The Sensitivity of College Football Rankings to Several Modeling Choices

Karl, Andrew T.

doi:10.1515/1559-0410.1471

Cited by 5 publications

(9 citation statements)

References 42 publications

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“…We consider sports for which ties are necessarily settled in overtime. Typically, teams are ranked using either the scores or the win-loss records (Karl, 2012); the multiresponse model (1) allows rankings to be done using both. Annis and Craig (2005) consider a similar approach for ranking college football teams.…”

Section: Example: Poisson and Binarymentioning

confidence: 99%

Computation of maximum likelihood estimates for multiresponse generalized linear mixed models with non-nested, correlated random effects

Karl¹,

Yang

Lohr

2014

Computational Statistics & Data Analysis

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Abstract. Estimation of generalized linear mixed models (GLMMs) with non-nested random effects structures requires approximation of high-dimensional integrals. Many existing methods are tailored to the lowdimensional integrals produced by nested designs. We explore the modifications that are required in order to adapt an EM algorithm with first-order and fully exponential Laplace approximations to a non-nested, multiple response model. The equations in the estimation routine are expressed as functions of the first four derivatives of the conditional likelihood of an arbitrary GLMM, providing a template for future applications. We apply the method to a joint Poisson-binary model for ranking sporting teams, and discuss the estimation of a correlated random effects model designed to evaluate the sensitivity of value-added models for teacher evaluation to assumptions about the missing data process. Source code in R is provided in the online supplementary material.

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Section: Example: Poisson and Binarymentioning

confidence: 99%

Computation of maximum likelihood estimates for multiresponse generalized linear mixed models with non-nested, correlated random effects

Karl¹,

Yang

Lohr

2014

Computational Statistics & Data Analysis

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“…Although the RealVAMS model may be used in a variety of contexts in which multimembership data occur (Karl, 2012), we choose to present it within an educational context. In this context, the model is generally referred to as a multidimensional value-added model (VAM).…”

Section: Application Of the Realvams Packagementioning

confidence: 99%

RealVAMS: An R Package for Fitting a Multivariate Value-added Model (VAM)

Broatch¹,

Green²,

Karl³

2018

The R Journal

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We present RealVAMS, an R package for fitting a generalized linear mixed model to multimembership data with partially crossed and partially nested random effects. RealVAMS utilizes a multivariate generalized linear mixed model with pseudo-likelihood approximation for fitting normally distributed continuous response(s) jointly with a binary outcome. In an educational context, the model is referred to as a multidimensional value-added model, which extends previous theory to estimate the relationships between potential teacher contributions toward different student outcomes and to allow the consideration of a binary, real-world outcome such as graduation. The simultaneous joint modeling of continuous and binary outcomes was not available prior to RealVAMS due to computational difficulties. In this paper, we discuss the multidimensional model, describe RealVAMS, and demonstrate the use of this package and its modeling options with an educational data set.

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“…The offense and defense ratings for each team are calculated while controlling for the quality of opponent, implicitly considering strength of schedule as in Harville (1977), Annis and Craig (2005), and Karl (2012). By contrast, raw offensive and defensive totals inflate the ranking of teams that play a set of easy opponents and penalize those that play a difficult schedule.…”

Section: The Modelmentioning

confidence: 99%

“…Traditionally, algorithms for ranking sports teams and predicting sporting outcomes utilize either the observed margin of victory (MOV) (Henderson, 1975) or the binary win/loss information (Mease, 2003, Karl, 2012, along with potential covariates such as game location (home, away, neutral). In contrast, we jointly model either MOV or win/loss along with a separate game-level response, which is shown to improve predictions under certain model specifications.…”

Section: Introductionmentioning

confidence: 99%

“…The binary win/loss indicators are jointly modeled with the team scores or other responses by allowing the random team effects in the models for each response to be correlated. Assuming a normal distribution for the team effects imposes a form of regularization, allowing the binary model to be fit in the presence of undefeated or winless teams (Karl, 2012).…”

Section: Introductionmentioning

confidence: 99%

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Multivariate Generalized Linear Mixed Models for Joint Estimation of Sporting Outcomes

Broatch,

Karl

2017

Preprint

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This paper explores improvements in prediction accuracy and inference capability when allowing for potential correlation in team-level random effects across multiple game-level responses from different assumed distributions. First-order and fully exponential Laplace approximations are used to fit normal-binary and Poisson-binary multivariate generalized linear mixed models with non-nested random effects structures. We have built these models into the R package mvglmmRank, which is used to explore several seasons of American college football and basketball data.

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The Sensitivity of College Football Rankings to Several Modeling Choices

Cited by 5 publications

References 42 publications

Computation of maximum likelihood estimates for multiresponse generalized linear mixed models with non-nested, correlated random effects

Computation of maximum likelihood estimates for multiresponse generalized linear mixed models with non-nested, correlated random effects

RealVAMS: An R Package for Fitting a Multivariate Value-added Model (VAM)

Multivariate Generalized Linear Mixed Models for Joint Estimation of Sporting Outcomes

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