Split Continuous and Categorical Predictors

Splits the design matrix into categorical and continuous predictors. Categorical variables are variables that are factors, ordered factors, or character.

splitFrame(mf, x = model.matrix(mt, mf),
      type = c("f","fi", "fii"))

Arguments

mf: model frame (as returned by model.frame).
x: (optional) design matrix, defaulting to the derived model.matrix.
type: a character string specifying the split type (see details).

Details

Which split type is used can be controlled with the setting split.type in lmrob.control.

There are three split types. The only differences between the types are how interactions between categorical and continuous variables are handled. The extra types of splitting can be used to avoid Too many singular resamples errors.

Type "f", the default, assigns only the intercept, categorical and interactions of categorical variables to x1. Interactions of categorical and continuous variables are assigned to x2.

Type "fi" assigns also interactions between categorical and continuous variables to x1.

Type "fii" assigns not only interactions between categorical and continuous variables to x1, but also the (corresponding) continuous variables themselves.

Value

A list that includes the following components:

x1: design matrix containing only categorical variables
x1.idx: logical vectors of the variables considered categorical in the original design matrix
x2: design matrix containing the continuous variables

References

Maronna, R. A., and Yohai, V. J. (2000). Robust regression with both continuous and categorical predictors. Journal of Statistical Planning and Inference 89, 197–214.

Author

Manuel Koller

Examples

data(education)
education <- within(education, Region <- factor(Region))
educaCh   <- within(education, Region <- as.character(Region))

## no interactions -- same split for all types:
fm1 <- lm(Y ~ Region + X1 + X2 + X3, education)
fmC <- lm(Y ~ Region + X1 + X2 + X3, educaCh  )
splt <- splitFrame(fm1$model) ; str(splt)
#> List of 3
#>  $ x1    : num [1:50, 1:4] 1 1 1 1 1 1 1 1 1 1 ...
#>   ..- attr(*, "dimnames")=List of 2
#>   .. ..$ : chr [1:50] "1" "2" "3" "4" ...
#>   .. ..$ : chr [1:4] "(Intercept)" "Region2" "Region3" "Region4"
#>  $ x1.idx: Named logi [1:7] TRUE TRUE TRUE TRUE FALSE FALSE ...
#>   ..- attr(*, "names")= chr [1:7] "(Intercept)" "Region2" "Region3" "Region4" ...
#>  $ x2    : num [1:50, 1:3] 508 564 322 846 871 774 856 889 715 753 ...
#>   ..- attr(*, "dimnames")=List of 2
#>   .. ..$ : chr [1:50] "1" "2" "3" "4" ...
#>   .. ..$ : chr [1:3] "X1" "X2" "X3"
splC <- splitFrame(fmC$model)
stopifnot(identical(splt, splC))

## with interactions:
fm2 <- lm(Y ~ Region:X1:X2 + X1*X2, education)
s1 <- splitFrame(fm2$model, type="f"  )
s2 <- splitFrame(fm2$model, type="fi" )
s3 <- splitFrame(fm2$model, type="fii")
cbind(s1$x1.idx,
      s2$x1.idx,
      s3$x1.idx)
#>                [,1]  [,2]  [,3]
#> (Intercept)    TRUE  TRUE  TRUE
#> X1            FALSE FALSE FALSE
#> X2            FALSE FALSE FALSE
#> X1:X2         FALSE FALSE  TRUE
#> Region2:X1:X2 FALSE  TRUE  TRUE
#> Region3:X1:X2 FALSE  TRUE  TRUE
#> Region4:X1:X2 FALSE  TRUE  TRUE
rbind(p.x1 = c(ncol(s1$x1), ncol(s2$x1), ncol(s3$x1)),
      p.x2 = c(ncol(s1$x2), ncol(s2$x2), ncol(s3$x2)))
#>      [,1] [,2] [,3]
#> p.x1    1    4    5
#> p.x2    6    3    2