This function is intended for users who know exactly what they're doing and want complete control over the fitting process: no standardization is applied, no intercept is included, no path is fit. All of these things are best practices for data analysis, so if you are choosing not to do them, you are on your own – there is no guarantee that your results will be meaningful. Some things in particular that you should pay attention to:
If your model has an intercept, it is up to you to (un)penalize it properly, typically
by settings its corresponding element of penalty.factor to zero.
You should provide initial values for the coefficients; in nonconvex optimization, initial values are very important in determining which local solution an algorithm converges to.
Design matrix; no intercept will be added, no standardization will occur (n x p matrix)
Response vector (length n vector)
Initial values for beta. Default: zero (length p vector)
Residuals corresponding to init; these will be calculated if not
supplied, but if they have already been calculated elsewhere, it is
more efficient to pass them as an argument. WARNING: If you supply
an incorrect value of r, the solution will be incorrect. (length
n vector)
X scales: the jth element should equal crossprod(X[,j])/n. These
will be calculated if not supplied, but if they have already been
calculated elsewhere, it is more efficient to pass them as an
argument. In particular, if X is standardized, one should pass
xtx = rep(1, p). WARNING: If you supply an incorrect value of
xtx, the solution will be incorrect. (length p vector)
Penalty function to be applied, either "MCP" (default), "SCAD", or "lasso")
Tuning parameter of the MCP/SCAD penalty, as in ncvreg(); default
is 3 for MCP and 3.7 for SCAD.
Tuning paramter controlling the ridge component of penalty, as in
ncvreg(); default is 1 (meaning no ridge penalty)
Regularization parameter value at which to estimate beta; must be
scalar – for pathwise optimization, see ncvreg()
Convergence threshhold. The algorithm iterates until the RMSD for the change in linear predictors for each coefficient is less than eps. Default is 1e-4.
Maximum number of allowed iterations; if this number is reached, algorithm will terminate prior to convergence. Default: 1000.
Multiplicative factor for the penalty applied to each coefficient,
as in ncvreg(). In particular, note that if you include an
intercept, you probably want to set its entry to zero here.
Return warning messages for failures to converge and model saturation? Default is TRUE.
A list containing:
beta: The estimated regression coefficients
iter: The number of iterations required to solve for `beta
loss: The loss (residual sum of squares) at convergence
resid: The residuals at convergence
lambda: See above
penalty: See above
gamma: See above
alpha: See above
penalty.factor: See above
n: Sample size
At the moment, this function only works for least-squares loss functions. Additional functionality for other loss functions (logistic, Cox) is in development.
data(Prostate)
X <- cbind(1, Prostate$X)
y <- Prostate$y
fit <- ncvfit(X, y, lambda=0.1, penalty.factor=c(0, rep(1, ncol(X)-1)))
fit$beta
#> lcavol lweight age lbph svi
#> 2.268444208 0.677388754 0.000000000 -0.013317940 0.143711214 0.000000000
#> lcp gleason pgg45
#> 0.000000000 0.000000000 0.005398707
# Compare with:
coef(ncvreg(X, y), 0.1)
#> (Intercept) lcavol lweight age lbph
#> -0.6973059 0.0000000 0.5387509 0.6382717 0.0000000 0.0000000
#> svi lcp gleason pgg45
#> 0.6102800 0.0000000 0.0000000 0.0000000
# The unstandardized version makes little sense here, as it fails to account
# for differences in the scales of the predictors.