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# compute Delta = exp(X * theta) for external data
# compute delta_i = exp(X_1i * alp + X_2i * bet) for ith auxiliary model
tilt.ccr <- function(para, map, data, ref){
the <- para[map$the]
fx <- as.matrix(ref[, names(the), drop = FALSE])
Delta <- as.vector(exp(fx %*% the))
nmodel <- length(map$bet)
n <- nrow(ref)
delta <- matrix(NA, nrow = n, ncol = nmodel)
for(i in 1:nmodel){
id <- c(alp.index.cc(map, i), map$bet[[i]])
gam <- para[id]
rx <- as.matrix(ref[, names(gam), drop = FALSE])
delta[, i] <- as.vector(exp(rx %*% gam))
}
ome <- para[map$ome]
fx0 <- as.matrix(data[, names(the), drop = FALSE])
Delta0 <- as.vector(exp(ome + fx0 %*% the))
list(Delta = Delta, delta = delta, Delta0 = Delta0)
}
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