Statistical Modelling 22 (6) (2022), 546–565
A regularized hidden Markov model for analyzing the ‘hot shoe’ in football
Marius ötting,
Department of Business Administration and Economics,
Bielefeld University,
Bielefeld,
Germany.
e-mail: marius.oetting@uni-bielefeld.de
Andreas Groll,
Department of Statistics,
TU Dortmund University,
Dortmund,
Germany.
Abstract:
We propose a penalized likelihood approach in hidden Markov models (HMMs) to perform automated variable selection. To account for a potential large number of covariates, which also may be substantially correlated, we consider the elastic net penalty containing LASSO and ridge as special cases. By quadratically approximating the non-differentiable penalty, we ensure that the likelihood can be maximized numerically. The feasibility of our approach is assessed in simulation experiments. As a case study, we examine the ‘hot hand’ effect, whose existence is highly debated in different fields, such as psychology and economics. In the present work, we investigate a potential ‘hot shoe’ effect for the performance of penalty takers in (association) football, where the (latent) states of the HMM serve for the underlying form of a player.
Keywords:
Hidden Markov model, Regularization, elastic net, football, sports analytics
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