R version 4.6.0 beta (2026-04-12 r89874 ucrt) -- "Because it was There"
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> 
> library("mvtnorm")
> 
> options(digits = 4)
> 
> J <- 5
> 
> set.seed(290875)
> 
> lxd <- ltMatrices(runif(J * (J + 1) / 2) + 1, diag = TRUE, names = LETTERS[seq_len(J)])
> m <- matrix(1:J, ncol = 1)
> d <- Mult(lxd, m)
> 
> d0 <- mvnorm(invchol = lxd)
> Y <- as.data.frame(t(simulate(d0, nsim = 1e6, seed = 29)))
> mlm <- lm(D ~ 0 + A + B + C, data = Y)
> (cf <- coef(d0, which = "D"))
     A      B      C 
-1.265 -1.178 -1.687 
attr(,"sigma")
     D 
0.9072 
> coef(mlm)
     A      B      C 
-1.263 -1.176 -1.684 
> summary(mlm)$sigma
[1] 0.9062
> md <- margDist(d0, which = 1:4)
> cd <- condDist(md, which_given = 1:3, given = diag(3))
> class(cd$scale)
[1] "invchol"    "ltMatrices" "matrix"     "array"     
> coef(cd)
    [,1]   [,2]   [,3]
D -1.265 -1.178 -1.687
attr(,"sigma")
[1] 0.9072
> 
> d0 <- mvnorm(chol = solve(lxd))
> Y <- as.data.frame(t(simulate(d0, nsim = 1e6, seed = 29)))
> mlm <- lm(D ~ 0 + A + B + C, data = Y)
> (cf <- coef(d0, which = "D"))
     A      B      C 
-1.265 -1.178 -1.687 
attr(,"sigma")
     D 
0.9072 
> coef(mlm)
     A      B      C 
-1.263 -1.176 -1.684 
> summary(mlm)$sigma
[1] 0.9062
> md <- margDist(d0, which = 1:4)
> cd <- condDist(md, which_given = 1:3, given = diag(3))
> coef(cd)
    [,1]   [,2]   [,3]
D -1.265 -1.178 -1.687
attr(,"sigma")
[1] 0.9072
> 
> (d1 <- mvnorm(invchol = lxd, mean = m))
$scale
, , 1

      A     B     C     D     E
A 1.512     .     .     .     .
B 1.058 1.234     .     .     .
C 1.910 1.516 1.818     .     .
D 1.394 1.298 1.859 1.102     .
E 1.661 1.075 1.374 1.117 1.796


$mean
  [,1]
A    1
B    2
C    3
D    4
E    5

attr(,"class")
[1] "mvnorm"
> Y <- as.data.frame(t(simulate(d1, nsim = 1e6, seed = 29)))
> mlm <- lm(D ~ A + B + C, data = Y)
> (cf <- coef(d1, which = "D"))
(Intercept)           A           B           C 
     12.680      -1.265      -1.178      -1.687 
attr(,"sigma")
     D 
0.9072 
> coef(mlm)
(Intercept)           A           B           C 
     12.666      -1.263      -1.176      -1.684 
> summary(mlm)$sigma
[1] 0.9062
> md <- margDist(d1, which = 1:4)
> 
> cd <- condDist(md, which_given = 1:3, given = diag(3))
> class(cd$scale)
[1] "invchol"    "ltMatrices" "matrix"     "array"     
> coef(cd)
   [,1] [,2]  [,3]
D 11.41 11.5 10.99
attr(,"sigma")
[1] 0.9072
> cf[1] + cf[-1]
    A     B     C 
11.41 11.50 10.99 
> 
> d2 <- mvnorm(invchol = lxd, invcholmean = d)
> Y <- as.data.frame(t(simulate(d2, nsim = 1e6, seed = 29)))
> mlm <- lm(D ~ A + B + C, data = Y)
> coef(d2, which = "D")
(Intercept)           A           B           C 
     12.680      -1.265      -1.178      -1.687 
attr(,"sigma")
     D 
0.9072 
> coef(mlm)
(Intercept)           A           B           C 
     12.666      -1.263      -1.176      -1.684 
> summary(mlm)$sigma
[1] 0.9062
> coef(condDist(margDist(d2, which = 1:4), which_given = 1:3, given = diag(3)))
   [,1] [,2]  [,3]
D 11.41 11.5 10.99
attr(,"sigma")
[1] 0.9072
> cf[1] + cf[-1]
    A     B     C 
11.41 11.50 10.99 
> 
> d3 <- mvnorm(chol = solve(lxd), invcholmean = d)
> Y <- as.data.frame(t(simulate(d3, nsim = 1e6, seed = 29)))
> mlm <- lm(D ~ A + B + C, data = Y)
> coef(d3, which = "D")
(Intercept)           A           B           C 
     12.680      -1.265      -1.178      -1.687 
attr(,"sigma")
     D 
0.9072 
> coef(mlm)
(Intercept)           A           B           C 
     12.666      -1.263      -1.176      -1.684 
> summary(mlm)$sigma
[1] 0.9062
> coef(condDist(margDist(d3, which = 1:4), which_given = 1:3, given = diag(3)))
   [,1] [,2]  [,3]
D 11.41 11.5 10.99
attr(,"sigma")
[1] 0.9072
> cf[1] + cf[-1]
    A     B     C 
11.41 11.50 10.99 
> 
> d4 <- mvnorm(chol = solve(lxd), mean = m)
> Y <- as.data.frame(t(simulate(d4, nsim = 1e6, seed = 29)))
> mlm <- lm(D ~ A + B + C, data = Y)
> coef(d4, which = "D")
(Intercept)           A           B           C 
     12.680      -1.265      -1.178      -1.687 
attr(,"sigma")
     D 
0.9072 
> coef(mlm)
(Intercept)           A           B           C 
     12.666      -1.263      -1.176      -1.684 
> summary(mlm)$sigma
[1] 0.9062
> coef(condDist(margDist(d4, which = 1:4), which_given = 1:3, given = diag(3)))
   [,1] [,2]  [,3]
D 11.41 11.5 10.99
attr(,"sigma")
[1] 0.9072
> cf[1] + cf[-1]
    A     B     C 
11.41 11.50 10.99 
> 
> 
> proc.time()
   user  system elapsed 
   8.75    2.14   10.86