Formula: l_p = l(beta; y) - lambda sum_c beta_c'beta_c (ridge) or - lambda sum_c
sum_j |beta_cj| (lasso)
Usage
Mnpenlik(X, y, beta0, beta, lam, penalty = "ridge")
Arguments
- X
Design matrix without an intercept column.
- y
Observed category index per record, 1-based.
- beta0
Category intercepts.
- beta
Category slope coefficients.
- lam
Penalty strength lambda.
- penalty
'ridge' or 'lasso'.
Value
List with loglik, penalty, penalized_loglik, n.
References
Montesinos Lopez, Montesinos Lopez and Crossa (2022), Multivariate
Statistical Machine Learning Methods for Genomic Prediction, Springer,
doi:10.1007/978-3-030-89010-0. Chapter 7, Eq. (7.7) p. 226 for the ridge penalty and
Eq. (7.10) p. 227 for the lasso penalty. The book states on p. 226 that only the
slopes are penalized, never the intercepts.
Examples
set.seed(4)
X <- matrix(rnorm(40), 20, 2)
y <- sample(1:3, 20, TRUE)
Mnpenlik(X, y, beta0 = c(0, 0, 0), beta = matrix(0, 3, 2), lam = 1)$penalized_loglik # 20 log(1/3) at zero
#> [1] -27.72589
