# Predict Method for SVEM Models (Gaussian and Binomial) Generate predictions from a fitted SVEM model (Gaussian or binomial), with optional bootstrap uncertainty and family-appropriate output scales. ```r ## S3 method for class 'svem_model' predict( object, newdata, type = c("response", "link", "class"), debias = FALSE, se.fit = FALSE, interval = FALSE, level = 0.95, ... ) ``` ## Arguments - `object`: A fitted SVEM model (class `svem_model`; binomial models typically also inherit class `svem_binomial`). Created by `SVEMnet()`. - `newdata`: A data frame of new predictor values. - `type`: (Binomial only) One of: * `"response"` (default): predicted probabilities in $[0,1]$. * `"link"`: linear predictor (log-odds). * `"class"`: 0/1 class labels (threshold 0.5). Uncertainty summaries are not available for this type. Ignored for Gaussian models. - `debias`: (Gaussian only) Logical; default `FALSE`. If `TRUE`, apply the linear calibration fit `lm(y ~ y_pred)` learned at training when available. Ignored (and internally set to `FALSE`) for binomial models. - `se.fit`: Logical; if `TRUE`, return bootstrap standard errors computed from member predictions (requires `coef_matrix`). Not available for `type = "class"`. For Gaussian models, this forces use of bootstrap member predictions instead of aggregate coefficients. - `interval`: Logical; if `TRUE`, return percentile confidence limits from member predictions (requires `coef_matrix`). Not available for `type = "class"`. For Gaussian models, this forces use of bootstrap member predictions instead of aggregate coefficients. - `level`: Confidence level for percentile intervals. Default `0.95`. - `...`: Currently unused. ## Returns If `se.fit = FALSE` and `interval = FALSE`: * Gaussian : a numeric vector of predictions on the response (identity) scale. * Binomial : a numeric vector for `type = "response"` (probabilities) or `type = "link"` (log-odds), or an integer vector of 0/1 labels for `type = "class"`. If `se.fit` and/or `interval` are `TRUE` (and `type != "class"`), a list with components: * `fit`: predictions on the requested scale. * `se.fit`: bootstrap standard errors (when `se.fit = TRUE`). * `lwr`, `upr`: percentile confidence limits (when `interval = TRUE`). Rows containing unseen or missing factor levels produce `NA` predictions (and `NA` SEs/intervals), with a warning. ## Details This method dispatches on `object$family`: * Gaussian : returns predictions on the response (identity) scale. Optional linear calibration ("debias") learned at training may be applied. * Binomial : supports glmnet-style `type = "link"`, `"response"`, or `"class"` predictions. No debiasing is applied; `type = "response"` returns probabilities in $[0,1]$. Uncertainty summaries (`se.fit`, `interval`) and all binomial predictions are based on per-bootstrap member predictions obtained from the coefficient matrix stored in `object$coef_matrix`. If `coef_matrix` is `NULL`, these options are not available (and binomial prediction will fail). For Gaussian models with `se.fit = FALSE` and `interval = FALSE`, predictions are computed directly from the aggregated coefficients. ## Design-matrix reconstruction The function rebuilds the design matrix for `newdata` to match the training design: * Uses the training `terms` (with environment set to `baseenv()`). * Harmonizes factor and character predictors to the training `xlevels`. * Reuses stored per-factor `contrasts` when available; otherwise falls back to saved global contrast options. * Zero-fills any columns present at training but absent in `newdata`, and reorders columns to match the training order. Rows containing unseen factor levels yield `NA` predictions (with a warning). ## Aggregation and debiasing For Gaussian SVEM models: - **Point predictions**: When `se.fit = FALSE` and `interval = FALSE`, predictions are computed from the aggregated coefficients saved at fit time (`object$parms`; or `object$parms_debiased` when `debias = TRUE`). This is algebraically equivalent to averaging member predictions when the coefficients were formed as bootstrap means. - **Bootstrap-based summaries**: When `se.fit = TRUE` and/or `interval = TRUE`, predictions are computed from per-bootstrap member predictions using `object$coef_matrix`. For `debias = TRUE`, the linear calibration is applied to member predictions before summarizing. For binomial SVEM models, predictions are always aggregated from member predictions on the requested scale (probability or link) using `coef_matrix`; the stored coefficient averages (`parms`, `parms_debiased`) are retained for diagnostics but are not used in prediction. The `debias` argument is ignored and treated as `FALSE` for binomial models. For Gaussian fits, if `debias = TRUE` and a calibration model `lm(y ~ y_pred)` was learned at training, predictions (and, when applicable, member predictions) are transformed by that calibration. This debiasing is never applied for binomial fits. ## Uncertainty When `se.fit = TRUE`, standard errors are computed as the row-wise standard deviations of member predictions on the requested scale. When `interval = TRUE`, percentile intervals are computed from member predictions on the requested scale, using the requested `level`. Both require a non-null `coef_matrix`. For `type = "class"` (binomial), uncertainty summaries are not available. ## Examples ```r ## ---- Gaussian example ------------------------------------------------- set.seed(1) n <- 60 X1 <- rnorm(n); X2 <- rnorm(n); X3 <- rnorm(n) y <- 1 + 0.8 * X1 - 0.6 * X2 + 0.2 * X3 + rnorm(n, 0, 0.4) dat <- data.frame(y, X1, X2, X3) fit_g <- SVEMnet( y ~ (X1 + X2 + X3)^2, dat, nBoot = 40, glmnet_alpha = c(1, 0.5), relaxed = TRUE, family = "gaussian" ) ## Aggregate-coefficient predictions (with and without debiasing) p_g <- predict(fit_g, dat) # debias = FALSE (default) p_gd <- predict(fit_g, dat, debias = TRUE) # apply calibration, if available ## Bootstrap-based uncertainty (requires coef_matrix) out_g <- predict( fit_g, dat, debias = TRUE, se.fit = TRUE, interval = TRUE, level = 0.90 ) str(out_g) ## ---- Binomial example ------------------------------------------------ set.seed(2) n <- 120 X1 <- rnorm(n); X2 <- rnorm(n); X3 <- rnorm(n) eta <- -0.3 + 1.1 * X1 - 0.8 * X2 + 0.5 * X1 * X3 p <- plogis(eta) yb <- rbinom(n, 1, p) db <- data.frame(yb = yb, X1 = X1, X2 = X2, X3 = X3) fit_b <- SVEMnet( yb ~ (X1 + X2 + X3)^2, db, nBoot = 50, glmnet_alpha = c(1, 0.5), relaxed = TRUE, family = "binomial" ) ## Probabilities, link, and classes p_resp <- predict(fit_b, db, type = "response") p_link <- predict(fit_b, db, type = "link") y_hat <- predict(fit_b, db, type = "class") # 0/1 labels (no SE or interval) ## Bootstrap-based uncertainty on the probability scale out_b <- predict( fit_b, db, type = "response", se.fit = TRUE, interval = TRUE, level = 0.90 ) str(out_b) ``` ## See Also `SVEMnet`

predict.svem_model function