R Under development (unstable) (2024-09-23 r87189 ucrt) -- "Unsuffered Consequences"
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> 
> library("tram")
Loading required package: mlt
Loading required package: basefun
Loading required package: variables
Loading required package: mvtnorm
> library("survival")
> library("sandwich")
> library("numDeriv")
> library("mvtnorm")
> 
> ### check mmlt for wild model combinations and weights
> 
> set.seed(290875)
> 
> chk <- function(x, y, tol = 1e-3) stopifnot(all.equal(x, y, tol = tol))
> 
> N <- 100
> J <- 3
> 
> ### weights
> w <- as.double(sample(0:5, size = N, replace = TRUE))
> ### X1, X2, X3 correlated
> z <- matrix(rnorm(N * J), nrow = J)
> L <- ltMatrices(runif(J * (J - 1) / 2))
> y <- t(solve(standardize(L), z))
> ### uncorrelated ordered
> x <- sample(gl(5, N / 5, ordered = TRUE))
> ### X3 right censored
> e <- sample(c(TRUE, FALSE), size = N, replace = TRUE)
> X3 <- exp(y[,3])
> X3 <- Surv(X3, event = e)
> d <- data.frame(y[,1:2], X3, x, e)
> dw <- d[rep(1:nrow(d), w),,drop = FALSE]
> idx <- sample(1:N, size = N / 2)
> 
> ### global options (speed-up estimation)
> M <- 200
> args <- list(type = "ghalton", M = M)
> op <- mltoptim()	### no hessian
> 
> ### marginal models (use Lm to reduce number of parameters)
> m1 <- Lm(X1 ~ 1, data = d)
> m2 <- Lm(X2 ~ 1, data = d)
> m3 <- Lm(X3 ~ 1, data = d)
> m4 <- Polr(x ~ 1, data = d, method = "probit")
> 
> ### joint distribution of X1, X2 (continuous), X3 (continuous and
> ### right-censored) and x (discrete)
> m <- mmlt(m1, m2, m3, m4, data = d, args = args, optim = op)
Warning message:
In .MCw(J = dJ, M = args$M, seed = args$seed, args$type) :
  package qrng is not available for ghalton(); using type = MC
> l1 <- logLik(m)
> ## check gradient
> s1 <- -colSums(estfun(m))
> s2 <- grad(function(parm) logLik(m, parm = parm), coef(m))
> chk(s2, unname(s1))
> L1 <- aperm(coef(m, type = "Lambda"), perm = c("X1", "X2", "X3", "x"))
> 
> ## change order of variables
> m <- mmlt(m2, m4, m1, m3, data = d, args = args, optim = op)
Warning message:
In .MCw(J = dJ, M = args$M, seed = args$seed, args$type) :
  package qrng is not available for ghalton(); using type = MC
> l2 <- logLik(m)
> L2 <- aperm(coef(m, type = "Lambda"), perm = c("X1", "X2", "X3", "x"))
> 
> ## use less evaluation points for normal integrals
> m <- mmlt(m2, m4, m1, m3, data = d, optim = op,
+           args = list(type = "ghalton", M = 100))
Warning message:
In .MCw(J = dJ, M = args$M, seed = args$seed, args$type) :
  package qrng is not available for ghalton(); using type = MC
> l3 <- logLik(m)
> L3 <- aperm(coef(m, type = "Lambda"), perm = c("X1", "X2", "X3", "x"))
> ## check near identity: This can't be exact, because the evaluation points
> ## correspond to different dimensions in the different calls
> chk(l2, l1)
> chk(l3, l1)
> chk(L2, L1, tol = 1e-2)
> chk(L3, L1, tol = 1e-2)
> 
> ### continuous and ordered only
> m <- mmlt(m1, m2, m4, data = d, optim = op)
> l1 <- logLik(m)
> l1a <- logLik(m, newdata = d[idx,]) + logLik(m, newdata = d[-idx,])
> s1 <- -colSums(estfun(m))
> s2 <- grad(function(parm) logLik(m, parm = parm), coef(m))
> chk(s2, unname(s1))
> L1 <- aperm(coef(m, type = "Lambda"), perm = c("X1", "X2", "x"))
> 
> m <- mmlt(m2, m1, m4, data = d, optim = op)
> l2 <- logLik(m)
> l2a <- logLik(m, newdata = d[idx,]) + logLik(m, newdata = d[-idx,])
> L2 <- aperm(coef(m, type = "Lambda"), perm = c("X1", "X2", "x"))
> 
> m <- mmlt(m4, m2, m1, data = d, optim = op)
> l3 <- logLik(m)
> l3a <- logLik(m, newdata = d[idx,]) + logLik(m, newdata = d[-idx,])
> L3 <- aperm(coef(m, type = "Lambda"), perm = c("X1", "X2", "x"))
> chk(l2, l1)
> chk(l3, l1)
> chk(L2, L1)
> chk(L3, L1)
> 
> ### weighted observations (1)
> m1 <- Lm(X1 ~ 1, data = dw)
> m2 <- Lm(X2 ~ 1, data = dw)
> m3 <- Lm(X3 ~ 1, data = dw)
> m4 <- Polr(x ~ 1, data = dw, method = "probit")
> 
> m <- mmlt(m1, m2, m4, data = dw, optim = op)
> l1 <- logLik(m)
> s1 <- -colSums(estfun(m))
> s2 <- grad(function(parm) logLik(m, parm = parm), coef(m))
> chk(s2, unname(s1))
> L1 <- aperm(coef(m, type = "Lambda"), perm = c("X1", "X2", "x"))
> 
> m <- mmlt(m2, m1, m4, data = dw, optim = op)
> l2 <- logLik(m)
> L2 <- aperm(coef(m, type = "Lambda"), perm = c("X1", "X2", "x"))
> 
> m <- mmlt(m4, m2, m1, data = dw, optim = op)
> l3 <- logLik(m)
> L3 <- aperm(coef(m, type = "Lambda"), perm = c("X1", "X2", "x"))
> ### check if order matters
> chk(l2, l1)
> chk(l3, l1)
> chk(L2, L1)
> chk(L3, L1)
> 
> ### weighted observations (2) via weights
> m1 <- Lm(X1 ~ 1, data = d, weights = w)
> m2 <- Lm(X2 ~ 1, data = d, weights = w)
> m3 <- Lm(X3 ~ 1, data = d, weights = w)
> m4 <- Polr(x ~ 1, data = d, method = "probit", weights = w)
> 
> m <- mmlt(m1, m2, m4, data = d, optim = op)
> l1w <- logLik(m)
> l1wa <- logLik(m, newdata = d[idx,], w = w[idx]) + 
+         logLik(m, newdata = d[-idx,], w = w[-idx])
> s1 <- -colSums(estfun(m))
> s2 <- grad(function(parm) logLik(m, parm = parm, w = w), coef(m))
> chk(s2, unname(s1))
> L1w <- aperm(coef(m, type = "Lambda"), perm = c("X1", "X2", "x"))
> 
> m <- mmlt(m2, m1, m4, data = d, optim = op)
> l2w <- logLik(m)
> l2wa <- logLik(m, newdata = d[idx,], w = w[idx]) + 
+         logLik(m, newdata = d[-idx,], w = w[-idx])
> L2w <- aperm(coef(m, type = "Lambda"), perm = c("X1", "X2", "x"))
> 
> m <- mmlt(m4, m2, m1, data = dw, optim = op)
> l3w <- logLik(m)
> l3wa <- logLik(m, newdata = d[idx,], w = w[idx]) + 
+         logLik(m, newdata = d[-idx,], w = w[-idx])
> L3w <- aperm(coef(m, type = "Lambda"), perm = c("X1", "X2", "x"))
> 
> ## check if order matters
> chk(l2w, l1w)
> chk(l3w, l1w)
> chk(L2w, L1w)
> chk(L3w, L1w)
> 
> ## check if weights and expanded data give the same results
> chk(l1w, l1wa)
> chk(l2w, l2wa)
> chk(l3w, l3wa)
> chk(l1w, l1)
> chk(l2w, l2)
> chk(l3w, l3)
> chk(L1w, L1)
> chk(L2w, L2)
> chk(L3w, L2)
> 
> ### continuous and some right-censored observations
> ### with expanded data
> m1 <- Lm(X1 ~ 1, data = dw)
> m2 <- Lm(X2 ~ 1, data = dw)
> m3 <- Lm(X3 ~ 1, data = dw)
> m4 <- Polr(x ~ 1, data = dw, method = "probit")
> 
> m <- mmlt(m1, m2, m3, data = dw, optim = op)
> l1 <- logLik(m)
> s1 <- -colSums(estfun(m))
> s2 <- grad(function(parm) logLik(m, parm = parm), coef(m))
> chk(s2, unname(s1))
> L1 <- aperm(coef(m, type = "Lambda"), perm = c("X1", "X2", "X3"))
> 
> m <- mmlt(m2, m1, m3, data = dw, optim = op)
> l2 <- logLik(m)
> L2 <- aperm(coef(m, type = "Lambda"), perm = c("X1", "X2", "X3"))
> 
> m <- mmlt(m3, m2, m1, data = dw, optim = op)
> l3 <- logLik(m)
> L3 <- aperm(coef(m, type = "Lambda"), perm = c("X1", "X2", "X3"))
> ## check if order matters
> chk(l2, l1)
> chk(l3, l1)
> chk(L2, L1)
> chk(L3, L1)
> 
> ### continuous and some right-censored with weights
> m1 <- Lm(X1 ~ 1, data = d, weights = w)
> m2 <- Lm(X2 ~ 1, data = d, weights = w)
> m3 <- Lm(X3 ~ 1, data = d, weights = w)
> m4 <- Polr(x ~ 1, data = d, method = "probit", weights = w)
> 
> m <- mmlt(m1, m2, m3, data = d, optim = op)
> l1w <- logLik(m)
> s1 <- -colSums(estfun(m))
> s2 <- grad(function(parm) logLik(m, parm = parm, w = w), coef(m))
> chk(s2, unname(s1))
> L1w <- aperm(coef(m, type = "Lambda"), perm = c("X1", "X2", "X3"))
> 
> m <- mmlt(m2, m1, m3, data = d, optim = op)
> l2w <- logLik(m)
> L2w <- aperm(coef(m, type = "Lambda"), perm = c("X1", "X2", "X3"))
> 
> m <- mmlt(m3, m2, m1, data = d, optim = op)
> l3w <- logLik(m)
> L3w <- aperm(coef(m, type = "Lambda"), perm = c("X1", "X2", "X3"))
> 
> ## check if order matters
> chk(l2w, l1w)
> chk(l3w, l1w)
> chk(L2w, L1w)
> chk(L3w, L1w)
> 
> ## check if weights and expanded data give the same results
> chk(l1w, l1)
> chk(l2w, l2)
> chk(l3w, l3)
> chk(L1w, L1)
> chk(L2w, L2)
> chk(L3w, L2)
> 
> ### simulation from fitted / unfitted models
> data("iris")
> 
> m1 <- BoxCox(Sepal.Length ~ Species, data = iris)
> m2 <- BoxCox(Petal.Length ~ Species, data = iris)
> 
> ### fit model
> m <- mmlt(m1, m2, data = iris)
> cf <- coef(m)
> 
> ### resample data
> s1 <- as.data.frame(simulate(m, newdata = iris, seed = 290875))
> 
> ### change coeffcient (to zero correlation)
> cf[length(cf)] <- 0
> coef(m) <- cf
> 
> s2 <- as.data.frame(simulate(m, newdata = iris, seed = 290875))
> 
> ### expect _different_ results
> stopifnot(!isTRUE(all.equal(s1, s2)))
> 
> ### set-up model shell
> m0 <- mmlt(m1, m2, data = iris, theta = cf, dofit = FALSE)
> 
> s3 <- as.data.frame(simulate(m, newdata = iris, seed = 290875))
> ### these are identical
> chk(s2, s3)
> 
> proc.time()
   user  system elapsed 
  22.15    0.46   22.60