qic.select.rq.pen.seq {rqPen} | R Documentation |
Select tuning parameters using IC
Description
Selects tuning parameter and a according to information criterion of choice. For a given
the information criterion is calculated
as
where d is the number of nonzero coefficients and b depends on the method used. For AIC ,
for BIC
and for PBIC
where p is the dimension of
.
If septau set to FALSE then calculations are made across the quantiles. Let
be the coefficient vector for the qth quantile of Q quantiles. In addition let
and
be d and b values from the qth quantile model. Note, for all of these we are assuming eqn and a are the same. Then the summary across all quantiles is
where is the weight assigned for the qth quantile model.
Usage
## S3 method for class 'rq.pen.seq'
qic.select(
obj,
method = c("BIC", "AIC", "PBIC"),
septau = ifelse(obj$penalty != "gq", TRUE, FALSE),
tauWeights = NULL,
...
)
Arguments
obj |
A rq.pen.seq or rq.pen.seq.cv object. |
method |
Choice of BIC, AIC or PBIC, a large p BIC. |
septau |
If optimal values of |
tauWeights |
Weights for each quantile. Useful if you set septau to FALSE but want different weights for the different quantiles. If not specified default is to have |
... |
Additional arguments. |
Value
- coefficients
Coefficients of the selected models.
- ic
Information criterion values for all considered models.
- modelsInfo
Model info for the selected models related to the original object obj.
- gic
Information criterion summarized across all quantiles. Only returned if septau set to FALSE
Author(s)
Ben Sherwood, ben.sherwood@ku.edu
References
Lee ER, Noh H, Park BU (2014). “Model Selection via Bayesian Information Criterion for Quantile Regression Models.” Journal of the American Statistical Association, 109(505), 216–229. ISSN 01621459.
Examples
set.seed(1)
x <- matrix(runif(800),ncol=8)
y <- 1 + x[,1] + x[,8] + (1+.5*x[,3])*rnorm(100)
m1 <- rq.pen(x,y,penalty="ENet",a=c(0,.5,1),tau=c(.25,.75))
qic.select(m1)