custom split rule with partykit

Question

this post follows this question : https://stackoverflow.com/questions/31234329/rpart-user-defined-implementation

I'm very interested in tools which could handle tree growing with customized criteria, such that I could test different model.

I tried to use the partykit R package to grow a tree for which the split rule is given by the negative log-likelihood of a Cox model (which is log-quasi-likelihood in case of the Cox model) and a Cox model is fitted in each leaf.

As I understood reading the vignette about the MOB function, there are two way to implement my own split criteria, namely to get the fit function return either a list or a model object.

For my purpose, I tried the two solutions but I failed to make it work.

Solution 1 : return a list object :

I take as an example the "breast cancer dataset" as in the "mob" vignette.

I tried this :

cox1 = function(y,x, start = NULL, weights = NULL, offset = NULL, ...,
           estfun = FALSE, object = TRUE){
  res_cox = coxph(formula = y ~ x )
list(
  coefficients = res_cox$coefficients,
  objfun = - res_cox$loglik[2],
  object = res_cox)
}


mob(formula = Surv(time, cens) ~ horTh + pnodes - 1 | age + tsize + tgrade + progrec +
  estrec + menostat , 
    data = GBSG2 ,
    fit = cox1,
    control = mob_control(alpha = 0.0001) )

There is a warning about the singularity of the X matrix, and the mob function a tree with a single node (even with smaller values for alpha).

Note that there is no singularity problem with the X matrix when running the coxph function :

res_cox = coxph( formula = Surv(time, cens) ~ horTh + pnodes  ,
             data = GBSG2 )

Solution 2 : Return a coxph.object :

I tried this :

cox2 = function(y,x, start = NULL, weights = NULL, offset = NULL, ... ){
  res_cox = coxph(formula = y ~ x )
}

logLik.cox2 <- function(object, ...)
  structure( - object$loglik[2], class = "logLik")

mob(formula = Surv(time, cens) ~ horTh + pnodes - 1 | age + tsize + tgrade + progrec +
  estrec + menostat , 
    data = GBSG2 ,
    fit = cox2,
    control = mob_control(alpha = 0.0001 ) )

So this time I get a split along the "progrec" variable :

Model-based recursive partitioning (cox2)

Model formula:
Surv(time, cens) ~ horTh + pnodes - 1 | age + tsize + tgrade + 
progrec + estrec + menostat

Fitted party:
[1] root
|   [2] progrec <= 21: n = 281
|         xhorThno  xhorThyes    xpnodes 
|       0.19306661         NA 0.07832756 
|   [3] progrec > 21: n = 405
|         xhorThno  xhorThyes    xpnodes 
|       0.64810352         NA 0.04482348 

Number of inner nodes:    1
Number of terminal nodes: 2
Number of parameters per node: 3
Objective function: 1531.132
Warning message:
In coxph(formula = y ~ x) : X matrix deemed to be singular; variable 2

I would like to know what's wrong with my Solution 1.

I also tried a similar thing for a regression problem and get the same result, ending with a single leaf :

data("BostonHousing", package = "mlbench")

BostonHousing <- transform(BostonHousing,
                       chas = factor(chas, levels = 0:1, labels = c("no", "yes")),
                       rad = factor(rad, ordered = TRUE))


linear_reg = function(y,x, start = NULL, weights = NULL, offset = NULL, ...,
                  estfun = FALSE, object = TRUE){
  res_lm = glm(formula = y ~ x , family = "gaussian")
  list(
    coefficients = res_lm$coefficients,
    objfun = res_lm$deviance,
    object = res_lm )
}

mob( formula = medv ~ log(lstat) + I(rm^2) | zn + indus + chas + nox +
   + age + dis + rad + tax + crim + b + ptratio, 
     data = BostonHousing ,
     fit = linear_reg)

Also I would like to know if there is no problem using a variable for both "fit the model in a node" and "make a split".

Thank you in advance.

I will probably have other questions about partykit functioning.

custom split rule with partykit

1 Answers