Extract residuals from a PENSE (or LS-EN) regularization path with hyper-parameters chosen by cross-validation.
# S3 method for pense_cvfit
residuals(
object,
alpha = NULL,
lambda = "min",
se_mult = 1,
exact = deprecated(),
correction = deprecated(),
...
)PENSE with cross-validated hyper-parameters to extract coefficients from.
Either a single number or NULL (default).
If given, only fits with the given alpha value are considered.
If lambda is a numeric value and object was fit with multiple alpha
values and no value is provided, the first value in object$alpha is used with a warning.
either a string specifying which penalty level to use
("min", "se", "{m}-se")
or a single numeric value of the penalty parameter. See details.
If lambda = "se", the multiple of standard errors to tolerate.
deprecated. Always gives a warning if lambda is not part of the fitted sequence and coefficients
are interpolated.
defunct.
currently not used.
a numeric vector of residuals for the given penalization level.
If lambda = "{m}-se" and object contains fitted estimates for every penalization
level in the sequence, use the fit the most parsimonious model with prediction performance
statistically indistinguishable from the best model.
This is determined to be the model with prediction performance within m * cv_se
from the best model.
If lambda = "se", the multiplier m is taken from se_mult.
By default all alpha hyper-parameters available in the fitted object are considered.
This can be overridden by supplying one or multiple values in parameter alpha.
For example, if lambda = "1-se" and alpha contains two values, the "1-SE" rule is applied
individually for each alpha value, and the fit with the better prediction error is considered.
In case lambda is a number and object was fit for several alpha hyper-parameters,
alpha must also be given, or the first value in object$alpha is used with a warning.
Other functions for extracting components:
coef.pense_cvfit(),
coef.pense_fit(),
predict.pense_cvfit(),
predict.pense_fit(),
residuals.pense_fit()
# Compute the LS-EN regularization path for Freeny's revenue data
# (see ?freeny)
data(freeny)
x <- as.matrix(freeny[ , 2:5])
regpath <- elnet(x, freeny$y, alpha = 0.75)
# Predict the response using a specific penalization level
predict(regpath, newdata = freeny[1:5, 2:5],
lambda = regpath$lambda[[1]][[10]])
#> 1962.25 1962.5 1962.75 1963 1963.25
#> 9.071638 9.075877 9.082341 9.091051 9.103643
# Extract the residuals at a certain penalization level
residuals(regpath, lambda = regpath$lambda[[1]][[5]])
#> Qtr1 Qtr2 Qtr3 Qtr4
#> 1962 -0.396169224 -0.398919454 -0.378220695
#> 1963 -0.384593892 -0.294338479 -0.278030430 -0.259140970
#> 1964 -0.265543684 -0.219857551 -0.206023748 -0.173545125
#> 1965 -0.192086388 -0.146253918 -0.133786817 -0.096671191
#> 1966 -0.090347926 -0.044601264 -0.027307275 -0.015531362
#> 1967 0.006739697 0.037235389 0.038869333 0.071407419
#> 1968 0.086275062 0.102036759 0.141643505 0.167310507
#> 1969 0.175437660 0.211500792 0.222942549 0.260029329
#> 1970 0.247870647 0.296181577 0.294470169 0.278217170
#> 1971 0.306686546 0.334684047 0.353729154 0.367702082
# Select penalization level via cross-validation
set.seed(123)
cv_results <- elnet_cv(x, freeny$y, alpha = 0.5,
cv_repl = 10, cv_k = 4)
# Predict the response using the "best" penalization level
predict(cv_results, newdata = freeny[1:5, 2:5])
#> 1962.25 1962.5 1962.75 1963 1963.25
#> 8.795162 8.807070 8.824535 8.842175 8.882970
# Extract the residuals at the "best" penalization level
residuals(cv_results)
#> Qtr1 Qtr2 Qtr3 Qtr4
#> 1962 -0.002801588 -0.015699794 -0.009674689
#> 1963 -0.029165027 0.024539756 0.012794692 0.013400637
#> 1964 -0.014177641 0.006727561 -0.001786569 0.012847301
#> 1965 -0.026214283 -0.003738367 -0.010414370 -0.002497682
#> 1966 -0.014953173 0.014923561 0.008857587 0.002955549
#> 1967 -0.002438578 0.011336771 -0.004817002 -0.002203485
#> 1968 -0.014622332 -0.016038521 0.004783442 0.009509723
#> 1969 0.008935501 0.025135859 0.011008309 0.028171208
#> 1970 -0.021812388 0.015300404 -0.005936032 -0.018484409
#> 1971 -0.011338929 0.005850584 0.003783641 0.007952774
# Extract the residuals at a more parsimonious penalization level
residuals(cv_results, lambda = "1.5-se")
#> Qtr1 Qtr2 Qtr3 Qtr4
#> 1962 -0.0133914763 -0.0253025812 -0.0180073467
#> 1963 -0.0375085950 0.0197904960 0.0063674275 0.0071084444
#> 1964 -0.0199445085 0.0028559476 -0.0059886764 0.0089958759
#> 1965 -0.0300906249 -0.0052788324 -0.0128420949 -0.0036364879
#> 1966 -0.0166186511 0.0137904162 0.0073750895 0.0016121587
#> 1967 -0.0021618673 0.0116385091 -0.0046227113 0.0002016235
#> 1968 -0.0117185912 -0.0127504673 0.0088610048 0.0131305182
#> 1969 0.0114094522 0.0285319822 0.0147126545 0.0325247699
#> 1970 -0.0158575338 0.0222103711 0.0004937030 -0.0127802705
#> 1971 -0.0035765461 0.0133307584 0.0117139290 0.0154227310