# Predict Method for cv.grpnet Fits Obtain predictions from a cross-validated group elastic net regularized GLM (cv.grpnet) object. ```r ## S3 method for class 'cv.grpnet' predict(object, newx, newdata, s = c("lambda.1se", "lambda.min"), type = c("link", "response", "class", "terms", "importance", "coefficients", "nonzero", "groups", "ncoefs", "ngroups", "norm", "znorm"), ...) ``` ## Arguments - `object`: Object of class "cv.grpnet" - `newx`: Matrix of new `x` scores for prediction (default S3 method). Must have $p$ columns arranged in the same order as the `x` matrix used to fit the model. - `newdata`: Data frame of new `data` scores for prediction (S3 "formula" method). Must contain all variables in the `formula` used to fit the model. - `s`: Lambda value(s) at which predictions should be obtained. Can input a character ("lambda.min" or "lambda.1se") or a numeric vector. Default of "lambda.min" uses the `lambda` value that minimizes the mean cross-validated error. - `type`: Type of prediction to return. "link" gives predictions on the link scale ($\eta$). "response" gives predictions on the mean scale ($\mu$). "class" gives predicted class labels (for "binomial" and "multinomial" families). "terms" gives the predictions for each term (group) in the model ($\eta_k$). "importance" gives the variable importance index for each term (group) in the model. "coefficients" returns the coefficients used for predictions. "nonzero" returns a list giving the indices of non-zero coefficients for each `s`. "groups" returns a list giving the labels of non-zero groups for each `s`. "ncoefs" returns the number of non-zero coefficients for each `s`. "ngroups" returns the number of non-zero groups for each `s`. "norm" returns the L2 norm of each group's (raw) coefficients for each `s`. "znorm" returns the L2 norm of each group's standardized coefficients for each `s`. - `...`: Additional arguments (ignored) ## Details Predictions are calculated from the `grpnet` object fit to the full sample of data, which is stored as `object$grpnet.fit` See `predict.grpnet` for further details on the calculation of the different types of predictions. ## Returns Depends on three factors... 1. the exponential family distribution 2. the length of the input `s` 3. the `type` of prediction requested See `predict.grpnet` for details ## References Friedman, J., Hastie, T., & Tibshirani, R. (2010). Regularization paths for generalized linear models via coordinate descent. **Journal of Statistical Software, 33**(1), 1-22. tools:::Rd_expr_doi("10.18637/jss.v033.i01") Helwig, N. E. (2024). Versatile descent algorithms for group regularization and variable selection in generalized linear models. **Journal of Computational and Graphical Statistics**. tools:::Rd_expr_doi("10.1080/10618600.2024.2362232") ## Author(s) Nathaniel E. Helwig ## Note Syntax is inspired by the `predict.cv.glmnet` function in the glmnet package (Friedman, Hastie, & Tibshirani, 2010). ## See Also `cv.grpnet` for k-fold cross-validation of `lambda` `predict.grpnet` for predicting from `grpnet` objects ## Examples ```r ######***###### family = "gaussian" ######***###### # load data data(auto) # 10-fold cv (formula method, response = mpg) set.seed(1) mod <- cv.grpnet(mpg ~ ., data = auto) # get fitted values at "lambda.1se" fit.1se <- predict(mod, newdata = auto) # get fitted values at "lambda.min" fit.min <- predict(mod, newdata = auto, s = "lambda.min") # compare mean absolute error for two solutions mean(abs(auto$mpg - fit.1se)) mean(abs(auto$mpg - fit.min)) ######***###### family = "binomial" ######***###### # load data data(auto) # redefine origin (Domestic vs Foreign) auto$origin <- ifelse(auto$origin == "American", "Domestic", "Foreign") # 10-fold cv (default method, response = origin with 2 levels) set.seed(1) mod <- cv.grpnet(origin ~ ., data = auto, family = "binomial") # get predicted classes at "lambda.1se" fit.1se <- predict(mod, newdata = auto, type = "class") # get predicted classes at "lambda.min" fit.min <- predict(mod, newdata = auto, type = "class", s = "lambda.min") # compare misclassification rate for two solutions 1 - mean(auto$origin == fit.1se) 1 - mean(auto$origin == fit.min) ######***###### family = "multinomial" ######***###### # load data data(auto) # 10-fold cv (formula method, response = origin with 3 levels) set.seed(1) mod <- cv.grpnet(origin ~ ., data = auto, family = "multinomial") # get predicted classes at "lambda.1se" fit.1se <- predict(mod, newdata = auto, type = "class") # get predicted classes at "lambda.min" fit.min <- predict(mod, newdata = auto, type = "class", s = "lambda.min") # compare misclassification rate for two solutions 1 - mean(auto$origin == fit.1se) 1 - mean(auto$origin == fit.min) ######***###### family = "poisson" ######***###### # load data data(auto) # 10-fold cv (formula method, response = horsepower) set.seed(1) mod <- cv.grpnet(horsepower ~ ., data = auto, family = "poisson") # get fitted values at "lambda.1se" fit.1se <- predict(mod, newdata = auto, type = "response") # get fitted values at "lambda.min" fit.min <- predict(mod, newdata = auto, type = "response", s = "lambda.min") # compare mean absolute error for two solutions mean(abs(auto$horsepower - fit.1se)) mean(abs(auto$horsepower - fit.min)) ######***###### family = "negative.binomial" ######***###### # load data data(auto) # 10-fold cv (formula method, response = horsepower) set.seed(1) mod <- cv.grpnet(horsepower ~ ., data = auto, family = "negative.binomial") # get fitted values at "lambda.1se" fit.1se <- predict(mod, newdata = auto, type = "response") # get fitted values at "lambda.min" fit.min <- predict(mod, newdata = auto, type = "response", s = "lambda.min") # compare mean absolute error for two solutions mean(abs(auto$horsepower - fit.1se)) mean(abs(auto$horsepower - fit.min)) ######***###### family = "Gamma" ######***###### # load data data(auto) # 10-fold cv (formula method, response = origin) set.seed(1) mod <- cv.grpnet(mpg ~ ., data = auto, family = "Gamma") # get fitted values at "lambda.1se" fit.1se <- predict(mod, newdata = auto, type = "response") # get fitted values at "lambda.min" fit.min <- predict(mod, newdata = auto, type = "response", s = "lambda.min") # compare mean absolute error for two solutions mean(abs(auto$mpg - fit.1se)) mean(abs(auto$mpg - fit.min)) ######***###### family = "inverse.gaussian" ######***###### # load data data(auto) # 10-fold cv (formula method, response = origin) set.seed(1) mod <- cv.grpnet(mpg ~ ., data = auto, family = "inverse.gaussian") # get fitted values at "lambda.1se" fit.1se <- predict(mod, newdata = auto, type = "response") # get fitted values at "lambda.min" fit.min <- predict(mod, newdata = auto, type = "response", s = "lambda.min") # compare mean absolute error for two solutions mean(abs(auto$mpg - fit.1se)) mean(abs(auto$mpg - fit.min)) ```

predict.cv.grpnet function