# Make Prediction From a SMMA Object Given new covariate data this function computes the linear predictors based on the estimated model coefficients in an object produced by the function `softmaximin`. Note that the data can be supplied in two different formats: i) as a $n' \times p$ matrix ($p$ is the number of model coefficients and $n'$ is the number of new data points) or ii) as a list of two or three matrices each of size $n_i' \times p_i, i = 1, 2, 3$ ($n_i'$ is the number of new marginal data points in the $i$th dimension). ```r ## S3 method for class 'SMMA' predict(object, x = NULL, X = NULL, ...) ``` ## Arguments - `object`: An object of class SMMA, produced with `softmaximin` - `x`: a matrix of size $n' \times p$ with $n'$ is the number of new data points. - `X`: a list containing the data matrices each of size $n'_{i} \times p_i$, where $n'_{i}$ is the number of new data points in the $i$th dimension. - `...`: ignored ## Returns A list of length `nlambda` containing the linear predictors for each model. If new covariate data is supplied in one $n' \times p$ matrix `x` each item is a vector of length $n'$. If the data is supplied as a list of matrices each of size $n'_{i} \times p_i$, each item is an array of size $n'_1 \times \cdots \times n'_d$, with $d\in \{1,2,3\}$. ## Examples ```r ##size of example n1 <- 65; n2 <- 26; n3 <- 13; p1 <- 13; p2 <- 5; p3 <- 4 ##marginal design matrices (Kronecker components) X1 <- matrix(rnorm(n1 * p1, 0, 0.5), n1, p1) X2 <- matrix(rnorm(n2 * p2, 0, 0.5), n2, p2) X3 <- matrix(rnorm(n3 * p3, 0, 0.5), n3, p3) X <- list(X1, X2, X3) component <- rbinom(p1 * p2 * p3, 1, 0.1) Beta1 <- array(rnorm(p1 * p2 * p3, 0, .1) + component, c(p1 , p2, p3)) Beta2 <- array(rnorm(p1 * p2 * p3, 0, .1) + component, c(p1 , p2, p3)) mu1 <- RH(X3, RH(X2, RH(X1, Beta1))) mu2 <- RH(X3, RH(X2, RH(X1, Beta2))) Y1 <- array(rnorm(n1 * n2 * n3, mu1), dim = c(n1, n2, n3)) Y2 <- array(rnorm(n1 * n2 * n3, mu2), dim = c(n1, n2, n3)) Y <- array(NA, c(dim(Y1), 2)) Y[,,, 1] <- Y1; Y[,,, 2] <- Y2; fit <- softmaximin(X, Y, zeta = 10, penalty = "lasso", alg = "npg") ##new data in matrix form x <- matrix(rnorm(p1 * p2 * p3), nrow = 1) predict(fit, x = x)[[15]] ##new data in tensor component form X1 <- matrix(rnorm(p1), nrow = 1) X2 <- matrix(rnorm(p2), nrow = 1) X3 <- matrix(rnorm(p3), nrow = 1) predict(fit, X = list(X1, X2, X3))[[15]] ``` ## Author(s) Adam Lund

predict.SMMA function