#' @export
#'
em.fil.interaction <-
function(parameter, X, full.missing.data, observed.data,
full.data, k, family = family)
{ # parameter = (beta, alpha)
# X = design matrix with intercepts
p1 <- ncol(X)
beta <- parameter[1:p1]
alpha <- parameter[(p1 + 1):length(parameter)]
linear.pred.y <- X %*% beta
linear.pred.r <- cbind(X, X[, k + 1] * full.missing.data[, 1],
full.missing.data[, 1]) %*% alpha
likelihood.y <- exp(full.missing.data[, 1]*linear.pred.y)/(1 + exp(linear.pred.y))
likelihood.r <- exp(full.missing.data[, (p1 + 1)]*linear.pred.r)/(1 + exp(linear.pred.r))
likelihood.0 <- exp(0 * linear.pred.y)/(1 + exp(linear.pred.y))
likelihood.1 <- exp(1 * linear.pred.y)/(1 + exp(linear.pred.y))
weight.missing <- (likelihood.y*likelihood.r)/(likelihood.0*likelihood.r + likelihood.1*likelihood.r)
weight.observed <- rep(1, nrow(observed.data))
weight <- c(weight.observed, weight.missing)
full.x1 <- full.data[, -c(1, p1 + 1)]
full.y <- full.data[, 1]
full.r <- full.data[, p1 + 1]
brglm.fit.y <- brglm::brglm(formula = full.y ~ full.x1,
family = family,
weights = weight)
# For Firth correction use brglm otherwise use glm2
temp.y <- full.y * full.x1[, k]
glm.fit.r <- brglm::brglm(formula = full.r ~ full.x1 + temp.y + full.y,
family = family)
# brglm is used to overcome the seperation problem
alpha.hat <- stats::coef(glm.fit.r)
beta.hat.firth <- stats::coef(brglm.fit.y)
Fisher <- brglm.fit.y$FisherInfo
weights <- brglm.fit.y$weights
current.Q.firth <- brglm.fit.y$deviance/(-2) + glm.fit.r$deviance/(-2)
parameter.hat.firth <- c(beta.hat.firth, alpha.hat)
Fisher.alpha <- glm.fit.r$FisherInfo
result <- list(Q.firth = current.Q.firth, parameter.firth = parameter.hat.firth,
Fisher.firth = Fisher, weights = weights,
Fisher.firth.alpha = Fisher.alpha)
return(result)
}
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