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Calculate Linear Predictor (eta) for SIR Model

eta_tab.Rd

Computes the linear predictor \(\eta_{i,j,t} = \theta^T z_{i,j,t} + \sum_{k,l} X_{k,l,t} A_{i,k} B_{j,l}\), combining exogenous covariate effects with the bilinear network influence term. Handles both static (3D) and dynamic (4D) W arrays.

Usage

eta_tab(tab, W, X, Z, fix_receiver = FALSE)

Arguments

tab

Numeric vector of parameters. For the standard model, ordered as [theta, alpha_2:p, beta_1:p] (length q + 2p - 1). For fix_receiver mode, ordered as [theta, alpha_1:p] (length q + p).

W

Three-dimensional array (m x m x p) of influence covariates. Each slice W[,,r] parameterizes the influence structure. If NULL or p=0, no network influence is included.

X

Three-dimensional array (m x m x T) carrying network influence. Typically lagged outcomes. Required even if W is NULL (can be zeros).

Z

Array of exogenous covariates. Can be:

  • NULL or q=0: No exogenous effects

  • 3D array (m x m x T): Single covariate

  • 4D array (m x m x q x T): Multiple covariates

fix_receiver

Logical. If TRUE, B is fixed to the identity matrix and tab is parsed as [theta, alpha_1:p] with all alpha free. Default FALSE.

Value

Three-dimensional array (m x m x T) of linear predictors. Each element eta[i,j,t] is the linear predictor for outcome Y[i,j,t] before applying the link function.

Examples

if (FALSE) { # \dontrun{
# Setup
m <- 10; T <- 5; p <- 2; q <- 1
W <- array(rnorm(m*m*p), dim=c(m,m,p))
X <- array(rnorm(m*m*T), dim=c(m,m,T))
Z <- array(rnorm(m*m*q*T), dim=c(m,m,q,T))

# Parameter vector
tab <- c(0.5,      # theta (q=1)
         0.2,      # alpha_2 (alpha_1=1 fixed)
         0.3, 0.4) # beta_1, beta_2
         
# Compute linear predictor
eta <- eta_tab(tab, W, X, Z)
dim(eta)  # Returns c(10, 10, 5)
} # }