msgps (Model Selection Criteria via Generalized Path Seeking)
Description
This package computes the degrees of freedom of the lasso, elastic net, generalized elastic net and adaptive lasso based on the generalized path seeking algorithm. The optimal model can be selected by model selection criteria including Mallows' Cp, biascorrected AIC (AICc), generalized cross validation (GCV) and BIC.
Usage
1 2 
Arguments
X 
predictor matrix 
y 
response vector 
penalty 
The penalty term. The α/2β_2^2+(1α)β_1. Note that log(α+(1α)β_1). The w_iβ_1, where w_i is 1/(\hat{β}_i)^{γ}. Here γ>0 is a tuning parameter, and \hat{β}_i is the ridge estimate with regularization parameter being λ ≥ 0. 
alpha 
The value of α on 
gamma 
The value of γ on 
lambda 
The value of regularization parameter λ ≥ 0 for ridge regression, which is used to calculate the weight vector of 
tau2 
Estimator of error variance for Mallows' Cp. The default is the unbiased estimator of error vairance of the most complex model. When the unbiased estimator of error vairance of the most complex model is not available (e.g., the number of variables exceeds the number of samples), 
STEP 
The approximate number of steps. 
STEP.max 
The number of steps in this algorithm can often exceed 
DFtype 

p.max 
If the number of selected variables exceeds 
intercept 
When intercept is 
stand.coef 
When stand.coef is 
Author(s)
Kei Hirose
mail@keihirose.com
References
Friedman, J. (2008). Fast sparse regression and classification. Technical report, Standford University.
Hirose, K., Tateishi, S. and Konishi, S.. (2011). Efficient algorithm to select tuning parameters in sparse regression modeling with regularization. arXiv:1109.2411 (arXiv).
See Also
coef.msgps
, plot.msgps
, predict.msgps
and summary.msgos
objects.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27  #data
X < matrix(rnorm(100*8),100,8)
beta0 < c(3,1.5,0,0,2,0,0,0)
epsilon < rnorm(100,sd=3)
y < X %*% beta0 + epsilon
y < c(y)
#lasso
fit < msgps(X,y)
summary(fit)
coef(fit) #extract coefficients at t selected by model selection criteria
coef(fit,c(0, 0.5, 2.5)) #extract coefficients at some values of t
predict(fit,X[1:10,]) #predict values at t selected by model selection criteria
predict(fit,X[1:10,],c(0, 0.5, 2.5)) #predict values at some values of t
plot(fit,criterion="cp") #plot the solution path with a model selected by Cp criterion
#elastic net
fit2 < msgps(X,y,penalty="enet",alpha=0.5)
summary(fit2)
#generalized elastic net
fit3 < msgps(X,y,penalty="genet",alpha=0.5)
summary(fit3)
#adaptive lasso
fit4 < msgps(X,y,penalty="alasso",gamma=1,lambda=0)
summary(fit4)
