6.4.1 Estimation of fixed effects
Heterogeneous team ability is a possible explanation for the result in
Section 6.3. That
result simply indicates that the more goals a team scores, the higher the
probability
that it will score more. However, teams that can score more goals also
indicate teams
with greater ability, or just greater scoring ability, than their opponents.
As mentioned
in Section 6.1.1, it is very natural that the higher ability team will score
more, even
though that stronger team has decided to defend more. Therefore, we need to
control
for this in the estimation.
This problem is similar, but not identical, to the problem identified by
Heckman and
Singer (1984), that heterogeneous subjects will tend to yield decreasing
hazards
because a longer time of no failure indicates that the particular sample is
intrinsically
not likely to fail. Here, heterogeneous teams tend to yield a higher hazard
of scoring
for the leading team because such teams are intrinsically more likely to
score.
*For the estimation controlled for fixed effects, a series of dummy
variables are added.
Two dummy variables are added for each team, one for home ground and another
for
away ground (with the exception of Manchester City to prevent colinearity
and act as
baseline hazard). * As there are in total 25 teams6 involving in the English
Premiership,
there are 48 dummy variables added. Similarly, there are 22 and 25 teams in
the
German Bundesliga and Spanish Primera Liga and therefore I add 42 and 48
dummy
variables respectively.
Fitting the model by these dummy variables only can yield the ability
difference
between teams. Manchester City’s hazard ratio is equal to 1 in all columns
because it is the
benchmark. Arsenal is obviously a strong team as it has very high hazard
ratios for
scoring (1.40 of Manchester City’s hazard at home) and very low hazard
ratios for
being scored against (0.81 of Manchester City’s hazard at home)....
I am currently modelling soccer scoring process, may I know how do I set a
variable as baseline hazard benchmark (as Bold characters inside above
articles)? Hope some body willing to share your precious ideas. Thanks.
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