partykit minsize option drops branches that exceed minsize

Question

I'm using the lmtree() function from partykit to partition data using linear regressions. The regressions use a weight, and I want to ensure that each branch has a minimum total weight, which I specify with the minsize option. For instance, in the following example the tree only has two branches instead of three because x1=="C" has too small a weight to be in its own branch.

n <- 100
X <- rbind(
  data.frame(TT=1:n, x1="A", weight=2, y=seq(1,l=n,by=0.2)+rnorm(n,sd=.2)),
  data.frame(TT=1:n, x1="B", weight=2, y=seq(1,l=n,by=0.4)+rnorm(n,sd=.2)),
  data.frame(TT=1:n, x1="C", weight=1, y=seq(1,l=n,by=0.6)+rnorm(n,sd=.2))
)
X$x1 <- factor(X$x1)
tr <- lmtree(y ~ TT | x1, data=X, weight=weight, minsize=150)

Fitted party:
[1] root
|   [2] x1 in A: n = 200
|       (Intercept)          TT 
|         0.7724903   0.2002023 
|   [3] x1 in B, C: n = 300
|       (Intercept)          TT 
|         0.5759213   0.4659592

I also have some real-world data that unfortunately is confidential but is leading to some behavior that I do not understand. When I do not specify minsize it builds a tree with 30 branches, where in every branch the total weight n is a large number. However, when I specify a minsize that is well below the total weight of every branch from this first tree the result is a new tree with many fewer branches. I would not have expected the tree to change at all because it seems that minsize is not binding. Is there any explanation for this result?

UPDATE

Providing an example

n <- 100
X <- rbind(
  data.frame(TT=1:n, x1=runif(n, 0.0, 0.3), weight=2, y=seq(1,l=n,by=0.2)+rnorm(n,sd=.2)),
  data.frame(TT=1:n, x1=runif(n, 0.3, 0.7), weight=2, y=seq(1,l=n,by=0.4)+rnorm(n,sd=.2)),
  data.frame(TT=1:n, x1=runif(n, 0.7, 1.0), weight=1, y=seq(1,l=n,by=0.6)+rnorm(n,sd=.2))
)
tr <- lmtree(y ~ TT | x1, data=X, weights = weight)

Fitted party:
[1] root
|   [2] x1 <= 0.29787: n = 200
|       (Intercept)          TT 
|         0.8431985   0.1994021 
|   [3] x1 > 0.29787
|   |   [4] x1 <= 0.69515: n = 200
|   |       (Intercept)          TT 
|   |         0.6346980   0.3995678 
|   |   [5] x1 > 0.69515: n = 100
|   |       (Intercept)          TT 
|   |         0.4792462   0.5987472

Now let's set minsize=150. The tree no longer has any splits even though x1 <= 0.3 and x1 > 0.3 would work.

tr <- lmtree(y ~ TT | x1, data=X, weights = weight, minsize=150)

Fitted party:
[1] root: n = 500
    (Intercept)          TT 
      0.6870078   0.3593374

partykit minsize option drops branches that exceed minsize

1 Answers