R Under development (unstable) (2025-11-17 r89032 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("multcomp")
Loading required package: survival
Loading required package: TH.data
Loading required package: MASS

Attaching package: 'TH.data'

The following object is masked from 'package:MASS':

    geyser

> 
> m <- BoxCox(dist ~ speed, data = cars)
> m$negative
[1] TRUE
> coef(m)
    speed 
0.3059938 
> nd <- data.frame(speed = as.double(1:5 * 5))
> 
> PI(m, newdata = nd)
          [,1]      [,2]      [,3]      [,4] [,5]
[1,] 0.8603407 0.9847564 0.9994139 0.9999925    1
> lp15 <- c(predict(m, newdata = data.frame(speed = 15)))
> PI(m, newdata = nd, reference = lp15)
           [,1]      [,2] [,3]      [,4]      [,5]
[1,] 0.01524358 0.1396593  0.5 0.8603407 0.9847564
> PI(m, newdata = nd, reference = nd[3,,drop = FALSE])
           [,1]      [,2] [,3]      [,4]      [,5]
[1,] 0.01524358 0.1396593  0.5 0.8603407 0.9847564
> PI(m, newdata = nd, reference = nd)
          1         2         3         4
2 0.8603407                              
3 0.9847564 0.8603407                    
4 0.9994139 0.9847564 0.8603407          
5 0.9999925 0.9994139 0.9847564 0.8603407
> 
> F <- m$model$todistr$p
> Q <- m$model$todistr$q
> f <- function(p, b) F(Q(p) - b)
> lp <- predict(m, newdata = nd, type = "lp")
> integrate(f, lower = 0, upper = 1, b = lp[2] - lp[1])
0.1396592 with absolute error < 0.00012
> 
> OVL(m, newdata = nd)
          [,1]      [,2]       [,3]        [,4]         [,5]
[1,] 0.4442808 0.1260244 0.02173579 0.002213829 0.0001308133
> lp15 <- c(predict(m, newdata = data.frame(speed = 15)))
> OVL(m, newdata = nd, reference = lp15)
          [,1]      [,2] [,3]      [,4]      [,5]
[1,] 0.1260244 0.4442808    1 0.4442808 0.1260244
> OVL(m, newdata = nd, reference = nd[3,,drop = FALSE])
          [,1]      [,2] [,3]      [,4]      [,5]
[1,] 0.1260244 0.4442808    1 0.4442808 0.1260244
> OVL(m, newdata = nd, reference = nd)
            1           2           3           4
2 0.444280785                                    
3 0.126024411 0.444280785                        
4 0.021735792 0.126024411 0.444280785            
5 0.002213829 0.021735792 0.126024411 0.444280785
> 
> d <- m$model$todistr$d
> Q <- m$model$todistr$q
> f <- function(p, b) pmin(1, d(Q(p) - b) / d(Q(p)))
> lp <- predict(m, newdata = nd, type = "lp")
> integrate(f, lower = 0, upper = 1, b = lp[2] - lp[1])
0.4442814 with absolute error < 8.4e-05
> 
> m <- Colr(dist ~ speed, data = cars)
> m$negative
[1] FALSE
> coef(m)
     speed 
-0.5297381 
> nd <- data.frame(speed = as.double(1:5 * 5))
> 
> PI(m, newdata = nd)
         [,1]      [,2]      [,3]      [,4]      [,5]
[1,] 0.859135 0.9782508 0.9975389 0.9997597 0.9999783
> lp15 <- c(predict(m, newdata = data.frame(speed = 15)))
> PI(m, newdata = nd, reference = lp15)
           [,1]     [,2] [,3]     [,4]      [,5]
[1,] 0.02174923 0.140865  0.5 0.859135 0.9782508
> PI(m, newdata = nd, reference = nd[3,,drop = FALSE])
           [,1]     [,2] [,3]     [,4]      [,5]
[1,] 0.02174923 0.140865  0.5 0.859135 0.9782508
> PI(m, newdata = nd, reference = nd)
          1         2         3         4
2 0.8591350                              
3 0.9782508 0.8591350                    
4 0.9975389 0.9782508 0.8591350          
5 0.9997597 0.9975389 0.9782508 0.8591350
> 
> F <- m$model$todistr$p
> Q <- m$model$todistr$q
> f <- function(p, b) F(Q(p) + b)
> lp <- predict(m, newdata = nd, type = "lp")
> integrate(f, lower = 0, upper = 1, b = lp[2] - lp[1])
0.140865 with absolute error < 9.4e-05
> 
> 
> OVL(m, newdata = nd)
          [,1]      [,2]       [,3]        [,4]        [,5]
[1,] 0.4201925 0.1321395 0.03693743 0.009959524 0.002658723
> lp15 <- c(predict(m, newdata = data.frame(speed = 15)))
> OVL(m, newdata = nd, reference = lp15)
          [,1]      [,2] [,3]      [,4]      [,5]
[1,] 0.1321395 0.4201925    1 0.4201925 0.1321395
> OVL(m, newdata = nd, reference = nd[3,,drop = FALSE])
          [,1]      [,2] [,3]      [,4]      [,5]
[1,] 0.1321395 0.4201925    1 0.4201925 0.1321395
> OVL(m, newdata = nd, reference = nd)
            1           2           3           4
2 0.420192533                                    
3 0.132139533 0.420192533                        
4 0.036937428 0.132139533 0.420192533            
5 0.009959524 0.036937428 0.132139533 0.420192533
> 
> d <- m$model$todistr$d
> Q <- m$model$todistr$q
> f <- function(p, b) pmin(1, d(Q(p) + b) / d(Q(p)))
> lp <- predict(m, newdata = nd, type = "lp")
> integrate(f, lower = 0, upper = 1, b = lp[2] - lp[1])
0.4201909 with absolute error < 8.9e-05
> 
> 
> m <- Coxph(dist ~ speed, data = cars)
> m$negative
[1] FALSE
> coef(m)
     speed 
-0.2781254 
> nd <- data.frame(speed = as.double(1:5 * 5))
> 
> PI(m, newdata = nd)
          [,1]      [,2]     [,3]      [,4]      [,5]
[1,] 0.8006923 0.9416544 0.984811 0.9961755 0.9990453
> lp15 <- c(predict(m, newdata = data.frame(speed = 15)))
> PI(m, newdata = nd, reference = lp15)
           [,1]      [,2] [,3]      [,4]      [,5]
[1,] 0.05834563 0.1993077  0.5 0.8006923 0.9416544
> PI(m, newdata = nd, reference = nd[3,,drop = FALSE])
           [,1]      [,2] [,3]      [,4]      [,5]
[1,] 0.05834563 0.1993077  0.5 0.8006923 0.9416544
> PI(m, newdata = nd, reference = nd)
          1         2         3         4
2 0.8006923                              
3 0.9416544 0.8006923                    
4 0.9848110 0.9416544 0.8006923          
5 0.9961755 0.9848110 0.9416544 0.8006923
> 
> F <- m$model$todistr$p
> Q <- m$model$todistr$q
> f <- function(p, b) F(Q(p) + b)
> lp <- predict(m, newdata = nd, type = "lp")
> integrate(f, lower = 0, upper = 1, b = lp[2] - lp[1])
0.1993077 with absolute error < 2.2e-16
> 
> 
> OVL(m, newdata = nd)
          [,1]      [,2]       [,3]       [,4]        [,5]
[1,] 0.5262693 0.2193864 0.07770965 0.02496709 0.007578244
> lp15 <- c(predict(m, newdata = data.frame(speed = 15)))
> OVL(m, newdata = nd, reference = lp15)
          [,1]      [,2] [,3]      [,4]      [,5]
[1,] 0.2193864 0.5262693    1 0.5262693 0.2193864
> OVL(m, newdata = nd, reference = nd[3,,drop = FALSE])
          [,1]      [,2] [,3]      [,4]      [,5]
[1,] 0.2193864 0.5262693    1 0.5262693 0.2193864
> OVL(m, newdata = nd, reference = nd)
           1          2          3          4
2 0.52626927                                 
3 0.21938642 0.52626927                      
4 0.07770965 0.21938642 0.52626927           
5 0.02496709 0.07770965 0.21938642 0.52626927
> 
> d <- m$model$todistr$d
> Q <- m$model$todistr$q
> f <- function(p, b) pmin(1, d(Q(p) + b) / d(Q(p)))
> lp <- predict(m, newdata = nd, type = "lp")
> integrate(f, lower = 0, upper = 1, b = lp[2] - lp[1])
0.5262692 with absolute error < 1.3e-05
> 
> 
> m <- Lehmann(dist ~ speed, data = cars)
> m$negative
[1] TRUE
> coef(m)
    speed 
0.3486759 
> nd <- data.frame(speed = as.double(1:5 * 5))
> 
> PI(m, newdata = nd)
          [,1]      [,2]      [,3]      [,4]      [,5]
[1,] 0.8511158 0.9703087 0.9946757 0.9990645 0.9998362
> lp15 <- c(predict(m, newdata = data.frame(speed = 15)))
> PI(m, newdata = nd, reference = lp15)
           [,1]      [,2] [,3]      [,4]      [,5]
[1,] 0.02969132 0.1488842  0.5 0.8511158 0.9703087
> PI(m, newdata = nd, reference = nd[3,,drop = FALSE])
           [,1]      [,2] [,3]      [,4]      [,5]
[1,] 0.02969132 0.1488842  0.5 0.8511158 0.9703087
> PI(m, newdata = nd, reference = nd)
          1         2         3         4
2 0.8511158                              
3 0.9703087 0.8511158                    
4 0.9946757 0.9703087 0.8511158          
5 0.9990645 0.9946757 0.9703087 0.8511158
> 
> F <- m$model$todistr$p
> Q <- m$model$todistr$q
> f <- function(p, b) F(Q(p) - b)
> lp <- predict(m, newdata = nd, type = "lp")
> integrate(f, lower = 0, upper = 1, b = lp[2] - lp[1])
0.1488842 with absolute error < 5.7e-15
> 
> 
> OVL(m, newdata = nd)
          [,1]      [,2]       [,3]        [,4]        [,5]
[1,] 0.4298802 0.1316324 0.03295825 0.007444731 0.001590555
> lp15 <- c(predict(m, newdata = data.frame(speed = 15)))
> OVL(m, newdata = nd, reference = lp15)
          [,1]      [,2] [,3]      [,4]      [,5]
[1,] 0.1316324 0.4298802    1 0.4298802 0.1316324
> OVL(m, newdata = nd, reference = nd[3,,drop = FALSE])
          [,1]      [,2] [,3]      [,4]      [,5]
[1,] 0.1316324 0.4298802    1 0.4298802 0.1316324
> OVL(m, newdata = nd, reference = nd)
            1           2           3           4
2 0.429880208                                    
3 0.131632372 0.429880208                        
4 0.032958249 0.131632372 0.429880208            
5 0.007444731 0.032958249 0.131632372 0.429880208
> 
> d <- m$model$todistr$d
> Q <- m$model$todistr$q
> f <- function(p, b) pmin(1, d(Q(p) - b) / d(Q(p)))
> lp <- predict(m, newdata = nd, type = "lp")
> integrate(f, lower = 0, upper = 1, b = lp[2] - lp[1])
0.4298796 with absolute error < 8e-05
> 
> OVL(m, newdata = nd)
          [,1]      [,2]       [,3]        [,4]        [,5]
[1,] 0.4298802 0.1316324 0.03295825 0.007444731 0.001590555
> OVL(m, newdata = nd, conf.level = .95)
     Estimate          lwr        upr
1 0.429880208 0.3195347036 0.56348429
2 0.131632372 0.0626460732 0.26059831
3 0.032958249 0.0097367882 0.10414840
4 0.007444731 0.0013661293 0.03792029
5 0.001590555 0.0001815124 0.01304557
attr(,"conf.level")
[1] 0.95
attr(,"calpha")
[1] 1.960371
> 
> lp15 <- c(predict(m, newdata = data.frame(speed = 15)))
> OVL(m, newdata = nd, reference = lp15)
          [,1]      [,2] [,3]      [,4]      [,5]
[1,] 0.1316324 0.4298802    1 0.4298802 0.1316324
> OVL(m, newdata = nd, reference = lp15, conf.level = .95)
      Estimate          lwr        upr
1 0.1239285626 5.770966e-02 0.25051630
2 0.0308307221 8.910322e-03 0.09958496
3 0.0069411137 1.246156e-03 0.03614028
4 0.0014800955 1.652543e-04 0.01240826
5 0.0003051263 2.118117e-05 0.00411399
attr(,"conf.level")
[1] 0.95
attr(,"calpha")
[1] 1.960371
> 
> OVL(m, newdata = nd[-3,,drop = FALSE], reference = nd[3,,drop = FALSE])
          [,1]      [,2]      [,3]      [,4]
[1,] 0.1316324 0.4298802 0.4298802 0.1316324
> OVL(m, newdata = nd[-3,,drop = FALSE], reference = nd[3,,drop = FALSE], conf.level = .95)
     Estimate        lwr       upr
3-1 0.1316324 0.06264718 0.2605944
3-2 0.4298802 0.31953697 0.5634810
3-4 0.4298802 0.31953697 0.5634810
3-5 0.1316324 0.06264718 0.2605944
attr(,"conf.level")
[1] 0.95
attr(,"calpha")
[1] 1.960326
> 
> OVL(m, newdata = nd, reference = nd)
            1           2           3           4
2 0.429880208                                    
3 0.131632372 0.429880208                        
4 0.032958249 0.131632372 0.429880208            
5 0.007444731 0.032958249 0.131632372 0.429880208
> OVL(m, newdata = nd, reference = nd, conf.level = .95)
       Estimate         lwr        upr
1-2 0.429880208 0.319535191 0.56348358
1-3 0.131632372 0.062646310 0.26059748
2-3 0.429880208 0.319535191 0.56348358
1-4 0.032958249 0.009736848 0.10414784
2-4 0.131632372 0.062646310 0.26059748
3-4 0.429880208 0.319535191 0.56348358
1-5 0.007444731 0.001366141 0.03791999
2-5 0.032958249 0.009736848 0.10414784
3-5 0.131632372 0.062646310 0.26059748
4-5 0.429880208 0.319535191 0.56348358
attr(,"conf.level")
[1] 0.95
attr(,"calpha")
[1] 1.960362
> 
> OVL(m, newdata = nd, reference = nd, conf.level = .95, 
+     calpha = univariate_calpha())
       Estimate         lwr        upr
1-2 0.429880208 0.319555197 0.56345424
1-3 0.131632372 0.062656040 0.26056336
2-3 0.429880208 0.319555197 0.56345424
1-4 0.032958249 0.009739304 0.10412457
2-4 0.131632372 0.062656040 0.26056336
3-4 0.429880208 0.319555197 0.56345424
1-5 0.007444731 0.001366617 0.03790786
2-5 0.032958249 0.009739304 0.10412457
3-5 0.131632372 0.062656040 0.26056336
4-5 0.429880208 0.319555197 0.56345424
attr(,"conf.level")
[1] 0.95
attr(,"calpha")
[1] 1.959964
> OVL(m, newdata = nd, reference = nd, conf.level = .95, 
+     calpha = adjusted_calpha())
       Estimate         lwr        upr
1-2 0.429880208 0.319535191 0.56348358
1-3 0.131632372 0.062646310 0.26059748
2-3 0.429880208 0.319535191 0.56348358
1-4 0.032958249 0.009736848 0.10414784
2-4 0.131632372 0.062646310 0.26059748
3-4 0.429880208 0.319535191 0.56348358
1-5 0.007444731 0.001366141 0.03791999
2-5 0.032958249 0.009736848 0.10414784
3-5 0.131632372 0.062646310 0.26059748
4-5 0.429880208 0.319535191 0.56348358
attr(,"conf.level")
[1] 0.95
attr(,"calpha")
[1] 1.960362
> 
> proc.time()
   user  system elapsed 
   1.68    0.25    1.92