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1. Consider the Bradley-Terry model with home advantage (BTHA) which is defined as v di vdi+d j X₁ di + vdj P(i beats j) = if i is at home, if j is at home, where > 0 measures home advantage (> 1) or disadvantage ( < 1), and A₁, A, are the ability parameters for competitors i and j, respectively. It can be shown that the log likelihood of A, based on results of n independent matches is K l(A, y) = H log(v) + Σw; log (A;) - ΣΣn¡j log(vλ¡ +Aj), i=1 i=1 ji K (1) where w; denotes the number of wins for i, H denotes the total number of home wins, and nij denotes the number of times that i plays at home against j.

1. Consider the Bradley-Terry model with home advantage (BTHA) which is defined as v di vdi+d j X₁ di + vdj P(i beats j) = if i is at home, if j is at home, where > 0 measures home advantage (> 1) or disadvantage ( < 1), and A₁, A, are the ability parameters for competitors i and j, respectively. It can be shown that the log likelihood of A, based on results of n independent matches is K l(A, y) = H log(v) + Σw; log (A;) - ΣΣn¡j log(vλ¡ +Aj), i=1 i=1 ji K (1) where w; denotes the number of wins for i, H denotes the total number of home wins, and nij denotes the number of times that i plays at home against j.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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1. Consider the Bradley-Terry model with home advantage (BTHA) which is defined as P(i beats j) & di vdi + Aj Xi Ai + vλ j if i is at home, if j is at home, where > 0 measures home advantage (½ > 1) or disadvantage (½ < 1), and \¡, λj are the ability parameters for competitors i and j, respectively. It can be shown that the log likelihood of A, & based on results of n independent matches is K l(A, y) = H log(y) + Σw; log(A;) - ΣΣn¡¡ log(VA¡ + Aj), i=1 ji K (1) where w, denotes the number of wins for i, H denotes the total number of home wins, and nij denotes the number of times that i plays at home against j.
Transcribed Image Text:1. Consider the Bradley-Terry model with home advantage (BTHA) which is defined as P(i beats j) & di vdi + Aj Xi Ai + vλ j if i is at home, if j is at home, where > 0 measures home advantage (½ > 1) or disadvantage (½ < 1), and \¡, λj are the ability parameters for competitors i and j, respectively. It can be shown that the log likelihood of A, & based on results of n independent matches is K l(A, y) = H log(y) + Σw; log(A;) - ΣΣn¡¡ log(VA¡ + Aj), i=1 ji K (1) where w, denotes the number of wins for i, H denotes the total number of home wins, and nij denotes the number of times that i plays at home against j.
2. The likelihood function under the Bradley-Terry model with home advantage can be written hij di ZA) -ĤIII(A)(^.^). L(A, &) = + λ; K aij + j where hij denotes the number of home wins for i against j and aij denotes the number of away wins for i against j. Show that the log likelihood is given by the expression in (1). i=1 ji
Transcribed Image Text:2. The likelihood function under the Bradley-Terry model with home advantage can be written hij di ZA) -ĤIII(A)(^.^). L(A, &) = + λ; K aij + j where hij denotes the number of home wins for i against j and aij denotes the number of away wins for i against j. Show that the log likelihood is given by the expression in (1). i=1 ji
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