Scottish independence vote is too close to call

 
Scottish actor Sean Connery waves in 2008 as he promotes his new book, “Being a Scot,” at the Edinburgh International Book Festival in Charlotte Square gardens, Edinburgh. (Ed Jones/AFP/Getty Images)
The following is a guest post from social scientist Arkadiusz Wiśniowski of the University of Southampton.
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On 18th September, Scottish residents will go to the polls to decide whether Scotland should become an independent country. Despite a great deal of column inches and political debate the outcome of the independence referendum remains uncertain as the Yes and No campaigns enter the closing stretch. The result could have far-reaching repercussions for policymakers and citizens on both sides of the border.
Polling companies regularly ask representative samples of the Scottish population how they would vote in the referendum if it “were held tomorrow.” While the polls have fluctuated quite a lot, and there has been intense debate over polling methods producing different results for the Yes and No camps, the No campaign has been in the lead in the vast majority. As part of the ESRC funded project The Future of the UK and Scotland at the ESRC Centre for Population Change, we have collected all polling data about the referendum so far. The main focus of our project is predicting levels of Scottish migration until 2021, but political forecasting has proved to be a crucial component of our task. The full context and some of the underlying methodological details are available in a recently-published paper.
To forecast the outcome of the independence referendum, we use a statistical model that combines a time series model of changes in public opinion over time, which takes into account variable spacing in the timing of the polls, with another model that accounts for the percentage of responses for Yes (independence), No (status quo), and those undecided or not intending to vote.
The parameters of our model are estimated by using a Bayesian approach. This provides probability distributions for all unknown parameters of the model, in particular for the shares of votes for or against independence on referendum day. Probability distributions have a great advantage over point estimates (such as means and standard deviations), or even confidence intervals, because they describe the complete uncertainty of the unknown outcome.
In the figure below, the blue line indicates the time trend in the percentage of responses favoring independence (excluding undecided and those not voting) in the polls. The probability distribution, shown in red on the right-hand side of the figure, indicates the predicted share of votes for Scottish independence on referendum day. Our forecast suggests a close result, which might surprise some readers given that support for independence has never been ahead in the polls. However, this reflects the narrowing of the polls in the past few months, and our model picks up this trend – and projects it forward. The distribution of possible outcomes is centered at 49 percent, and the 95 percent predictive interval ranges from 44 percent to 54 percent. This means that we cannot conclude with any certainty about the final outcome. In other words, just two months before the referendum, the estimated odds of Scotland gaining independence against remaining in the UK remain almost even, with a very slight tendency towards the status quo.

Despite the preponderance of polling pointing towards a victory for the No campaign, our model suggests that the result is still too close to call. As the referendum fast approaches and the campaign intensifies, everything is still to play for.