BTdecayLassoC: Bradley-Terry Model with Exponential Decayed weighted...

In BTdecayLasso: Bradley-Terry Model with Exponential Time Decayed Log-Likelihood and Adaptive Lasso

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")

BTdecayLasso documentation built on May 1, 2019, 8:24 p.m.