R Under development (unstable) (2023-12-17 r85691 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
> options(digits = 1) ## make M1 happy
> 
> ## dgp
> set.seed(29)
> N <- 1000
> x <- runif(N)
> y <- rchisq(N, df = 4)
> d <- data.frame(y = y, x = x, one = 1)
> 
> d$xx <- d$x - 5 ## shift x
> 
> 
> ## no h-intercept; additional mu-intercept
> m0 <- Survreg(y ~ x | x, data = d, remove_intercept = FALSE)
> coef(as.mlt(m0))
     log(y) (Intercept)           x       scl_x 
       1.52        2.38       -0.10       -0.04 
> sqrt(diag(vcov(m0)))
(Intercept)           x       scl_x 
        0.1         0.2         0.2 
> 
> m1 <- Survreg(y ~ xx | x, data = d, remove_intercept = FALSE)
> coef(as.mlt(m1))
     log(y) (Intercept)          xx       scl_x 
       1.52        1.86       -0.10       -0.04 
> sqrt(diag(vcov(m1)))
(Intercept)          xx       scl_x 
        1.1         0.2         0.2 
> 
> m2 <- Survreg(y ~ xx | xx, data = d, remove_intercept = FALSE)
> coef(as.mlt(m2))
     log(y) (Intercept)          xx      scl_xx 
       1.38        1.86       -0.10       -0.04 
> sqrt(diag(vcov(m2)))
(Intercept)          xx      scl_xx 
        1.1         0.2         0.2 
> 
> 
> ## h-intercept; scale_shift
> m0 <- Survreg(y ~ x | x, data = d, scale_shift = TRUE)
> coef(as.mlt(m0))
(Intercept)      log(y)           x       scl_x 
      -2.38        1.52       -0.06       -0.04 
> sqrt(diag(vcov(m0)))
    x scl_x 
  0.1   0.2 
> 
> m1 <- Survreg(y ~ xx | x, data = d, scale_shift = TRUE)
> coef(as.mlt(m1))
(Intercept)      log(y)          xx       scl_x 
      -2.08        1.52       -0.06       -0.04 
> sqrt(diag(vcov(m1)))
   xx scl_x 
  0.1   0.2 
> 
> m2 <- Survreg(y ~ xx | xx, data = d, scale_shift = TRUE)
> coef(as.mlt(m2))
(Intercept)      log(y)          xx      scl_xx 
      -1.88        1.38       -0.06       -0.04 
> sqrt(diag(vcov(m2)))
    xx scl_xx 
   0.1    0.2 
> 
> OR <- 1
> 
> d$ly <- log(y)
> 
> ## no h-intercept; additional mu-intercept
> m0 <- Coxph(ly ~ x | x, data = d, log_first = FALSE, order = OR, remove_intercept = FALSE)
Warning message:
In c.basis(bresponse = function (data, deriv = 0L, integrate = FALSE)  :
  more than one basis contains an intercept term
> coef(as.mlt(m0))
    Bs1(ly) (Intercept)           x       scl_x 
      -1.47       -0.68        0.07       -0.04 
> sqrt(diag(vcov(m0)))
(Intercept)           x       scl_x 
       0.08        0.14        0.16 
> 
> m1 <- Coxph(ly ~ xx | x, data = d, log_first = FALSE, order = OR, remove_intercept = FALSE)
Warning message:
In c.basis(bresponse = function (data, deriv = 0L, integrate = FALSE)  :
  more than one basis contains an intercept term
> coef(as.mlt(m1))
    Bs1(ly) (Intercept)          xx       scl_x 
      -1.47       -0.31        0.07       -0.04 
> sqrt(diag(vcov(m1)))
(Intercept)          xx       scl_x 
        0.6         0.1         0.2 
> 
> m2 <- Coxph(ly ~ xx | xx, data = d, log_first = FALSE, order = OR, remove_intercept = FALSE)
Warning message:
In c.basis(bresponse = function (data, deriv = 0L, integrate = FALSE)  :
  more than one basis contains an intercept term
> coef(as.mlt(m2))
    Bs1(ly) (Intercept)          xx      scl_xx 
      -1.34       -0.32        0.07       -0.04 
> sqrt(diag(vcov(m2)))
(Intercept)          xx      scl_xx 
        0.6         0.1         0.2 
> 
> OR <- 1
> 
> ## h-intercept; scale_shift
> m0 <- Coxph(y ~ x | x, data = d, scale_shift = TRUE, log_first = TRUE, order = OR)
> coef(as.mlt(m0))
Bs1(y) Bs2(y)      x  scl_x 
 -2.15   0.79   0.06  -0.04 
> sqrt(diag(vcov(m0)))
    x scl_x 
  0.1   0.2 
> 
> m1 <- Coxph(y ~ xx | x, data = d, scale_shift = TRUE, log_first = TRUE, order = OR)
> coef(as.mlt(m1))
Bs1(y) Bs2(y)     xx  scl_x 
 -1.84   1.10   0.06  -0.04 
> sqrt(diag(vcov(m1)))
   xx scl_x 
  0.1   0.2 
> 
> m2 <- Coxph(y ~ xx | xx, data = d, scale_shift = TRUE, log_first = TRUE, order = OR)
> coef(as.mlt(m2))
Bs1(y) Bs2(y)     xx scl_xx 
 -1.68   1.00   0.05  -0.04 
> sqrt(diag(vcov(m2)))
    xx scl_xx 
   0.1    0.2 
> 
> 
> proc.time()
   user  system elapsed 
    3.4     0.5     3.9