A dynamic multilevel Bayesian model to predict US presidential elections

State and national presidential election forecasting model

Last update on Thursday June 11, 2020 at 07:37 AM EDT

Code for a dynamic multilevel Bayesian model to predict US presidential elections. Written in R and Stan.

Improving on Pierre Kremp’s implementation of Drew Linzer’s dynamic linear model for election forecasting (Linzer 2013) , we (1) add corrections for partisan non-response, survey mode and survey population; (2) use informative state-level priors that update throughout the election year; and (3) specify empirical state-level correlations from political and demographic variables.

You can see the model’s predictions for 2020 here and read how it works here .

File dictionary

In terms of useful files, you should pay attention to the 3 scripts for the 2008, 2012 and 2016 US presidential elections are located in the scripts/model directory. There are three R scripts that import data, run models and parse results:

final_model_2008.R
final_model_2012.R
final_model_2016.R

And there are 3 different Stan scripts that will run different versions of our polling aggregate and election forecasting model:

poll_model_2020.stan
poll_model_2020_no_partisan_correction.stan
poll_model_2020_no_mode_adjustment.stan

The model diagnostics displayed below are all results of the poll_model_2020.stan script.

Model performance

Here is a graphical summary of the model’s performance in 2008, 2012 and 2016.

2008

Map

Final electoral-college histogram

National and state polling averages and the electoral college “now-cast” over time

States’ partisan leans over time

Model results vs polls vs the prior

Performance

outlet ev_wtd_brier unwtd_brier states_correct economist (backtest) 0.0333707 0.0302863 49

## [1] 0.02242826

Predictions for each state

state mean low high prob se NC 0.503 0.454 0.555 0.527 0.031 MO 0.510 0.461 0.561 0.635 0.030 IN 0.486 0.434 0.537 0.330 0.031 MT 0.483 0.427 0.534 0.297 0.031 FL 0.519 0.472 0.569 0.734 0.030 GA 0.476 0.425 0.528 0.201 0.031 VA 0.527 0.479 0.574 0.818 0.028 OH 0.527 0.478 0.576 0.818 0.029 AR 0.472 0.423 0.524 0.190 0.031 AZ 0.470 0.418 0.523 0.172 0.032 WV 0.469 0.420 0.520 0.154 0.031 NV 0.534 0.483 0.587 0.859 0.031 MS 0.465 0.412 0.522 0.134 0.034 CO 0.535 0.485 0.583 0.878 0.028 ND 0.463 0.403 0.520 0.150 0.034 LA 0.461 0.412 0.514 0.102 0.031 TX 0.458 0.407 0.508 0.092 0.030 – 0.544 0.513 0.575 0.996 0.018 SC 0.455 0.408 0.508 0.066 0.032 SD 0.453 0.401 0.506 0.074 0.031 NH 0.552 0.503 0.602 0.956 0.030 PA 0.557 0.508 0.606 0.966 0.029 WI 0.559 0.507 0.606 0.974 0.028 KY 0.440 0.391 0.491 0.030 0.031 NM 0.560 0.502 0.614 0.951 0.032 MN 0.561 0.512 0.611 0.976 0.030 TN 0.438 0.388 0.491 0.030 0.032 IA 0.564 0.512 0.612 0.978 0.029 MI 0.565 0.516 0.612 0.981 0.028 AK 0.427 0.375 0.479 0.007 0.031 OR 0.575 0.524 0.624 0.993 0.030 KS 0.424 0.375 0.475 0.009 0.030 ME 0.587 0.537 0.635 0.997 0.029 WA 0.587 0.536 0.636 0.998 0.030 NE 0.412 0.363 0.462 0.001 0.029 AL 0.407 0.359 0.460 0.009 0.031 NJ 0.594 0.543 0.644 0.999 0.030 DE 0.619 0.569 0.666 0.999 0.028 CA 0.621 0.569 0.669 1.000 0.028 OK 0.379 0.330 0.432 0.001 0.031 CT 0.623 0.576 0.670 1.000 0.028 WY 0.375 0.325 0.426 0.000 0.031 MD 0.629 0.568 0.687 0.999 0.034 IL 0.633 0.586 0.679 1.000 0.027 MA 0.636 0.586 0.686 1.000 0.030 ID 0.352 0.301 0.404 0.000 0.031 NY 0.649 0.599 0.699 1.000 0.029 UT 0.344 0.297 0.393 0.000 0.029 VT 0.660 0.611 0.707 1.000 0.028 RI 0.669 0.622 0.716 1.000 0.028 HI 0.677 0.618 0.727 1.000 0.030 DC 0.908 0.880 0.934 1.000 0.015

2012

Map

Final electoral-college histogram

National and state polling averages and the electoral college “now-cast” over time

States’ partisan leans over time

Model results vs polls vs the prior

Performance

outlet ev_wtd_brier unwtd_brier states_correct Linzer NA 0.003800 NA Wang/Ferguson NA 0.007610 NA Silver/538 NA 0.009110 NA Jackman/Pollster NA 0.009710 NA Desart/Holbrook NA 0.016050 NA economist (backtest) 0.0327484 0.021624 50 Intrade NA 0.028120 NA Enten/Margin of Error NA 0.050750 NA

## [1] 0.02187645

Predictions for each state

state mean low high prob se FL 0.497 0.450 0.542 0.468 0.027 VA 0.506 0.461 0.550 0.591 0.026 CO 0.510 0.465 0.557 0.645 0.028 OH 0.511 0.465 0.558 0.656 0.028 – 0.512 0.480 0.542 0.773 0.018 NC 0.488 0.442 0.534 0.343 0.027 NH 0.517 0.470 0.564 0.726 0.028 IA 0.518 0.473 0.561 0.749 0.026 NV 0.521 0.474 0.568 0.787 0.028 WI 0.524 0.478 0.569 0.805 0.027 PA 0.531 0.485 0.577 0.862 0.027 MO 0.463 0.416 0.510 0.095 0.028 MN 0.538 0.493 0.582 0.916 0.027 OR 0.539 0.492 0.585 0.919 0.027 AZ 0.459 0.412 0.504 0.072 0.027 MI 0.541 0.495 0.586 0.928 0.027 IN 0.458 0.413 0.504 0.062 0.027 NM 0.543 0.496 0.589 0.936 0.027 MT 0.455 0.409 0.502 0.056 0.028 GA 0.453 0.405 0.499 0.049 0.028 SC 0.441 0.386 0.496 0.043 0.033 NJ 0.559 0.510 0.606 0.975 0.028 SD 0.439 0.392 0.487 0.016 0.029 ME 0.561 0.515 0.606 0.982 0.027 WA 0.565 0.519 0.612 0.987 0.028 CT 0.571 0.523 0.619 0.993 0.029 ND 0.425 0.380 0.469 0.005 0.026 TN 0.425 0.378 0.472 0.004 0.028 NE 0.422 0.375 0.470 0.003 0.028 WV 0.418 0.368 0.469 0.002 0.031 MS 0.415 0.351 0.478 0.015 0.037 TX 0.415 0.373 0.461 0.002 0.027 CA 0.590 0.547 0.632 0.998 0.025 MA 0.590 0.541 0.637 0.996 0.028 LA 0.405 0.359 0.452 0.002 0.028 KY 0.405 0.354 0.455 0.000 0.030 KS 0.399 0.342 0.460 0.005 0.036 DE 0.604 0.549 0.659 0.997 0.033 IL 0.604 0.556 0.649 1.000 0.027 MD 0.607 0.559 0.653 1.000 0.027 AL 0.389 0.342 0.437 0.000 0.028 AR 0.378 0.333 0.425 0.000 0.028 RI 0.623 0.573 0.672 1.000 0.029 NY 0.623 0.576 0.668 1.000 0.027 AK 0.366 0.306 0.428 0.001 0.037 OK 0.339 0.290 0.393 0.000 0.032 HI 0.662 0.615 0.707 1.000 0.027 VT 0.674 0.622 0.721 1.000 0.028 ID 0.325 0.276 0.375 0.000 0.030 WY 0.317 0.250 0.391 0.000 0.044 UT 0.275 0.231 0.323 0.000 0.029 DC 0.899 0.848 0.938 1.000 0.023

2016

Map

Final electoral-college histogram

National and state polling averages and the electoral college “now-cast” over time

States’ partisan leans over time

Model results vs polls vs the prior

Performance

outlet ev_wtd_brier unwtd_brier states_correct economist (backtest) 0.0864787 0.0602528 47 538 polls-plus 0.0928000 0.0664000 46 538 polls-only 0.0936000 0.0672000 46 princeton 0.1169000 0.0744000 47 nyt upshot 0.1208000 0.0801000 46 kremp/slate 0.1210000 0.0766000 46 pollsavvy 0.1219000 0.0794000 46 predictwise markets 0.1272000 0.0767000 46 predictwise overall 0.1276000 0.0783000 46 desart and holbrook 0.1279000 0.0825000 44 daily kos 0.1439000 0.0864000 46 huffpost 0.1505000 0.0892000 46

## [1] 0.03073332

Predictions for each state

state mean low high prob se FL 0.502 0.457 0.547 0.509 0.027 NC 0.496 0.448 0.542 0.455 0.027 OH 0.492 0.447 0.537 0.386 0.027 IA 0.491 0.443 0.541 0.384 0.030 NV 0.514 0.465 0.562 0.676 0.029 – 0.517 0.487 0.547 0.846 0.018 PA 0.519 0.474 0.566 0.747 0.028 CO 0.520 0.475 0.566 0.763 0.028 NH 0.521 0.475 0.567 0.764 0.028 AZ 0.475 0.425 0.525 0.204 0.029 MI 0.527 0.482 0.572 0.844 0.027 WI 0.528 0.485 0.574 0.846 0.027 VA 0.528 0.483 0.572 0.857 0.026 GA 0.471 0.426 0.518 0.148 0.028 MN 0.534 0.486 0.580 0.884 0.027 NM 0.540 0.495 0.587 0.918 0.028 SC 0.456 0.410 0.501 0.052 0.027 ME 0.551 0.506 0.597 0.968 0.027 MO 0.446 0.401 0.492 0.025 0.028 OR 0.555 0.509 0.600 0.976 0.027 TX 0.442 0.397 0.488 0.018 0.027 MS 0.441 0.394 0.488 0.021 0.028 WA 0.573 0.528 0.619 0.996 0.027 CT 0.573 0.526 0.616 0.995 0.026 AK 0.426 0.380 0.470 0.003 0.026 IN 0.426 0.379 0.472 0.002 0.028 DE 0.576 0.532 0.621 0.997 0.027 NJ 0.580 0.532 0.626 0.997 0.028 MT 0.413 0.368 0.460 0.001 0.028 LA 0.412 0.368 0.456 0.002 0.027 KS 0.412 0.362 0.460 0.001 0.029 IL 0.589 0.542 0.635 0.999 0.028 TN 0.407 0.363 0.453 0.000 0.027 RI 0.594 0.545 0.643 0.999 0.029 SD 0.405 0.359 0.452 0.000 0.028 UT 0.395 0.325 0.452 0.000 0.034 NE 0.393 0.347 0.440 0.000 0.028 NY 0.610 0.566 0.655 1.000 0.027 AR 0.390 0.345 0.437 0.000 0.028 AL 0.389 0.344 0.434 0.000 0.027 ND 0.387 0.339 0.435 0.000 0.029 KY 0.378 0.334 0.422 0.000 0.026 CA 0.624 0.581 0.666 1.000 0.025 MA 0.631 0.585 0.676 1.000 0.027 MD 0.638 0.592 0.682 1.000 0.026 ID 0.359 0.317 0.407 0.000 0.028 WV 0.358 0.316 0.402 0.000 0.026 HI 0.653 0.605 0.700 1.000 0.028 OK 0.346 0.302 0.391 0.000 0.027 VT 0.676 0.629 0.719 1.000 0.026 WY 0.290 0.251 0.335 0.000 0.026 DC 0.906 0.870 0.936 1.000 0.018

Cumulative charts

Calibration plot

Licence

This software is published by The Economist under the MIT licence . The data generated by The Economist are available under the Creative Commons Attribution 4.0 International License .

The licences include only the data and the software authored by The Economist , and do not cover any Economist content or third-party data or content made available using the software. More information about licensing, syndication and the copyright of Economist content can be found here .