BTdecayLassoC {BTdecayLasso} | R Documentation |

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

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

`dataframe` |
Generated using |

`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 |

`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 |

`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) |

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.

`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/ |

`type` |
Type of model selection method |

`decay.rate` |
Decay rate of this model |

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 obtaining a whole Lasso path

##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]