David Firth, recent papers

Abstracts of recent unpublished research:

 

DYNAMIC BRADLEY-TERRY MODELS FOR SPORTS TOURNAMENTS

M Cattelan, University of Padova
C Varin, University of Venice
D Firth, University of Warwick

Abstract
In the course of national sports tournaments, usually lasting several months, it is expected that the abilities of teams taking part in the tournament change in time. A dynamic extension of the Bradley-Terry model for paired comparison data is introduced to model the outcomes of sporting contests allowing for time-varying abilities. It is assumed that teams' home and away abilities depend on past results through exponentially weighted moving average processes. The proposed model is applied to sports data with and without tied contests, namely the 2009-2010 regular season of the National Basketball Association tournament and the 2008-2009 Italian Serie A football season.

Paper available as CRiSM Working Paper 10-19

 

NONLINEAR DISCRETE-TIME HAZARD MODELS FOR WOMEN'S ENTRY INTO MARRIAGE

H L Turner, University of Warwick
A D Batchelor, University of Warwick
D Firth, University of Warwick

Abstract
When modeling the hazard of entry into marriage, the non-monotonic dependence on age needs to be taken into account. In this paper, nonlinear discrete-time hazard models based on a bell-shaped function are proposed, in which the support of the hazard function, the maximum hazard and the age of maximum hazard are estimated directly. Starting in the proportional hazards framework, the baseline hazard model proposed by Blossfeld and Huinink (American Journal of Sociology, 1991}) is extended to allow estimation of the support of the baseline hazard, a feature which affects the entire shape of the hazard curve. A straight-forward extension is shown to suffer from near-aliasing and thus an alternative parameterization is proposed. The new formulation incorporates parameters for the most notable features of the hazard function, namely the maximum hazard and the age at which this occurs, that are only weakly correlated to each other and to the remaining shape parameters. This allows non-proportional hazards models to be formulated in which the age of maximum hazard, as well as the maximum hazard itself depend on covariates. When applied to data on women's entry into marriage from the Living in Ireland Surveys conducted between 1994 and 2001, the proposed model is able to capture several interesting features of the data such a reduction in the propensity to marry over cohorts and an increasing delay in the timing of marriage with increasing education level.

[Paper available in PDF]