwhile. I think linear effect of PVI is probably too simple of an estimate -- squaring seems like a good idea. For one thing, even-PVI races will have a lot more resource investment than states with high PVI, so you'd expect things like national environment (and maybe incumbency?) to have a stronger effect in even PVI races than in high PVI ones.
