Guest post by Kevin Cunningham, TCD (posted by David Farrell, February 22, 2011)

Background
This article explains some of the problems of common polling interpretation and applies the leading solution to the general election campaign of 2011. It also offers a more accurate interpretation of trends and generates a current poll of polls as at Monday February 21st.
Why a new technique
Analyzing polls can be particularly fruitless in Ireland as each opinion poll typically has a confidence interval of approximately 3%. For example, some polls are giving Fianna Fail 12%, others 16%. IT is difficult to tell to what extent is the 12% incorrect, or within the realms of possibility.

One of the main outcomes of this is that we cannot rely on a single poll to determine what is going on now, or, with any degree of reliability what the trends, if any, have been. A typical approach to this problem is to aggregate all polls (i.e. a poll-of-polls). However, in the context of any underlying trend in the sample of polls, this method will yield skewed results because it attributes an equal weighting to the oldest polls as it does to the most recent polls. It also offers nothing in terms of trends.

A second approach is to combine recent polls only. There are difficulties and problems with this also. First, the more significant the trends, the more polls that need to be discarded and therefore we reduce the number of polls to be used. Furthermore, interpretation of which set of polls to use is inherently unclear due to the aforementioned variance of the polls themselves.

In this election psephologists are faced with the typical dilemma as there now appears to have been a trend in support from Fine Gael and away from Labour.

A standard approach to interpreting polling trends involves using loess regression. This generates a trend based on the entire dataset. It has huge benefits as it negates the influences of exceptional data and other sources of random variation. However, loess regression models have a big drawback. Computations using loess will only run smoothly when polls are plentiful, and in the case of Ireland, we simply do not have enough polls to deploy such a technique.

The solution to this problem involves employing technique known as Kalman Filtering and Backwards Smoothing (KF). It is a technique employed in a wide range of applications from trajectory estimation for the Apollo program to FM Radios.

Kalman Filtering
In relation to polling data, it applies a similar smoothing algorithm to the loess smoother in that it accounts for all data points (in this case, polls). However, KF also assigns weights to poll results, by taking into account such factors as sample size and the amount of time elapsed between polls. It further accounts for the relative spuriousness of different polls by conducting autoregression on the data at the outset (see Green, Gerber and DeBoef, 1999 for further details).

In essence, the technique yields estimates from polling data at each point in time based on a variety of factors. It minimizes error from the two sources of uncertainty in polling: the true level of support for a party, which may change on a day-to-day basis by some unknown amount; and the error in polling.

Results
I applied the KF and smoothing algorithm to the polling data thus far and ran the results again through a loess smoother. It produces the story of the election campaign as depicted in Figure 1. Each point is a polling result for a party at that date and the trend-line is the trend as determined by the technique.

Figure 1: Kalman Filtering and Smoothing Election Campaign 2011, data points relate to the actual polling data, the smoothed line is a loess curve of the KF estimates.

What we can say about the election is therefore that:
• Support for Fianna Fail, the Independents, Sinn Fein and the Green Party has remained constant.
• Support for Labour has fallen dramatically and the trend-line suggests this may continue to fall in the short-term future.
• Support for Fine Gael has increased, but appears to have stabilised at its current elevated level. It does not appear that they will continue to increase their support to levels where a single-party government is achievable.
• The Green party also appears to be dwindling of late.
• It appears that commentary in relation to changes in Fianna Fáil support so far has been spurious. Although, another poll like the 12% Millward Browne recently put them on might change this interpretation, that particular poll now looks open to scrutiny.
• Variance in relation to the Independent candidates is wider than other parties, this may be due to varying interpretations of independents and other candidates. Variance of the Labour party is also relatively wide, suggesting that they might be particularly difficult to predict on election day.

So, as according to the KF technique, upon the release of The Irish Times poll of February 21st, a poll of polls would give:
Fianna Fáil 15.81%
Fine Gael 36.62
Labour 19.73
Green 1.91
Sinn Féin 11.27
Ind. /Other 14.44