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Title: Asymmetric beta-transformed linear opinion pooling for modeling unbalanced binary data Authors:  Tim Bal - Ghent University (Belgium) [presenting]
Thierry Marchant - Ghent University (Belgium)
Abstract: Previous research in opinion pooling used the beta-distribution to transform linearly aggregated probabilities, in order to improve the predictions, in terms of the Brier Score. We propose a similar method, with the main difference that our method does not put any constraint on the shape parameters $\alpha$ and $\beta$ of the beta-distribution. Our method outperforms previous methods as well as logistic regression as soon as we start dealing with unbalanced data (i.e., when $\mathcal{P}(Y = 1) \neq \mathcal{P}(Y = 0)$), in terms of the Brier Score and more specifically the calibration. Next to this, we argue that our method is preferred over a recently proposed Bayesian approach since both methods achieve the same results in terms of the Brier Score, but where the Bayesian approach can take up to half an hour, our method needs only a matter of seconds. All methods are compared using simulation studies with the skew-normal distribution and real-life data concerning the validation of diagnosis of ADHD.