This state space model is used to estimate the vote intention of Canadian voters. The first model is produced using R and Stan, while the second is a similar version produced using Julia and Turing.jl. Both models deliver similar results.
The model assumes that there is an underlying latent voting intention for each of the six main parties (plus others) that is measured by a bunch of noisy polls.
The model is based on the model suggested by Simon Jackman in his book, Bayesian Analysis for the Social Sciences, and updated by Peter Ellis. My Stan and Turing versions differ from their versions in the following ways:
- I use the cholesky decomposition for the non-centered paramterization to improve sampling of the innovation sd (Stan)
- I anchor the election results, and use the polling error to predict voting intention for the period after the 2019 election
- In addition to house effects, I decompose the polling error into four sources:
- the margin of error based on simple random sampling
- a party-specific error
- a mode-by-party error
- pollster-by-party error
The Julia model is run using Turing.jl. The Turing model is coded using a different way of creating a covariance matrix, so that I am able to use Distributions.jl and Turing.jl. I will (hopefully) recode the model when (if?) Distributions.jl gets a native cholesky decomposition of the LKJ distribution.
The predictions for voting intention (that is, for the period after the 2021 federal election assume that the polling errors are the same after the election as before it. That may or may not be true. I suspect that polling errors are correlated between periods.
I have also coded a third version, which uses Julia to call and run the Stan model. This is the current version used to generate the results.
The new Julia version is run from a master script, which calls the subscripts for the different sections. A number of custom functions are used to simplify the scripts, at the cost of making it more difficult for outsiders to follow the steps.
The intent of the custom functions is to try standardize the steps so that plots are produced in the same style. Where I can, I try take advantage of Julia's multiple dispatch and kwargs... arguments.
House effects vary, but in general firms tended to overestimate PPC, NDP and Green Party vote share while underestimating LPC, CPC, and BQ vote share.
There will be an Ontario sometime around the beginning of June, 2022. I estimate the vote intention of Ontario voters using the models above.
I intend to update this model and estimate of latent voting intentions approximately "whenever I feel like it", or probably once every few weeks.
Eventually, I intend to use the Julia and Stan version of the code and slowly add in other provinces to the election results. Up next will be Quebec, followed by Alberta and BC. Besides adding provinces, I also intend to try add some interactive plots. We'll see how that turns out.
Bailey, J. (2021). britpol v0.1.0: User Guide and Data Codebook. Retrieved from https://doi.org/10.17605/OSF.IO/2M9GB.
Economist (2020.) Forecasting the US elections. Retrieved from https://projects.economist.com/us-2020-forecast/president.
Ellis, P. (2019). ozfedelect R package. Retrieved from https://github.com/ellisp/ozfedelect.
Savage, J.(2016). Trump for President? Aggregating National Polling Data. Retrieved from https://khakieconomics.github.io/2016/09/06/aggregating-polls-with-gaussian-Processes.html.
INWT Statistics GmbH (2021). Election forecast. Retrieved from https://github.com/INWTlab/lsTerm-election-forecast.
Bélanger, É., & Godbout, J. F. (2010). Forecasting Canadian federal elections. PS: Political Science & Politics, 43(4), 691-699.
Heidemanns, M., Gelman, A., & Morris, G. E. (2020). An updated dynamic Bayesian forecasting model for the US presidential election. Harvard Data Science Review, 2(4).
Linzer, D. A. (2013). Dynamic Bayesian forecasting of presidential elections in the states. Journal of the American Statistical Association, 108(501), 124-134.
MacInnis, B., Krosnick, J. A., Ho, A. S., & Cho, M. J. (2018). The accuracy of measurements with probability and nonprobability survey samples: Replication and extension. Public Opinion Quarterly, 82(4), 707-744.
Mongrain, P., Nadeau, R., & Jérôme, B. (2021). Playing the synthesizer with Canadian data: Adding polls to a structural forecasting model. International Journal of Forecasting, 37(1), 289-301.
Shirani-Mehr, H., Rothschild, D., Goel, S., & Gelman, A. (2018). Disentangling bias and variance in election polls. Journal of the American Statistical Association, 113(522), 607-614.
Walther, D. (2015). Picking the winner(s): Forecasting elections in multiparty systems. Electoral Studies, 40, 1-13.