select-grpreg: Select an value of lambda along a grpreg path

In grpreg: Regularization Paths for Regression Models with Grouped Covariates

Description

Selects a point along the regularization path of a fitted grpreg object according to the AIC, BIC, or GCV criteria.

Usage

select(obj,...)
## S3 method for class 'grpreg'
select(obj, criterion=c("BIC", "AIC", "GCV", "AICc",
"EBIC"), df.method=c("default","active"), smooth=FALSE, ...)

Arguments

obj	A fitted grpreg object.
criterion	The criterion by which to select the regularization parameter. One of "AIC", "BIC", "GCV", "AICc", or "EBIC"; default is "BIC".
df.method	How should effective model parameters be calculated? One of: "active", which counts the number of nonzero coefficients; or "default", which uses the calculated df returned by grpreg. Default is "default".
smooth	Applies a smoother to the information criteria before selecting the optimal value.
...	For S3 method compatibility.

Details

The criteria are defined as follows, where L is the deviance (i.e, -2 times the log-likelihood), df is the degrees of freedom, and n is the sample size:

AIC = L + 2*df

BIC = L + log(n)*df

GCV= L/((1-df/n)^2)

AICc = AIC + 2*df*(df+1)/(n-df-1)

EBIC = BIC + 2*log(p choose df)

Value

A list containing:

lambda	The selected value of the regularization parameter, lambda.
beta	The vector of coefficients at the chosen value of lambda.
df	The effective number of model parameters at the chosen value of lambda.
IC	A vector of the calculated model selection criteria for each point on the regularization path.

Author(s)

Patrick Breheny

See Also

grpreg

Examples

data(Birthwt)
X <- Birthwt$X
y <- Birthwt$bwt
group <- Birthwt$group
fit <- grpreg(X, y, group, penalty="grLasso")
select(fit)
select(fit,crit="AIC",df="active")
plot(fit)
abline(v=select(fit)$lambda)
par(mfrow=c(1,3))
l <- fit$lambda
xlim <- rev(range(l))
plot(l, select(fit)$IC, xlim=xlim, pch=19, type="o", ylab="BIC")
plot(l, select(fit,"AIC")$IC, xlim=xlim, pch=19, type="o",ylab="AIC")
plot(l, select(fit,"GCV")$IC, xlim=xlim, pch=19, type="o",ylab="GCV")

Example output

Loading required package: Matrix
$beta
(Intercept)        age1        age2        age3        lwt1        lwt2 
 3.02536524  0.12945631  0.51415003  0.30726166  0.62868704 -0.15121567 
       lwt3       white       black       smoke        ptl1       ptl2m 
 0.49385428  0.16776254 -0.05345302 -0.17442566 -0.15785358  0.04441707 
         ht          ui        ftv1        ftv2       ftv3m 
-0.26670074 -0.36973445  0.00000000  0.00000000  0.00000000 

$lambda
[1] 0.05613761

$df
[1] 7.802936

$IC
  [1] 426.4719 424.3328 422.5671 421.1159 419.9288 418.7393 417.4156 414.7527
  [9] 412.1531 410.0387 408.2984 407.0545 406.2688 405.8647 405.7733 405.9338
 [17] 406.2932 406.8058 407.4328 408.8683 410.5842 412.2879 413.9583 415.5797
 [25] 417.1405 418.6325 420.0505 421.3916 422.6544 423.8392 424.9472 425.9806
 [33] 426.9421 427.8346 428.6616 429.4265 430.1331 430.7847 431.3851 431.9377
 [41] 432.4457 432.9124 433.3408 433.7338 434.0940 434.4240 434.7262 435.0029
 [49] 435.2559 435.4874 435.6990 435.8924 436.0691 436.2306 436.3780 436.5126
 [57] 436.6355 436.7477 436.8501 436.9435 437.0287 437.1064 437.1774 437.2420
 [65] 437.3010 437.3548 437.4039 437.4486 437.4894 437.5265 437.5604 437.5913
 [73] 437.6195 437.6452 437.6685 437.6899 437.7093 437.7270 437.7432 437.7579
 [81] 437.7713 437.7835 437.7946 437.8048 437.8140 437.8225 437.8302 437.8371
 [89] 437.8435 437.8493 437.8546 437.8595 437.8639 437.8679 437.8715 437.8748
 [97] 437.8779 437.8806 437.8831 437.8854

$beta
(Intercept)        age1        age2        age3        lwt1        lwt2 
 3.04927431 -0.08976451  1.59151760  0.90968052  1.93600738  0.07121398 
       lwt3       white       black       smoke        ptl1       ptl2m 
 1.38273076  0.29582051 -0.15808854 -0.28371611 -0.29193287  0.23107109 
         ht          ui        ftv1        ftv2       ftv3m 
-0.56800347 -0.48190866  0.08817371  0.02497665 -0.17027810 

$lambda
[1] 2.064955e-05

$df
[1] 18

$IC
  0.2065   0.1882   0.1714   0.1562   0.1423   0.1297   0.1182   0.1077 
419.9884 419.3837 417.1936 415.3559 413.8165 414.1508 412.1160 417.1816 
  0.0981   0.0894   0.0814   0.0742   0.0676   0.0616   0.0561   0.0512 
411.8883 412.8994 413.0615 407.4569 402.6136 398.4455 394.8722 391.8192 
  0.0466   0.0425   0.0387   0.0353   0.0321   0.0293   0.0267   0.0243 
389.2187 387.0097 385.1378 389.3600 387.7910 386.4642 385.3446 384.4016 
  0.0221   0.0202   0.0184   0.0167   0.0153   0.0139   0.0127   0.0115 
383.6086 382.9427 382.3843 381.9166 381.5251 381.1978 380.9244 380.6961 
  0.0105   0.0096   0.0087    0.008   0.0073   0.0066    0.006   0.0055 
380.5056 380.3468 380.2144 380.1040 380.0121 379.9357 379.8720 379.8190 
   0.005   0.0046   0.0041   0.0038   0.0034   0.0031   0.0029   0.0026 
379.7749 379.7382 379.7077 379.6823 379.6612 379.6437 379.6291 379.6170 
  0.0024   0.0022    0.002   0.0018   0.0016   0.0015   0.0014   0.0012 
379.6069 379.5986 379.5916 379.5858 379.5810 379.5770 379.5738 379.5710 
  0.0011    0.001    9e-04    9e-04    8e-04    7e-04    6e-04    6e-04 
379.5687 379.5668 379.5652 379.5639 379.5628 379.5619 379.5612 379.5606 
   5e-04    5e-04    4e-04    4e-04    4e-04    3e-04    3e-04    3e-04 
379.5601 379.5596 379.5593 379.5590 379.5587 379.5585 379.5584 379.5582 
   3e-04    2e-04    2e-04    2e-04    2e-04    2e-04    1e-04    1e-04 
379.5581 379.5580 379.5579 379.5579 379.5578 379.5578 379.5577 379.5577 
   1e-04    1e-04    1e-04    1e-04    1e-04    1e-04    1e-04    1e-04 
379.5577 379.5576 379.5576 379.5576 379.5576 379.5576 379.5576 379.5576 
   1e-04    1e-04        0        0        0        0        0        0 
379.5576 379.5575 379.5575 379.5575 379.5575 379.5575 379.5575 379.5575 
       0        0        0        0 
379.5575 379.5575 379.5575 379.5575 

Warning message:
In select.grpreg(fit, crit = "AIC", df = "active") :
  minimum lambda selected for grLasso

grpreg documentation built on July 27, 2021, 1:08 a.m.