Various Bayesian models for modelling voting intention

I run a number of Bayesian models of voting intention for the next Australian Federal election. 

The first is a Gaussian Random Walk (GRW) which models the voting intention by assuming (1) voting intention on any single day only varies a little from the day before, (2) the polls are a noisy indication of population voting intention, and (3) individually pollsters have systemic biases but collectively across all pollsters the polls are unbiased. This is the same model I have used in past elections. It is also my preferred model. At the moment it shows Labor two-party preferred (2pp) voting intention at 50.7 per cent.

The second model I run - a Gaussian Random Walk with a Left Anchor (GRWLA) - augments the first model by anchoring the hidden voting intention to the result at the last election. By imposing a left anchor, I am assuming some things: First, that any honeymoon effect after the election is consistent with my assumption of minimal voting intention change from day to day. Second, that pollsters retain the same methodological approach from the time of the last election. I am not convinced by either of these assumptions. At the moment it has Labor's 2pp voting intention at 49.2 per cent.

The third model I run is a Gaussian Process (GP) model. Rather than model hidden voting intention on every day, it only models hidden voting intention on polling days. The model assumes that the hidden voting intention for polls that are nearby in time will be more correlated than for polls that are further away in time. This relationship between polls based on their temporal distance from each other is expressed mathematically in the model using an exponentiated quadratic kernel. Like the above models, this model also makes adjustments for systemic pollster biases. At the moment it has Labor's 2pp voting intention at 50.3 per cent.

I am still exploring this approach, however, it is sensitive to where the "mean" across the data points is set (with a strong tendency to mean reversion at each end of the series, and for periods through the series where there are few polls). I have set the mean to the average of the last 10 polls. 

We can compare the central tendencies of these approaches as follows. You will note the "mean reversion" evident in the early part of the GP series.

These models are encoded in Python and they can be seen on my github repository. If you want to look at the models closely, you should look at bayes_tools.py and the notebook _poll_agg.ipynb

The GRW and GRWLA models are based on the work of Simon Jackman in Bayesian Analysis for Social Sciences (2009).

Mid April 2024 Polling Update

 

Morgan Poll

Latest Roy Morgan poll is not good news for Labor. This is the second recent Morgan poll with Labor's 2pp vote share below 50%. Morgan has Labor's primary vote below 30 per cent for the first time this election cycle.

Updated polling charts

The updated localised regression chart suggests that two-party preferred voting intention for Labour continues to decline. 

However, this decline is not as marked on the Bayesian Gaussian Random Walk (GRW) model. This model assumes that:

• how the whole population will vote on any given day is very similar to the day before (this is the Gaussian Random Walk in the model)
• opinion polls provide an irregular and noisy indication of how people would vote; and
• the individual pollsters have unintended methodological biases that tend to favour one party over another over time. For the purposes of the model, these house effects are assumed to cancel each other out across all pollsters, ie. they sum to zero across all of the polling houses. 

With these three factors, the model finds the most likely day-to-day pathway for population voting intention. 

The Gaussian Process (GP) model, has a similar approach to identifying and managing house-effects as the Gaussian Random Walk, but it models voting intention using a covariance matrix, with a higher covariance for polls that are closer together in time. The covariance function I used is the exponentiated quadratic kernel (with a length scale of 50 - "ell" in the denominator). This model produces a similar aggregation result, although it suggests that the recent poll movement away from Labor is less intense.

Collectively, the central tendency of these models can be seen in the following chart. The following chart also includes a left-anchored series (labeled GRWLA) which is a Gaussian Random Walk that has been left-anchored to the election result at the previous election. The house effects in the the GRWLA model do not sum to zero.

Turning to primary votes. The most significant trend is Labor's decline. The Coalition is up on where it was six months ago (but may be in decline at the moment). The Greens may be up on where they were six months ago. The vote for others and independents also looks up.

The data for these charts is sourced from Wikipedia. Before analysis, the polling data is treated to ensure that:

• undecided respondents are proportionately allocated where necessary, and 
• the two-party preferred and primary votes are normalised to sum to 100 per cent exactly. 

The notebooks that produced these charts are available on my github site.

Resolve strategic 57/43

The latest Resolve Strategic poll from 5 November has Labor with a two party preferred vote of 57 and the Coalition on 43. 

On my models, Resolve Strategic is around four percentage points more favourable to Labor than the average for all pollsters across the time-series of opinion polls. The first model is the Gaussian Random Walk [GRW] with house effects that sum to zero. [The "Normal" in the header is because I used a Normal likelihood distribution for fitting the underlying random walk to the polling observations. The "fixed" refers to the fact I used selected fixed value priors rather than let the model settle these.]

The second model is a Gaussian Process [GP], again with House effects that sum to zero.