Accepts a design matrix and returns a standardized version of that matrix (i.e., each column will have mean 0 and mean sum of squares equal to 1).
std(X, Xnew)A matrix (or object that can be coerced to a matrix, such as a data frame or numeric vector).
Optional. If supplied, X must be the output of std() and Xnew is to be standardized in the same way. See examples for why this might be useful.
The standardized design matrix, with the following attribues:
mean and standard deviation used to scale the columns
A vector indicating which columns of the original design matrix were able to be standardized (constant columns cannot be standardized to have a standard deviation of 1)
This function centers and scales each column of X so that
$$\sum_{i=1}^n x_{ij}=0$$
and
$$n^{-1} \sum_{i=1}^n x_{ij}^2 = 1$$
for all j. This is usually not necessary to call directly, as ncvreg internally
standardizes the design matrix, but inspection of the standardized design matrix
can sometimes be useful. This differs from the base R function scale() in two ways:
scale() uses the sample standard deviation sqrt(sum(x^2)/(n-1)), while std() uses the root-mean-square standard deviation sqrt(mean(sum(x^2)) without the \(n/(n-1)\) correction
std is faster.
data(Prostate)
S <- std(Prostate$X)
apply(S, 2, sum)
#> lcavol lweight age lbph svi
#> 4.211909e-15 6.637225e-14 4.140785e-14 1.110223e-16 -2.886580e-15
#> lcp gleason pgg45
#> 1.576864e-14 -4.218847e-15 4.982126e-15
apply(S, 2, function(x) mean(x^2))
#> lcavol lweight age lbph svi lcp gleason pgg45
#> 1 1 1 1 1 1 1 1
# Standardizing new observations
X1 <- Prostate$X[1:90,]
X2 <- Prostate$X[91:97,]
S <- std(X1)
head(std(S, X2))
#> lcavol lweight age lbph svi lcp gleason
#> 91 1.845841 1.1196037 0.5439694 -1.0472200 -0.4472136 -0.8399653 -1.0076612
#> 92 1.197790 0.1447897 -0.4241118 0.8380061 2.2360680 -0.8399653 0.3459136
#> 93 1.467844 0.6016472 0.5439694 -1.0472200 2.2360680 1.2129092 0.3459136
#> 94 2.367589 0.6487805 -2.7751661 -1.0472200 2.2360680 1.8552150 0.3459136
#> 95 1.537935 -0.5017477 -1.6687876 -1.0472200 2.2360680 2.0786918 0.3459136
#> 96 1.515337 0.3661621 0.5439694 0.9828411 2.2360680 1.3921070 0.3459136
#> pgg45
#> 91 -0.8476607
#> 92 -0.3129215
#> 93 1.2912962
#> 94 0.5783106
#> 95 -0.4911679
#> 96 2.0042819
# Useful if you fit to a standardized X, but then get new obs:
y <- Prostate$y[1:90]
fit <- ncvreg(S, y)
predict(fit, std(S, X2), lambda=0.1)
#> 91 92 93 94 95 96 97
#> 3.514077 2.938705 3.408371 3.813543 2.900628 3.445538 3.617198
# Same as
predict(ncvreg(X1, y), X2, lambda=0.1)
#> 91 92 93 94 95 96 97
#> 3.514077 2.938705 3.408371 3.813543 2.900628 3.445538 3.617198