摘要:

This article addresses the problem of comparing abilities of players from different eras in professional sports. We study National Hockey League players, professional golfers, and Major League Baseball players from the perspectives of home run hitting and hitting for average. Within each sport, the careers of the players overlap to some extent. This network of overlaps, or bridges, is used to compare players whose careers took place in different eras. The goal is not to judge players relative to their contemporaries, but rather to compare all players directly. Hence the model that we use is a statistical time machine. We use additive models to estimate the innate ability of players, the effects of aging on performance, and the relative difficulty of each year within a sport. We measure each of these effects separated from the others. We use hierarchical models to model the distribution of players and specify separate distributions for each decade, thus allowing the “talent pool” within each sport to change. We study the changing talent pool in each sport and address Gould's conjecture about the way in which populations change. Nonparametric aging functions allow us to estimate the league-wide average aging function. Hierarchical random curves allow for individuals to age differently from the average of athletes in that sport. We characterize players by their career profile rather than a one-number summary of their career.

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10474163

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10474164

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10474165

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10474166

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10474167

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

We provide sufficient conditions for estimating from longitudinal data the causal effect of a time-dependent exposure or treatment on the marginal probability of response for a dichotomous outcome. We then show how one can estimate this effect under these conditions using the g-computation algorithm of Robins. We also derive the conditions under which some current approaches to the analysis of longitudinal data, such as the generalized estimating equations (GEE) approach of Zeger and Liang, the feedback model techniques of Liang and Zeger, and within-subject conditional methods, can provide valid tests and estimates of causal effects. We use our methods to estimate the causal effect of maternal stress on the marginal probability of a child's illness from the Mothers' Stress and Children's Morbidity data and compare our results with those previously obtained by Zeger and Liang using a GEE approach.

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10474168

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10474169

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10474170

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10474171

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10474172

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor