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State and national presidential election forecasting model

Last update on Thursday October 15, 2020 at 12:29 PM 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 - the final model we use for the 2020 presidential election
  • poll_model_2020_no_mode_adjustment.stan - a model that removes the correction for partisan non-response bias in the polls and the adjustments for the mode in which a survey is conducted (live phone, online, other) and its population (adult, likely voter, registered voter)

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 polls and the electoral college over time

State vs national deltas over time

Model results vs polls vs the prior

Performance

outlet ev_wtd_brier unwtd_brier states_correct
economist (backtest) 0.0321964 0.0289902 49 

## [1] 0.02318035

Predictions for each state

state mean low high prob se
NC 0.502 0.466 0.538 0.545 0.021
MO 0.509 0.474 0.543 0.704 0.020
FL 0.514 0.479 0.548 0.788 0.020
IN 0.484 0.448 0.519 0.179 0.021
AR 0.477 0.439 0.516 0.124 0.023
OH 0.524 0.489 0.559 0.917 0.021
MT 0.475 0.437 0.512 0.094 0.022
VA 0.527 0.491 0.564 0.917 0.022
GA 0.473 0.437 0.511 0.083 0.022
WV 0.470 0.434 0.507 0.058 0.022
AZ 0.468 0.429 0.507 0.055 0.023
NV 0.532 0.494 0.568 0.952 0.022
CO 0.533 0.496 0.571 0.961 0.022
– 0.539 0.517 0.562 1.000 0.013
LA 0.460 0.421 0.500 0.025 0.024
MS 0.457 0.418 0.497 0.019 0.024
TX 0.454 0.413 0.495 0.015 0.024
SD 0.453 0.413 0.492 0.008 0.023
SC 0.450 0.412 0.488 0.003 0.023
NH 0.550 0.514 0.587 0.998 0.022
ND 0.449 0.409 0.487 0.006 0.023
PA 0.554 0.518 0.588 0.999 0.020
TN 0.445 0.406 0.484 0.003 0.023
WI 0.557 0.521 0.592 0.999 0.021
KY 0.442 0.405 0.478 0.001 0.021
MN 0.559 0.523 0.595 1.000 0.021
NM 0.561 0.522 0.599 0.998 0.023
IA 0.562 0.526 0.597 1.000 0.021
MI 0.565 0.530 0.598 1.000 0.020
OR 0.572 0.535 0.608 1.000 0.021
KS 0.424 0.387 0.460 0.000 0.022
AK 0.417 0.377 0.458 0.000 0.024
WA 0.584 0.548 0.620 1.000 0.021
ME 0.584 0.545 0.620 1.000 0.021
NJ 0.590 0.552 0.627 1.000 0.022
AL 0.405 0.368 0.444 0.000 0.023
NE 0.402 0.365 0.440 0.000 0.023
DE 0.616 0.577 0.652 1.000 0.022
CA 0.617 0.578 0.653 1.000 0.022
MD 0.618 0.572 0.664 1.000 0.027
CT 0.619 0.579 0.655 1.000 0.022
OK 0.378 0.340 0.417 0.000 0.023
IL 0.629 0.591 0.663 1.000 0.020
WY 0.366 0.331 0.404 0.000 0.022
MA 0.642 0.603 0.680 1.000 0.023
ID 0.354 0.318 0.392 0.000 0.022
NY 0.647 0.610 0.683 1.000 0.021
VT 0.654 0.615 0.693 1.000 0.023
UT 0.343 0.306 0.381 0.000 0.023
HI 0.663 0.622 0.703 1.000 0.024
RI 0.670 0.633 0.706 1.000 0.021
DC 0.933 0.917 0.946 1.000 0.008

2012

Map

Final electoral college histogram

National and state polls and the electoral college over time

State vs national deltas over time

Model results vs polls vs the prior

Performance

outlet ev_wtd_brier unwtd_brier states_correct
Linzer NA 0.0038000 NA
Wang/Ferguson NA 0.0076100 NA
Silver/538 NA 0.0091100 NA
Jackman/Pollster NA 0.0097100 NA
Desart/Holbrook NA 0.0160500 NA
economist (backtest) 0.0324297 0.0193188 50
Intrade NA 0.0281200 NA
Enten/Margin of Error NA 0.0507500 NA 

## [1] 0.02247233

Predictions for each state

state mean low high prob se
VA 0.504 0.467 0.539 0.586 0.021
CO 0.505 0.471 0.541 0.617 0.021
FL 0.495 0.457 0.531 0.394 0.021
OH 0.510 0.474 0.545 0.704 0.021
– 0.510 0.489 0.533 0.773 0.014
NH 0.513 0.478 0.548 0.758 0.021
IA 0.514 0.480 0.550 0.785 0.021
NC 0.485 0.451 0.521 0.212 0.022
NV 0.516 0.478 0.554 0.797 0.022
WI 0.521 0.486 0.556 0.876 0.021
PA 0.528 0.492 0.563 0.937 0.021
MN 0.534 0.500 0.568 0.974 0.021
MI 0.537 0.502 0.572 0.979 0.021
OR 0.538 0.499 0.575 0.971 0.022
MO 0.460 0.424 0.496 0.015 0.022
NM 0.540 0.500 0.580 0.976 0.023
IN 0.455 0.420 0.492 0.006 0.022
MT 0.453 0.417 0.489 0.006 0.022
GA 0.452 0.413 0.492 0.009 0.024
AZ 0.452 0.414 0.491 0.009 0.023
NJ 0.556 0.518 0.593 0.999 0.022
ME 0.557 0.520 0.593 0.999 0.021
WA 0.561 0.526 0.596 1.000 0.021
SC 0.438 0.395 0.483 0.004 0.026
CT 0.567 0.529 0.603 1.000 0.022
SD 0.431 0.392 0.470 0.000 0.023
ND 0.422 0.385 0.461 0.000 0.023
MS 0.421 0.375 0.468 0.000 0.028
TN 0.419 0.383 0.458 0.000 0.023
WV 0.416 0.378 0.456 0.000 0.024
CA 0.585 0.549 0.622 1.000 0.022
MA 0.588 0.552 0.623 1.000 0.021
TX 0.409 0.372 0.448 0.000 0.023
NE 0.407 0.370 0.444 0.000 0.022
IL 0.599 0.562 0.635 1.000 0.021
LA 0.401 0.363 0.442 0.000 0.024
DE 0.602 0.555 0.646 1.000 0.026
KY 0.398 0.360 0.438 0.000 0.024
KS 0.395 0.355 0.435 0.000 0.024
MD 0.607 0.565 0.646 1.000 0.023
RI 0.616 0.575 0.654 1.000 0.023
AR 0.384 0.346 0.423 0.000 0.023
AL 0.383 0.342 0.423 0.000 0.024
NY 0.620 0.584 0.655 1.000 0.021
AK 0.363 0.320 0.407 0.000 0.026
VT 0.660 0.620 0.697 1.000 0.022
HI 0.661 0.620 0.699 1.000 0.023
ID 0.331 0.295 0.369 0.000 0.022
OK 0.330 0.293 0.369 0.000 0.023
WY 0.313 0.277 0.350 0.000 0.022
UT 0.291 0.257 0.326 0.000 0.021
DC 0.903 0.880 0.924 1.000 0.012

2016

Map

Final electoral college histogram

National and state polls and the electoral college over time

State vs national deltas over time

Model results vs polls vs the prior

Performance

outlet ev_wtd_brier unwtd_brier states_correct
economist (backtest) 0.0725679 0.0508319 48
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] 0.02724916

Predictions for each state

state mean low high prob se
FL 0.496 0.457 0.536 0.435 0.024
NV 0.508 0.467 0.548 0.652 0.024
NC 0.492 0.451 0.532 0.340 0.024
– 0.512 0.485 0.540 0.791 0.017
NH 0.514 0.475 0.554 0.736 0.024
PA 0.514 0.475 0.553 0.745 0.024
CO 0.516 0.476 0.555 0.774 0.023
OH 0.484 0.445 0.523 0.217 0.023
MI 0.518 0.479 0.558 0.816 0.024
WI 0.521 0.483 0.561 0.844 0.024
IA 0.478 0.439 0.517 0.148 0.023
VA 0.523 0.482 0.562 0.863 0.023
MN 0.527 0.489 0.568 0.909 0.024
AZ 0.471 0.430 0.510 0.077 0.024
GA 0.470 0.430 0.508 0.069 0.023
NM 0.532 0.489 0.575 0.926 0.025
ME 0.542 0.503 0.582 0.985 0.024
SC 0.452 0.411 0.493 0.011 0.024
OR 0.549 0.509 0.590 0.992 0.025
TX 0.443 0.403 0.483 0.002 0.024
MO 0.439 0.401 0.478 0.001 0.023
MS 0.436 0.397 0.476 0.001 0.024
CT 0.565 0.525 0.607 1.000 0.024
WA 0.567 0.528 0.607 1.000 0.024
DE 0.568 0.525 0.609 1.000 0.025
AK 0.425 0.384 0.468 0.000 0.026
NJ 0.578 0.537 0.619 1.000 0.024
IN 0.419 0.380 0.458 0.000 0.023
IL 0.583 0.543 0.623 0.999 0.024
LA 0.410 0.371 0.449 0.000 0.024
MT 0.406 0.368 0.446 0.000 0.024
RI 0.595 0.555 0.636 1.000 0.024
KS 0.403 0.368 0.441 0.000 0.022
TN 0.403 0.365 0.442 0.000 0.023
SD 0.398 0.361 0.438 0.000 0.023
NY 0.611 0.571 0.649 1.000 0.023
ND 0.389 0.352 0.429 0.000 0.024
NE 0.388 0.351 0.428 0.000 0.023
AL 0.384 0.346 0.423 0.000 0.023
AR 0.382 0.345 0.421 0.000 0.023
CA 0.620 0.581 0.658 1.000 0.023
UT 0.375 0.337 0.412 0.000 0.022
KY 0.373 0.336 0.411 0.000 0.023
MA 0.629 0.591 0.668 1.000 0.023
MD 0.639 0.598 0.677 1.000 0.023
WV 0.353 0.316 0.390 0.000 0.022
ID 0.349 0.313 0.386 0.000 0.022
OK 0.342 0.305 0.378 0.000 0.022
VT 0.658 0.619 0.696 1.000 0.023
HI 0.661 0.620 0.699 1.000 0.023
WY 0.289 0.255 0.324 0.000 0.021
DC 0.908 0.885 0.928 1.000 0.012

Cumulative charts

Probability calibration plot

Confidence interval coverage

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.

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

projects.economist.com/us-2020-forecast/president

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