# Cross-validation for rbridge Does k-fold cross-validation for rbridge, produces a plot, and returns a value for lambda ```r cv.rbridge(X, y, q, R, r, lambda, nfolds = 10, lambda.min = ifelse(n > p, 0.001, 0.05), nlambda = 100, eta = 1e-07, converge = 10^10, num_threads = 10) ``` ## Arguments - `X`: `X` matrix as in rbridge. - `y`: response `y` as in rbridge. - `q`: is the degree of norm which includes ridge regression with `q=2` and lasso estimates with `q=1` as special cases - `R`: is `m` by `p` `(mp` is `0.001` and `0.05` otherwise. - `nlambda`: The number of lambda values - default is `100` - `eta`: is a preselected small positive threshold value. It is deleted `jth` variable to make the algorithm stable and also is excluded `jth` variable from the final model. Default is `1e-07`. - `converge`: is the value of converge. Defaults is `10^10`. In each iteration, it is calculated by sum of square the change in linear predictor for each coefficient. The algorithm iterates until `converge > eta`. - `num_threads`: Number of threads used for parallel computation over the folds, ## Returns An object of class rbridge, a list with entries - **cve**: the mean cross-validated error. - **cvse**: estimate of standard error of `cvm`. - **cvup**: upper curve = `cvm+cvsd`. - **cvlo**: lower curve = `cvm-cvsd`. - **lambda**: the values of `lambda` used in the fits - **nz**: number of non-zero coefficients at each `lambda`. - **betas**: estimated coefficient at each `lambda`. - **lambda.min**: value of lambda that gives minimum `cve` - **lambda.1se**: largest value of `lambda` such that error is within 1 standard error of the minimum ## Details Computes cv.rbridge ## Examples ```r set.seed(2019) beta <- c(3, 1.5, 0, 0, 2, 0, 0, 0) p <- length(beta) beta <- matrix(beta, nrow = p, ncol = 1) p.active <- which(beta != 0) ### Restricted Matrix and vector ### Res 1 c1 <- c(1,1,0,0,1,0,0,0) R1.mat <- matrix(c1,nrow = 1, ncol = p) r1.vec <- as.matrix(c(6.5),1,1) ### Res 2 c2 <- c(-1,1,0,0,1,0,0,0) R2.mat <- matrix(c2,nrow = 1, ncol = p) r2.vec <- matrix(c(0.5),nrow = 1, ncol = 1) ### Res 3 R3.mat <- t(matrix(c(c1,c2),nrow = p, ncol = 2)) r3.vec <- matrix(c(6.5,0.5),nrow = 2, ncol = 1) ### Res 4 R4.mat = diag(1,p,p)[-p.active,] r4.vec <- matrix(rep(0,p-length(p.active)),nrow = p-length(p.active), ncol = 1) n = 100 X = matrix(rnorm(n*p),n,p) y = X%*%beta + rnorm(n) ######## Model 1 based on first restrictions model1 <- cv.rbridge(X, y, q = 1, R1.mat, r1.vec) print(model1) coef(model1,s='lambda.min') coef(model1,s='lambda.1se') predict(model1,newx=X[1:5,], s="lambda.min", type="response") predict(model1, s="lambda.min",type="coefficient") predict(model1, s="lambda.1se",type="coefficient") ######## Model 2 based on second restrictions model2 <- cv.rbridge(X, y, q = 1, R2.mat, r2.vec) print(model2) coef(model2,s='lambda.min') coef(model2,s='lambda.1se') predict(model2,newx=X[1:5,], s="lambda.min", type="response") predict(model2, s="lambda.min",type="coefficient") predict(model2, s="lambda.1se",type="coefficient") ######## Model 3 based on third restrictions model3 <- cv.rbridge(X, y, q = 1, R3.mat, r3.vec) print(model3) coef(model3,s='lambda.min') coef(model3,s='lambda.1se') predict(model3,newx=X[1:5,], s="lambda.min", type="response") predict(model3, s="lambda.min",type="coefficient") predict(model3, s="lambda.1se",type="coefficient") ######## Model 4 based on fourth restrictions model4 <- cv.rbridge(X, y, q = 1, R4.mat, r4.vec) print(model4) coef(model4,s='lambda.min') coef(model4,s='lambda.1se') predict(model4,newx=X[1:5,], s="lambda.min", type="response") predict(model4, s="lambda.min",type="coefficient") predict(model4, s="lambda.1se",type="coefficient") ``` ## See Also `rbridge` ## Author(s) Bahadir Yuzbasi, Mohammad Arashi and Fikri Akdeniz Maintainer: Bahadir Yuzbasi b.yzb@hotmail.com

cv.rbridge function