State and national presidential election forecasting model

Last update on Wednesday August 05, 2020 at 09:53 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 - 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)	0.0327228	0.0290726	49

## [1] 0.02310776

Predictions for each state

state	mean	low	high	prob	se
NC	0.501	0.471	0.533	0.525	0.019
MO	0.509	0.479	0.539	0.693	0.018
FL	0.513	0.483	0.545	0.774	0.019
IN	0.483	0.454	0.513	0.178	0.018
AR	0.477	0.443	0.508	0.112	0.019
OH	0.524	0.495	0.554	0.908	0.018
VA	0.526	0.495	0.557	0.922	0.018
MT	0.474	0.445	0.505	0.082	0.018
GA	0.473	0.441	0.504	0.078	0.019
NV	0.531	0.500	0.562	0.949	0.018
WV	0.469	0.439	0.501	0.053	0.019
AZ	0.468	0.437	0.500	0.048	0.019
CO	0.533	0.502	0.564	0.956	0.018
LA	0.460	0.425	0.494	0.026	0.021
–	0.540	0.520	0.557	1.000	0.011
MS	0.456	0.423	0.490	0.019	0.020
TX	0.453	0.418	0.488	0.015	0.020
SD	0.452	0.421	0.483	0.005	0.019
NH	0.550	0.519	0.580	0.996	0.018
SC	0.449	0.416	0.482	0.005	0.020
ND	0.448	0.417	0.480	0.004	0.019
PA	0.553	0.524	0.583	0.998	0.018
TN	0.444	0.414	0.476	0.002	0.019
WI	0.557	0.526	0.586	0.999	0.017
KY	0.441	0.412	0.472	0.001	0.018
MN	0.559	0.528	0.588	0.999	0.017
NM	0.560	0.527	0.592	0.997	0.019
IA	0.561	0.531	0.591	1.000	0.018
MI	0.564	0.534	0.593	1.000	0.017
OR	0.571	0.542	0.600	1.000	0.017
KS	0.423	0.393	0.454	0.000	0.018
ME	0.583	0.552	0.614	1.000	0.018
WA	0.584	0.553	0.613	1.000	0.018
AK	0.416	0.383	0.449	0.000	0.020
NJ	0.590	0.559	0.620	1.000	0.018
AL	0.405	0.373	0.438	0.000	0.020
NE	0.402	0.370	0.434	0.000	0.019
DE	0.615	0.582	0.648	1.000	0.020
CA	0.616	0.584	0.648	1.000	0.019
CT	0.618	0.586	0.649	1.000	0.018
MD	0.618	0.580	0.654	1.000	0.021
OK	0.378	0.347	0.411	0.000	0.020
IL	0.629	0.597	0.660	1.000	0.018
WY	0.366	0.335	0.396	0.000	0.018
MA	0.642	0.611	0.673	1.000	0.018
NY	0.646	0.617	0.675	1.000	0.017
ID	0.354	0.324	0.383	0.000	0.018
VT	0.654	0.623	0.683	1.000	0.018
UT	0.342	0.312	0.373	0.000	0.018
HI	0.662	0.628	0.697	1.000	0.021
RI	0.670	0.639	0.698	1.000	0.017
DC	0.933	0.920	0.944	1.000	0.007

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)	0.0320587	0.0188167	50
Intrade	NA	0.0281200	NA
Enten/Margin of Error	NA	0.0507500	NA

## [1] 0.02241299

Predictions for each state

state	mean	low	high	prob	se
VA	0.504	0.475	0.533	0.589	0.017
FL	0.495	0.466	0.525	0.391	0.018
CO	0.506	0.476	0.535	0.620	0.017
–	0.509	0.490	0.529	0.785	0.012
OH	0.510	0.482	0.539	0.721	0.017
NH	0.513	0.483	0.543	0.768	0.018
NC	0.486	0.457	0.515	0.212	0.017
IA	0.515	0.486	0.544	0.793	0.017
NV	0.516	0.486	0.547	0.807	0.018
WI	0.521	0.491	0.551	0.884	0.018
PA	0.528	0.498	0.558	0.936	0.018
MN	0.534	0.504	0.564	0.971	0.018
MI	0.538	0.509	0.568	0.983	0.018
OR	0.539	0.508	0.571	0.979	0.019
MO	0.460	0.430	0.491	0.014	0.018
NM	0.540	0.509	0.572	0.983	0.019
IN	0.456	0.426	0.487	0.009	0.018
MT	0.453	0.423	0.484	0.004	0.018
AZ	0.453	0.421	0.483	0.006	0.018
GA	0.452	0.420	0.484	0.006	0.019
NJ	0.556	0.525	0.587	0.999	0.018
ME	0.558	0.527	0.589	0.999	0.018
SC	0.439	0.401	0.475	0.004	0.022
WA	0.562	0.531	0.591	1.000	0.017
CT	0.567	0.537	0.596	1.000	0.017
SD	0.431	0.398	0.465	0.000	0.020
ND	0.423	0.393	0.454	0.000	0.019
MS	0.420	0.382	0.458	0.000	0.023
TN	0.419	0.388	0.450	0.000	0.019
WV	0.416	0.384	0.452	0.000	0.021
CA	0.585	0.555	0.615	1.000	0.018
MA	0.588	0.559	0.617	1.000	0.017
TX	0.409	0.378	0.442	0.000	0.019
NE	0.408	0.377	0.438	0.000	0.018
LA	0.401	0.368	0.434	0.000	0.020
IL	0.600	0.569	0.629	1.000	0.018
KY	0.399	0.366	0.434	0.000	0.020
DE	0.602	0.565	0.638	1.000	0.021
KS	0.396	0.360	0.431	0.000	0.021
MD	0.607	0.573	0.639	1.000	0.019
RI	0.616	0.584	0.648	1.000	0.019
AR	0.384	0.352	0.418	0.000	0.020
AL	0.383	0.350	0.415	0.000	0.020
NY	0.620	0.590	0.649	1.000	0.017
AK	0.364	0.326	0.401	0.000	0.022
VT	0.660	0.628	0.693	1.000	0.019
HI	0.661	0.630	0.692	1.000	0.019
ID	0.332	0.301	0.364	0.000	0.019
OK	0.331	0.298	0.363	0.000	0.019
WY	0.313	0.281	0.347	0.000	0.020
UT	0.291	0.261	0.320	0.000	0.018
DC	0.903	0.884	0.920	1.000	0.010

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)	0.0746651	0.0520891	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] 0.0274812

Predictions for each state

state	mean	low	high	prob	se
FL	0.497	0.458	0.536	0.436	0.023
NC	0.493	0.453	0.534	0.367	0.024
NV	0.509	0.468	0.549	0.667	0.023
–	0.514	0.483	0.543	0.831	0.017
PA	0.514	0.475	0.554	0.757	0.024
NH	0.514	0.474	0.555	0.746	0.024
OH	0.485	0.446	0.524	0.233	0.023
CO	0.516	0.476	0.556	0.773	0.024
MI	0.519	0.479	0.558	0.821	0.023
WI	0.521	0.481	0.559	0.860	0.022
IA	0.479	0.438	0.518	0.147	0.023
VA	0.523	0.482	0.564	0.862	0.025
MN	0.528	0.488	0.568	0.919	0.024
AZ	0.471	0.431	0.511	0.081	0.024
GA	0.470	0.431	0.511	0.076	0.024
NM	0.533	0.492	0.576	0.941	0.025
ME	0.542	0.501	0.583	0.977	0.024
SC	0.452	0.411	0.493	0.011	0.024
OR	0.549	0.509	0.589	0.990	0.024
TX	0.443	0.403	0.485	0.002	0.025
MO	0.440	0.402	0.480	0.001	0.024
MS	0.437	0.396	0.478	0.001	0.025
CT	0.565	0.524	0.606	0.999	0.025
WA	0.568	0.528	0.608	1.000	0.024
DE	0.569	0.527	0.612	1.000	0.026
AK	0.425	0.384	0.468	0.000	0.026
NJ	0.578	0.538	0.619	1.000	0.025
IN	0.419	0.379	0.458	0.000	0.023
IL	0.584	0.543	0.625	1.000	0.025
LA	0.411	0.373	0.451	0.000	0.024
MT	0.406	0.367	0.445	0.000	0.023
RI	0.596	0.553	0.637	1.000	0.025
TN	0.404	0.365	0.443	0.000	0.023
KS	0.404	0.365	0.442	0.000	0.023
SD	0.399	0.360	0.437	0.000	0.023
ND	0.390	0.351	0.429	0.000	0.023
NY	0.611	0.570	0.651	1.000	0.024
NE	0.388	0.351	0.427	0.000	0.023
AL	0.385	0.346	0.425	0.000	0.024
AR	0.382	0.344	0.423	0.000	0.024
CA	0.621	0.582	0.658	1.000	0.022
UT	0.375	0.338	0.414	0.000	0.023
KY	0.374	0.337	0.412	0.000	0.023
MA	0.629	0.590	0.668	1.000	0.023
MD	0.639	0.598	0.681	1.000	0.025
WV	0.353	0.316	0.391	0.000	0.023
ID	0.349	0.312	0.386	0.000	0.023
OK	0.342	0.305	0.381	0.000	0.023
VT	0.659	0.618	0.696	1.000	0.022
HI	0.662	0.622	0.700	1.000	0.023
WY	0.289	0.255	0.324	0.000	0.021
DC	0.908	0.886	0.928	1.000	0.012

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.