The Economistin ennustemallin takana oleva Andrew Gelman esitti kriittisiä huomioita aiemmin 538:n mallista ja tekee kootusti nyt samaa "omasta" mallistaan. Todella mielenkiintoista juttua ja kiinnostuneille vahva suositus! Ping
@steierwrass .
statmodeling.stat.columbia.edu
Mielenkiintoinen ero mallien välillä tuo, että 538:lla vähägalluppisissa osavaltioissa epävarmuus liioitellunkin suurta, kun taas Economistin ennusteessa muuta informaatiota huomioiden pienempää, ja kuten Gelman pohdiskelee, ehkä liiankin pientä.
The next thing I noticed is that the Fivethirtyeight intervals get really wide for some of the states that don’t have a lot of polling: look at, for example, Hawaii, Vermont, and California, all of which Fivethirtyeight show with an outside chance of Trump making it close, or Oklahoma, West Virgina, and Wyoming at the other end.
And look how wide the Fivethirtyeight interval is for South Dakota! They have Biden with a 6% chance of winning this very strongly Republican state. But they have just about no poll data: just one poll from Mason-Dixon and seven polls from Survey Monkey. Seven polls doesn’t seem too bad, but they give Survey Monkey a “D-” rating. In contrast, we give Trump more than a 99% chance of winning the state, even though our inference is based only on . . . one poll, that Mason-Dixon survey from October. We don’t include the Survey Monkey polls at all.
What’s the difference between the two forecasts: We make more use of the national polls, along with the relative positions of the states as observed in previous elections. As Pearce notes, the Fivethirtyeight forecast implicitly allows for the possibility of a major realignment, whereby South Dakota becomes competitive in a way that our model does not allow.
Which forecast is better? I can’t say. I’m no expert on South Dakota and have never even been to the state. The point is that the two models are different. We’re using the previous relative positions of the states as a prior (with national polls and other state polls available to estimate the national average); Fivethirtyeight is mostly trying to learn about each state from its own polls. From our model’s perspective, South Dakota is an essentially certain Trump win; from their model’s perspective, they have very little data so all sorts of unusual things can happen.
The Fivethirtyeight intervals for sparsely-polled states are too wide for my taste. Look at Hawaii and Vermont, for example. I think that by not fully accounting for the relative positions of the states in recent elections, as well as the many national polls, their forecast is leaving valuable information on the table.
On the other hand, it’s suspicious that our distributions for all 50 states have roughly the same width (forget about DC; it’s on the edge which has something to do with the logit transformation, and in any case I don’t know that I’d take our forecast or the Fivethirtyeight forecast for DC seriously). No way that I’d want our intervals for Hawaii, Vermont, and California to be as wide as Fivethirtyeight’s, but is it right that our intervals for those states are approximately as narrow as our intervals for Pennsylvania, Michigan, Florida, and other intensively-polled states? Maybe not.
Toinen mielenkiintoinen juttu on, että Gelmanin mielestä heidän olisi pitänyt käyttää t-jakautuneita virheitä normaalien sijaan (sallii suuremman todennäköisyyden äärimmäisille virheille), minkä ero näkyy lähinnä tilanteessa jossa toinen vaikuttaa melko ylivoimaiselta (kuten Biden nyt).
