Extract Coefficient Estimates

Extract coefficients from an adaptive PENSE (or LS-EN) regularization path fitted by pense() or elnet().

Usage

# S3 method for class 'pense_fit'
coef(object, lambda, alpha = NULL, sparse = NULL, standardized = FALSE, ...)

Arguments

object

PENSE regularization path to extract coefficients from.

lambda

a single number for the penalty level.

alpha

Either a single number or NULL (default). If given, only fits with the given alpha value are considered. If object was fit with multiple alpha values, and no value is provided, the first value in object$alpha is used with a warning.

sparse

should coefficients be returned as sparse or dense vectors? Defaults to the sparsity setting in object. Can also be set to sparse = 'matrix', in which case a sparse matrix is returned instead of a sparse vector.

standardized

return the standardized coefficients.

...

currently not used.

Value

either a numeric vector or a sparse vector of type dsparseVector of size \(p + 1\), depending on the sparse argument. Note: prior to version 2.0.0 sparse coefficients were returned as sparse matrix of type dgCMatrix. To get a sparse matrix as in previous versions, use sparse = 'matrix'.

See also

coef.pense_cvfit() for extracting coefficients from a PENSE fit with hyper-parameters chosen by cross-validation

Other functions for extracting components: coef.pense_cvfit(), predict.pense_cvfit(), predict.pense_fit(), residuals.pense_cvfit(), residuals.pense_fit()

Examples

# Compute the PENSE regularization path for Freeny's revenue data
# (see ?freeny)
data(freeny)
x <- as.matrix(freeny[ , 2:5])

regpath <- pense(x, freeny$y, alpha = 0.5)
plot(regpath)


# Extract the coefficients at a certain penalization level
coef(regpath, lambda = regpath$lambda[[1]][[40]])
#>           (Intercept) lag.quarterly.revenue           price.index 
#>            -6.5082299             0.2510560            -0.6879670 
#>          income.level      market.potential 
#>             0.7090986             0.9409940 

# What penalization level leads to good prediction performance?
set.seed(123)
cv_results <- pense_cv(x, freeny$y, alpha = 0.5,
                       cv_repl = 2, cv_k = 4)
plot(cv_results, se_mult = 1)


# Print a summary of the fit and the cross-validation results.
summary(cv_results)
#> PENSE fit with prediction performance estimated by 2 replications of 4-fold ris 
#> cross-validation.
#> 
#> 4 out of 4 predictors have non-zero coefficients:
#> 
#>               Estimate
#> (Intercept) -4.7921541
#> X1           0.3338834
#> X2          -0.6140406
#> X3           0.6954769
#> X4           0.7316339
#> ---
#> 
#> Hyper-parameters: lambda=0.0003364066, alpha=0.5

# Extract the coefficients at the penalization level with
# smallest prediction error ...
coef(cv_results)
#>           (Intercept) lag.quarterly.revenue           price.index 
#>            -4.7921541             0.3338834            -0.6140406 
#>          income.level      market.potential 
#>             0.6954769             0.7316339 
# ... or at the penalization level with prediction error
# statistically indistinguishable from the minimum.
coef(cv_results, lambda = '1-se')
#>           (Intercept) lag.quarterly.revenue           price.index 
#>           -11.4754472             0.2265866            -0.5739724 
#>          income.level      market.potential 
#>             0.5417608             1.3768215