BTdecayLassoC {BTdecayLasso}R Documentation

Bradley-Terry Model with Exponential Decayed weighted likelihood and weighted Lasso with AIC or BIC criteria

Description

Model selection via AIC or BIC criteria. For Lasso estimators, the degree of freedom is the number of distinct groups of estimated abilities.

Usage

BTdecayLassoC(dataframe, ability, weight = NULL, criteria = "AIC",
  type = "HYBRID", model = NULL, decay.rate = 0, fixed = 1,
  thersh = 1e-05, iter = 100, max = 100)

Arguments

dataframe

Generated using BTdataframe given raw data.

ability

A column vector of teams ability, the last row is the home parameter. The row number is consistent with the team's index shown in dataframe. It can be generated using BTdataframe given raw data.

weight

Weight for Lasso penalty on different abilities

criteria

"AIC" or "BIC"

type

"HYBRID" or "LASSO"

model

An Lasso path object with class wlasso or swlasso. If NULL, the whole lasso path will be run.

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 BTdataframe given raw data.

thersh

Threshold for convergence

iter

Number of iterations used in L-BFGS-B algorithm.

max

Maximum weight for w_ij (weight used for Adaptive Lasso)

Details

This function is usually run after the run of whole Lasso path. "model" parameter is obtained by whole Lasso pass's run using BTdecayLasso. If no model is provided, this function will run Lasso path first (time-consuming).

Users can select the information score added to HYBRID Lasso's likelihood or original Lasso's likelihood. ("HYBRID" is recommended)

summary() function can be applied to view the outputs.

Value

Score

Lowest AIC or BIC score

Optimal.degree

The degree of freedom where lowest AIC or BIC score is achieved

Optimal.ability

The ability where lowest AIC or BIC score is achieved

ability

Matrix contains all abilities computed in this algorithm

Optimal.lambda

The lambda where lowest score is attained

Optimal.penalty

The penalty (1- s/\max(s)) where lowest score is attained

type

Type of model selection method

decay.rate

Decay rate of this model

References

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.

See Also

BTdataframe for dataframe initialization, BTdecayLasso for obtaining a whole Lasso path

Examples

##Initializing Dataframe
x <- BTdataframe(NFL2010)

##The following code runs the main results

##Model selection through AIC
z <- BTdecayLassoC(x$dataframe, x$ability, weight = NULL, fixed = x$worstTeam,
                   criteria = "AIC", type = "LASSO")
summary(z)

##If the whole Lasso path is run, we use it's result for model selection (recommended)
##Note that the decay.rate used in model selection should be consistent with
##the one which is used in whole Lasso path's run (keep the same model)
y1 <- BTdecayLasso(x$dataframe, x$ability, lambda = 0.1, 
                   decay.rate = 0.005, fixed = x$worstTeam)
                   
z1 <- BTdecayLassoC(x$dataframe, x$ability, weight = NULL, model = z1,
                    decay.rate = 0.005,
                    fixed = x$worstTeam, criteria = "BIC", type = "HYBRID")



[Package BTdecayLasso version 0.1.0 Index]