A regularized hidden Markov model for analyzing the 'hot shoe' in football. (December 2022)

• Record Type: Journal Article
• Authors: Ötting, Marius; Andreas, Groll
• Is Part Of: Statistical modelling. Volume 22:Number 6(2022)
• Page Start: 546
• Page End: 565
• Publication Date: 2022-12
• Subjects: Hidden Markov model -- Regularization -- elastic net -- football -- sports analytics; Linear models (Statistics) -- Periodicals; Mathematical models -- Periodicals; Modèles linéaires (Statistique) -- Périodiques; Modèles mathématiques -- Périodiques; Modèle statistique; Modèle linéaire; Modélisation statistique; Périodique électronique (Descripteur de forme); Ressource Internet (Descripteur de forme); 519.5011
• DOI: 10.1177/1471082X211008014
• Languages: English
• ISSNs: 1471-082X

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.