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lkComputeTCTV = function(delta, Gamma, pg, fithg, m, G, sbj.obs, time.obs, n, T, observed){
time = rep(1:T, each = n)
sbj = rep(1:n, T)
fithg.temp = array(1, c(n*T, m, G))
fithg.temp[observed,,] = fithg
# FORWARD VARIABLES
A = array(1, c(n*T, m, G))
A[time == 1,,] = array(apply(fithg.temp[time == 1,,], 3, function(xx){xx %*% diag(delta)}), c(n,m,G))
for (t in 2:T){
## forward at time t-1
temp.A = array(A[time == (t-1),,], c(n, m, G))
A[time == t,,] = array(apply(temp.A, 3, function(xx){xx %*% Gamma}), c(n, m, G)) * fithg.temp[time == t,,]
}
li = rowSums(apply(A[time == T, ,], c(1,2), function(xx){xx %*% pg}))
lk = sum(log(li))
return(out = list(li = li, lk = lk, A = A))
}
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