Welcome to my first analysis of the polls regarding the Brexit. I will perform the same analysis as for the Scottish referendum, using graphs of local regressions. I will look at the likely change in support for the Brexit and at the differences between modes.
First, here is the graph that takes into account all the polls conducted since January 2016. The dots represent poll estimates. The lines represent the estimation of change using local regressions (epanechnikov .65 for the specialists).
The graph shows that the two sides are now practically at the same level according to the published polls. It also shows that the proportion of non-disclosers -- including the undecideds and those who say they will not vote -- has decreased since March, from around 17% to 11%. It is the Leave side that has gained most from the decrease of the non-disclosers. The proportion of supporters for Stay has remained the same over the period.
However, the graphs also allow to notice the the proportion of non-disclosers -- the dots in the graph -- varies much, from 4% to 30%. This proportion varies by pollster -- from an average of 4.7% for ORB to 27.8 for TNS.-- and by mode -- 16.8% for the Web polls, 10.2% for the telephone polls. Note that the proportion of non-disclosers was not published for three ORB polls. Since this would have biased the analyses, I attributed a proportion of 5% of undecideds to these ORB polls and modified the proportion of stay and leave accordingly.
The following graph illustrates the change in support when undecideds are allocated proportionally to each side, which is the usual procedure for all the pollsters. The portrait is quite the same as with the preceding graph, i.e., the two sides are at par, with a possible tiny advantage for stay.
For the Scottish referendum, I had suggested that a non-proportional attribution of non-disclosers be used as was the case for the Quebec 1995 referendum. I had proposed to attribute 67% of the non-disclosers to the No side and 33% to the Yes side. This procedure produced a very good prediction. I had predicted at least a 7 points difference between the two sides. It ended up at 10 percentage points. The argument here is not that the non-disclosers really distribute themselves in these proportions. This procedure is a way to correct for a number of phenomena. It is likely that partisans of the status quo are less likely to be in the samples since generally they are more likely to be older and harder to contact. It is even more likely with Web polls. It is also likely that partisans of the status quo are less prone to answer polls and, when they do, to reveal their vote. In addition, the fact that the proportion of non-disclosers vary between pollsters means that it is a feature of the methods used more than of the real proportion in the population. Using a non-proportional attribution means that the higher the proportion of non-disclosers the higher the proportion that is attributed to the status quo. Empirically, for the polls conducted in 2016, there is a positive correlation between the proportion of non-disclosers and the proportion of supporters for Leave. This tends to justify the non-proportional attribution.
One could argue that the situation is different than for the Scottish referendum since, for instance, the older people were more likely to support the No side in Scotland while it is the opposite for the Brexit. Older people seem more likely to support the Leave side. However, this may be partly due to a paradox where older people who are for Leave are more likely to answer polls.
Since I do not have a theoretical or empirical justification to change the attribution that I used in the Scottish referendum, I decided to use the same. Here is the graph that I get using this procedure. The two sides are now about five points apart, which is -- I think -- more realistic.
In conclusion, it will be very interesting to follow the campaign in the next two weeks. My next post will deal with the substantial differences in the portraits traced by web polls compared to telephone polls.