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.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 31E
Related questions
Question
100%
Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.Very very grateful!Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer.
You can borrow
ideas from gpt, but please do not believe its answer.Very very grateful!
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.
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
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 12 images
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning