# Function to Fit a Solution of a Group Lasso Problem Fits the solution of a group lasso problem for a model of type `grpl.model`. ```r grplasso(x, ...) ## S3 method for class 'formula' grplasso(formula, nonpen = ~ 1, data, weights, subset, na.action, lambda, coef.init, penscale = sqrt, model = LogReg(), center = TRUE, standardize = TRUE, control = grpl.control(), contrasts = NULL, ...) ## Default S3 method: grplasso(x, y, index, weights = rep(1, length(y)), offset = rep(0, length(y)), lambda, coef.init = rep(0, ncol(x)), penscale = sqrt, model = LogReg(), center = TRUE, standardize = TRUE, control = grpl.control(), ...) ``` ## Arguments - `x`: design matrix (including intercept) - `y`: response vector - `formula`: `formula` of the penalized variables. The response has to be on the left hand side of `~`. - `nonpen`: `formula` of the nonpenalized variables. This will be added to the `formula` argument above and doesn't need to have the response on the left hand side. - `data`: `data.frame` containing the variables in the model. - `index`: vector which defines the grouping of the variables. Components sharing the same number build a group. Non-penalized coefficients are marked with `NA`. - `weights`: vector of observation weights. - `subset`: an optional vector specifying a subset of observations to be used in the fitting process. - `na.action`: a function which indicates what should happen when the data contain 'NA's. - `offset`: vector of offset values; needs to have the same length as the response vector. - `lambda`: vector of penalty parameters. Optimization starts with the first component. See details below. - `coef.init`: initial vector of parameter estimates corresponding to the first component in the vector `lambda`. - `penscale`: rescaling function to adjust the value of the penalty parameter to the degrees of freedom of the parameter group. See the reference below. - `model`: an object of class `grpl.model` implementing the negative log-likelihood, gradient, hessian etc. See the documentation of `grpl.model` for more details. - `center`: logical. If true, the columns of the design matrix will be centered (except a possible intercept column). - `standardize`: logical. If true, the design matrix will be blockwise orthonormalized such that for each block $X^TX = n 1$ (*after* possible centering). - `control`: options for the fitting algorithm, see `grpl.control`. - `contrasts`: an optional list. See the 'contrasts.arg' of 'model.matrix.default'. - `...`: additional arguments to be passed to the functions defined in `model`. ## Details When using `grplasso.formula`, the grouping of the variables is derived from the type of the variables: The dummy variables of a factor will be automatically treated as a group. The optimization process starts using the first component of `lambda` as penalty parameter $\lambda$ and with starting values defined in `coef.init` for the parameter vector. Once fitted, the next component of `lambda` is considered as penalty parameter with starting values defined as the (fitted) coefficient vector based on the previous component of `lambda`. ## Returns A `grplasso` object is returned, for which `coef`, `print`, `plot` and `predict` methods exist. - **coefficients**: coefficients with respect to the **original** input variables (even if `standardize = TRUE` is used for fitting). - **lambda**: vector of lambda values where coefficients were calculated. - **index**: grouping index vector. ## References Lukas Meier, Sara van de Geer and Peter B\"uhlmann (2008), **The Group Lasso for Logistic Regression**, Journal of the Royal Statistical Society, 70 (1), 53 - 71 ## Author(s) Lukas Meier, meier@stat.math.ethz.ch ## Examples ```r ## Use the Logistic Group Lasso on the splice data set data(splice) ## Define a list with the contrasts of the factors contr <- rep(list("contr.sum"), ncol(splice) - 1) names(contr) <- names(splice)[-1] ## Fit a logistic model fit.splice <- grplasso(y ~ ., data = splice, model = LogReg(), lambda = 20, contrasts = contr, center = TRUE, standardize = TRUE) ## Perform the Logistic Group Lasso on a random dataset set.seed(79) n <- 50 ## observations p <- 4 ## variables ## First variable (intercept) not penalized, two groups having 2 degrees ## of freedom each index <- c(NA, 2, 2, 3, 3) ## Create a random design matrix, including the intercept (first column) x <- cbind(1, matrix(rnorm(p * n), nrow = n)) colnames(x) <- c("Intercept", paste("X", 1:4, sep = "")) par <- c(0, 2.1, -1.8, 0, 0) prob <- 1 / (1 + exp(-x %*% par)) mean(pmin(prob, 1 - prob)) ## Bayes risk y <- rbinom(n, size = 1, prob = prob) ## binary response vector ## Use a multiplicative grid for the penalty parameter lambda, starting ## at the maximal lambda value lambda <- lambdamax(x, y = y, index = index, penscale = sqrt, model = LogReg()) * 0.5^(0:5) ## Fit the solution path on the lambda grid fit <- grplasso(x, y = y, index = index, lambda = lambda, model = LogReg(), penscale = sqrt, control = grpl.control(update.hess = "lambda", trace = 0)) ## Plot coefficient paths plot(fit) ```

grplasso function