A stochastic rank ordered logit model for rating multi-competitor games and sports

2015 ◽  
Vol 11 (3) ◽  
Author(s):  
Mark E. Glickman ◽  
Jonathan Hennessy
Keyword(s):  
Logit Models ◽  
Ordered Logit ◽  
Extreme Value Distributions ◽  
Filtering Algorithm ◽  
Ordered Logit Model ◽  
Gaussian Random Walk ◽  
Mcmc Simulation ◽  
Downhill Skiing ◽  
Approximate Bayesian ◽  
Over Time

AbstractMany games and sports, including races, involve outcomes in which competitors are rank ordered. In some sports, competitors may play in multiple events over long periods of time, and it is natural to assume that their abilities change over time. We propose a Bayesian state-space framework for rank ordered logit models to rate competitor abilities over time from the results of multi-competitor games. Our approach assumes competitors’ performances follow independent extreme value distributions, with each competitor’s ability evolving over time as a Gaussian random walk. The model accounts for the possibility of ties, an occurrence that is not atypical in races in which some of the competitors may not finish and therefore tie for last place. Inference can be performed through Markov chain Monte Carlo (MCMC) simulation from the posterior distribution. We also develop a filtering algorithm that is an approximation to the full Bayesian computations. The approximate Bayesian filter can be used for updating competitor abilities on an ongoing basis. We demonstrate our approach to measuring abilities of 268 women from the results of women’s Alpine downhill skiing competitions recorded over the period 2002–2013.

A point-based Bayesian hierarchical model to predict the outcome of tennis matches

2019 ◽  
Vol 15 (4) ◽  
pp. 313-325 ◽  
Author(s):  
Martin Ingram
Keyword(s):  
Random Walk ◽  
Hierarchical Model ◽  
Bayesian Hierarchical Model ◽  
Bayesian Hierarchical ◽  
Gaussian Random Walk ◽  
Over Time ◽  
Modelling Approach ◽  
Independent And Identically Distributed

Abstract A well-established assumption in tennis is that point outcomes on each player’s serve in a match are independent and identically distributed (iid). With this assumption, it is enough to specify the serve probabilities for both players to derive a wide variety of event distributions, such as the expected winner and number of sets, and number of games. However, models using this assumption, which we will refer to as “point-based”, have typically performed worse than other models in the literature at predicting the match winner. This paper presents a point-based Bayesian hierarchical model for predicting the outcome of tennis matches. The model predicts the probability of winning a point on serve given surface, tournament and match date. Each player is given a serve and return skill which is assumed to follow a Gaussian random walk over time. In addition, each player’s skill varies by surface, and tournaments are given tournament-specific intercepts. When evaluated on the ATP’s 2014 season, the model outperforms other point-based models, predicting match outcomes with greater accuracy (68.8% vs. 66.3%) and lower log loss (0.592 vs. 0.641). The results are competitive with approaches modelling the match outcome directly, demonstrating the forecasting potential of the point-based modelling approach.

scholarly journals Intention to move and residential satisfaction: evidence from Poland

Equilibrium ◽  
2020 ◽  
Vol 15 (2) ◽  
pp. 341-360
Author(s):  
Piotr Maleszyk ◽  
Arleta Kędra
Keyword(s):  
International Migration ◽  
Life Stage ◽  
Value Added ◽  
Residential Satisfaction ◽  
Policy Implications ◽  
Urban Migration ◽  
Logit Models ◽  
Ordered Logit ◽  
Financial Situation ◽  
Intention To Move

Research background: Residential mobility affects the spatial structure of cities and urban development. Longer-distance migration has many additional implications: it affects the demographic situation of a sending area as well as its growth prospects. The literature on interregional and especially international migration regards residential satisfaction as being of at least secondary importance. More attention to this concept is given in research on intra-urban migration and suburbanisation. In a seminal paper of Speare (1974), residential satisfaction was found to be the best predictor of the willingness to move. However, determinants of mobility are country-specific. Purpose of the article: Answering the following research questions: 1) What is the scale and selectivity of the intention to move among city residents? 2) Does residential satisfaction explain variation in migration intentions? Methods: The data are derived from the PAPI survey on life quality in Lublin, Poland (sample: 1101 residents). We build ordered logit models explaining residents’ declarations regarding different types of migration (intra-urban migration, suburbanisation, interregional and international migration) with various proxies of residential satisfaction, as well as financial situation and demographic attributes. Findings & Value added: The propensity to migrate was declared by approx. 15–30% of respondents, depending on the type of migration, which indicates relatively low mobility as against EU countries. We confirm that the intention to move is highly selective. The estimated ordered logit models explaining the intention to move prove that satisfaction with housing and neighbourhood characteristics along with life-stage characteristics are relevant predictors of intention to move both within and outside the region. We disregard the opinion that unemployment and adverse financial situation are key drivers of mobility in contemporary Poland. In a more international context, we provide evidence on how long- and short-distance migration are different in nature and discuss some policy implications regarding countering depopulation in peripheral areas.

scholarly journals Air Transport Passengers’ Satisfaction: an Ordered Logit Model

2018 ◽  
Vol 33 ◽  
pp. 147-154 ◽  
Author(s):  
Maria Grazia Bellizzi ◽  
Laura Eboli ◽  
Carmen Forciniti ◽  
Gabriella Mazzulla
Keyword(s):  
Logit Model ◽  
Air Transport ◽  
Ordered Logit ◽  
Ordered Logit Model

scholarly journals Investigating the Impacts of Real-Time Weather Conditions on Freeway Crash Severity: A Bayesian Spatial Analysis

2020 ◽  
Vol 17 (8) ◽  
pp. 2768 ◽  
Author(s):  
Qiang Zeng ◽  
Wei Hao ◽  
Jaeyoung Lee ◽  
Feng Chen
Keyword(s):  
Real Time ◽  
Spatial Correlation ◽  
Logit Model ◽  
Weather Conditions ◽  
Crash Severity ◽  
Ordered Logit ◽  
Ordered Logit Model ◽  
Generalized Ordered Logit ◽  
Severity Levels ◽  
Generalized Ordered Logit Model

This study presents an empirical investigation of the impacts of real-time weather conditions on the freeway crash severity. A Bayesian spatial generalized ordered logit model was developed for modeling the crash severity using the hourly wind speed, air temperature, precipitation, visibility, and humidity, as well as other observed factors. A total of 1424 crash records from Kaiyang Freeway, China in 2014 and 2015 were collected for the investigation. The proposed model can simultaneously accommodate the ordered nature in severity levels and spatial correlation across adjacent crashes. Its strength is demonstrated by the existence of significant spatial correlation and its better model fit and more reasonable estimation results than the counterparts of a generalized ordered logit model. The estimation results show that an increase in the precipitation is associated with decreases in the probabilities of light and severe crashes, and an increase in the probability of medium crashes. Additionally, driver type, vehicle type, vehicle registered province, crash time, crash type, response time of emergency medical service, and horizontal curvature and vertical grade of the crash location, were also found to have significant effects on the crash severity. To alleviate the severity levels of crashes on rainy days, some engineering countermeasures are suggested, in addition to the implemented strategies.

scholarly journals A RANK-ORDERED LOGIT MODEL WITH UNOBSERVED HETEROGENEITY IN RANKING CAPABILITIES

2010 ◽  
Vol 27 (5) ◽  
pp. 831-846 ◽  
Author(s):  
Dennis Fok ◽  
Richard Paap ◽  
Bram Van Dijk
Keyword(s):  
Logit Model ◽  
Unobserved Heterogeneity ◽  
Ordered Logit ◽  
Ordered Logit Model

scholarly journals Chemical Use Reductions in Urban Fringe Agriculture

2010 ◽  
Vol 39 (3) ◽  
pp. 415-428
Author(s):  
Adesoji O. Adelaja ◽  
Kevin Sullivan ◽  
Yohannes G. Hailu ◽  
Ramu Govindasamy
Keyword(s):  
Urban Fringe ◽  
Regulatory Environment ◽  
Profit Function ◽  
Climate Factors ◽  
Logit Models ◽  
Business Climate ◽  
Over Time

Using an augmented profit function framework designed to account for externalities related to chemical use in agriculture, this paper explains the chemical use choices of farmers in an urban fringe farming environment. It further estimates empirical logit models of reduced insecticide, fungicide, herbicide, and fertilizer usage. Results suggest that farmers who perceive their regulatory environment to be strict, who have experienced right-to-farm conflicts, and who have farms larger in size are more likely to reduce their chemical use over time, vis-à-vis other farmers. The results also suggest the importance of other farm structural and business climate factors in determining chemical use reduction choices.

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