Predict the target function for new study-level covariates

Given a fitted d-fSPA basis decomposition and a fitted weight model, compute the predicted target function on the shared grid as $$\tilde f^{(0)}(\cdot) = \sum_{k=1}^{\hat K} \tilde\pi_{0k}\, \hat g_k(\cdot), \qquad \tilde\pi_0 = \widehat{\mathcal M}(\mathbf W_0).$$

Usage

predict_target(dfspa_fit, weight_model, W_new)

Arguments

dfspa_fit

A "dfspa" object produced by dfspa(). Its bases slot (K-by-G_grid matrix) provides the basis functions on the grid.

weight_model

A "metahunt_weight_model" object produced by fit_weight_model(). Must have weight_model$K == nrow(dfspa_fit$bases).

W_new

A matrix or data frame of study-level covariates for the new target studies, with columns matching those used to fit weight_model.

Value

An nrow(W_new)-by-G_grid numeric matrix; row j is the predicted target function on the grid for the j-th new study.

See also

apply_wrapper() to reduce predicted functions to scalars.

Examples

set.seed(1)
G <- 40; m <- 60; K_true <- 3
x <- seq(0, 1, length.out = G)
basis <- rbind(sin(pi * x), cos(pi * x), x)

# generate study-level covariates and softmax weights
W <- data.frame(w1 = rnorm(m), w2 = rnorm(m))
beta <- cbind(c(1, -0.8), c(-0.5, 1.2), c(0, 0))
eta  <- as.matrix(W) %*% beta
pi_true <- exp(eta) / rowSums(exp(eta))
F_hat <- pi_true %*% basis + matrix(rnorm(m * G, sd = 0.02), m, G)

fit    <- dfspa(F_hat, K = K_true)
pi_hat <- project_to_simplex(F_hat, fit$bases)
wm     <- fit_weight_model(pi_hat, W)

W_new   <- data.frame(w1 = c(0, 1), w2 = c(0, -1))
f_pred  <- predict_target(fit, wm, W_new)
dim(f_pred)   # 2 x G
#> [1]  2 40