R Under development (unstable) (2023-08-20 r84995 ucrt) -- "Unsuffered Consequences"
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> 
> library("mlt")
Loading required package: basefun
Loading required package: variables
> set.seed(29)
> 
> n <- 100
> p <- 2
> x <- matrix(runif(n * p), nrow = n)
> beta <- c(1, -1)
> y <- factor(rbinom(n, size = 1, prob = plogis(x %*% beta)))
> df <- data.frame(y = y, x)
> 
> m1 <- glm(y ~ X1 + X2, data = df, family = binomial())
> coef(m1)
(Intercept)          X1          X2 
  0.7372381  -0.3848546  -0.8292045 
> 
> m <- ctm(~ y, shift = ~ X1 + X2, todist = "Logis", data = df)
> m2 <- mlt(m, data = df, fixed = c("y1" = 0))
Warning message:
In R.factor(object = data[[response]]) : response is unordered factor;
             results may depend on order of levels
> coef(m2)
(Intercept)          y1          X1          X2 
 -0.7372250   0.0000000   0.3848409   0.8291921 
> 
> max(abs(coef(m1) + coef(m2)[-2]))
[1] 1.363248e-05
> 
> logLik(m1)
'log Lik.' -68.12815 (df=3)
> logLik(m2)
'log Lik.' -68.12815 (df=3)
> 
> ### compare multinomial models; iris was not good because
> ### of complete separation
> library("nnet")
> 
> n <- 5000
> p <- 1
> x <- as.data.frame(matrix(runif(n * p), nrow = n))
> x$y <- cut(x$V1, breaks = c(0, .25, .5, .75, 1))
> x$V1 <- x$V1 + rnorm(n, sd = .1)
> x$V1 <- x$V1 - min(x$V1)
> 
> m1 <- multinom(y ~ ., data = x)
# weights:  12 (6 variable)
initial  value 6931.471806 
iter  10 value 3015.580388
iter  20 value 2550.483531
final  value 2550.158016 
converged
> coef(m1)
           (Intercept)       V1
(0.25,0.5]   -9.305578 17.19805
(0.5,0.75]  -23.879104 35.48939
(0.75,1]    -40.319032 51.31745
> logLik(m1)
'log Lik.' -2550.158 (df=6)
> 
> ox <- x
> ox$y <- ordered(ox$y)
> 
> r <- as.basis(ox$y)
> 
> fm <- as.formula(paste("~ ", paste(names(x)[grep("^V", names(x))], collapse = "+")))
> ### don't scale, otherwise comparison with glm() is impossible
> m <- ctm(r, interacting = as.basis(fm, data = ox, scale = FALSE),
+            todistr = "Logis")
Warning message:
In model.matrix.box_bases(object = list(iresponse = function (data,  :
  use scale = TRUE in as.basis.formula with sumcontr = TRUE
> m2 <- mlt(m, data = ox, scale = TRUE)
Warning messages:
1: In model.matrix.box_bases(object = list(iresponse = function (data,  :
  use scale = TRUE in as.basis.formula with sumcontr = TRUE
2: In model.matrix.box_bases(object = list(iresponse = function (data,  :
  use scale = TRUE in as.basis.formula with sumcontr = TRUE
3: In model.matrix.box_bases(object = list(iresponse = function (data,  :
  use scale = TRUE in as.basis.formula with sumcontr = TRUE
4: In model.matrix.box_bases(object = list(iresponse = function (data,  :
  use scale = TRUE in as.basis.formula with sumcontr = TRUE
> ### fix of PR#17616, affects basefun
> unname(coef(m2))
[1]   9.642082  15.583592  17.447408 -17.893593 -19.588233 -16.747988
> logLik(m2)
'log Lik.' -2556.062 (df=6)
> 
> s <- sort(unique(ox$y))
> 
> pp2 <- predict(m2, newdata = ox, q = s, type = "density")
> 
> pp1 <- predict(m1, newdata = x, type = "prob")
> 
> max(abs(pp1 - t(pp2)))
[1] 0.01437037
> 
> cf1 <- coef(glm(I(y %in% levels(y)[1]) ~ V1, data = x, family = binomial()))
> cf2 <- coef(glm(I(y %in% levels(y)[1:2]) ~ V1, data = x, family = binomial()))
> cf3 <- coef(glm(I(y %in% levels(y)[1:3]) ~ V1, data = x, family = binomial()))
> 
> logLik(m2, parm = c(rbind(cf1, cf2, cf3)))
'log Lik.' -2556.123 (df=6)
> 
> 
> proc.time()
   user  system elapsed 
   2.45    0.31    2.75