log_likelihood_phi <- function(params, phi, data) {
lam2 <- params[1]; theta1 <- params[2]; theta2 <- params[3]
z1 <- data[1]; z2 <- data[2]; m01 <- data[3]; m02 <- data[4]
y01 <- data[5]; y02 <- data[6]; N0 <- data[7]; N <- data[8]
# m01 * log(phi * lam2) + m02 * log(lam2) - N0 * (phi * lam2 + lam2) +
# y01 * log(theta1) + (m01 - y01) * log(1 - theta1) +
# y02 * log(theta2) + (m02 - y02) * log(1 - theta2) +
# z1 * log(phi * lam2 * (1 - theta1) + lam2 * theta2) +
# z2 * log(lam2 * (1 - theta2) + phi * lam2 * theta1) -
# N * (phi * lam2 + lam2)
m01 * log(phi) + (m01 + m02 + z1 + z2) * log(lam2) -
lam2 * (phi + 1) * (N0 + N) +
z1 * log(phi * (1 - theta1) + theta2) +
z2 * log((1 - theta2) + phi * theta1) +
y01 * log(theta1) + (m01 - y01) * log(1 - theta1) +
y02 * log(theta2) + (m02 - y02) * log(1 - theta2)
}
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