# BTdecayLasso Bradley-Terry model is used for ranking in sports tournament. Given the standard Bradley-Terry model, we use an exponential decay rate to weight its log-likelihood function and apply Lasso penalty to achieve a variance reduction and team grouping.

## Installation

You can install BTdecayLasso from github with:

``````# install.packages("devtools")
devtools::install_github("heilokchow/BTdecayLasso")``````

## Example

This is a basic example which shows you how to solve a common problem:

First, given raw datasets (five columns are home teams, away teams, home wins, away wins, time until now), we convert this dataset into a dataframe which can be used for other function’s input.

``NFL <- BTdataframe(NFL2010)``

Then, we comput the whole Lasso path for further analysis’s use. In this example, to track the dynamically changing abilities, we set ‘decay.rate’ to be 0.005. A higher decay rate will give more unbiased results for current abilites’ estimation with a side effect of higher variance.

``BTM <- BTdecayLasso(NFL\$dataframe, NFL\$ability, decay.rate = 0.005, fixed = NFL\$worstTeam)``

We can use ‘plot’ function to view the whole Lasso path.

``plot(BTM)``

The optimal model is selected using AIC criteria on HYBRID Lasso’s run here.

``````BTO <- BTdecayLassoC(NFL\$dataframe, NFL\$ability, decay.rate = 0.005, fixed = NFL\$worstTeam,
model = BTM, criteria = "AIC", type = "HYBRID")
summary(BTO)``````

Finally, we use bootstrapping to obtain the standard deviation of this choosen model with 100 times of simulation.

``````BT <- boot.BTdecayLasso(NFL\$dataframe, NFL\$ability, BTO\$Optimal.lambda, decay.rate = 0.005,
fixed = NFL\$worstTeam, boot = 100)
summary(BT)``````