Description Usage Arguments Details Value References See Also Examples
View source: R/BTdecayLassoF.R
This function provides a method to computed the estimated abilities and lambda given an intuitive fixed Lasso penalty rate.
Since in Lasso method, the selection of lambda varies a lot with respect to different datasets. We can keep the consistency of
amount of Lasso penalty induced in different datasets from different period by setting a fixed Lasso penalty rate "penalty".
Please refer to BTdecayLasso
for the definition of "penalty" and its relationship with "lambda".
1 2 | BTdecayLassoF(dataframe, ability, penalty, decay.rate = 0, fixed = 1,
thersh = 1e-05, max = 100, iter = 100)
|
dataframe |
Generated using |
ability |
A column vector of teams ability, the last row is the home parameter. It can be generated using |
penalty |
The amount of Lasso penalty induced (1-s/max(s)) where is the sum of Lasso penalty part. |
decay.rate |
The exponential decay rate. Usually ranging from (0, 0.01), A larger decay rate weights more importance to most recent matches and the estimated parameters reflect more on recent behaviour. |
fixed |
A teams index whose ability will be fixed as 0. The worstTeam's index
can be generated using |
thersh |
Threshold for convergence |
max |
Maximum weight for w_ij (weight used for Adaptive Lasso) |
iter |
Number of iterations used in L-BFGS-B algorithm. |
The estimated ability given fixed penalty p = 1- s/\max(s) where s is the sum of Lasso penalty part. When p = 0, this model is reduced to a standard Bradley-Terry Model. When p = 1, all ability scores are shrinking to 0.
The parameter "penalty" should be ranging from 0.01 to 0.99 due to the iteration's convergent error.
summary() function can be applied to view the outputs.
The list with class "BTF" contains estimated abilities and other parameters.
ability |
Estimated ability scores |
df |
Degree of freedom (number of distinct μ) |
penalty |
Amount of Lasso Penalty |
decay.rate |
Exponential decay rate |
lambda |
Corresponding Lasso lambda given penalty rate |
Masarotto, G. and Varin, C.(2012) The Ranking Lasso and its Application to Sport Tournaments. *The Annals of Applied Statistics* **6** 1949–1970.
Zou, H. (2006) The adaptive lasso and its oracle properties. *J.Amer.Statist.Assoc* **101** 1418–1429.
BTdataframe
for dataframe initialization, BTdecayLasso
for detailed description
1 2 3 4 5 6 7 8 9 | ##Initializing Dataframe
x <- BTdataframe(NFL2010)
##The following code runs the main results
##BTdecayLasso run with exponential decay rate 0.005 and Lasso penaty 0.5
y <- BTdecayLassoF(x$dataframe, x$ability, 0.5, decay.rate = 0.005,
fixed = x$worstTeam)
summary(y)
|
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