Converting coefficient names to a formula in R

Question

When using formulas that have factors, the fitted models name the coefficients XY, where X is the name of the factor and Y is a particular level of it. I want to be able to create a formula from the names of these coefficients.

The reason: If I fit a lasso to a sparse design matrix (as I do below) I would like to create a new formula object that only contains terms for the nonzero coefficients.

require("MatrixModels")
require("glmnet")
set.seed(1)
n <- 200
Z <- data.frame(letter=factor(sample(letters,n,replace=T),letters),
                x=sample(1:20,200,replace=T))
f <- ~ letter + x:letter + I(x>5):letter
X <- sparse.model.matrix(f, Z)
beta <- matrix(rnorm(dim(X)[2],0,5),dim(X)[2],1)
y <- X %*% beta + rnorm(n)

myfit <- glmnet(X,as.vector(y),lambda=.05)
fnew <- rownames(myfit$beta)[which(myfit$beta != 0)]
 [1] "letterb"              "letterc"              "lettere"             
 [4] "letterf"              "letterg"              "letterh"             
 [7] "letterj"              "letterm"              "lettern"             
[10] "lettero"              "letterp"              "letterr"             
[13] "letters"              "lettert"              "letteru"             
[16] "letterw"              "lettery"              "letterz"             
[19] "lettera:x"            "letterb:x"            "letterc:x"           
[22] "letterd:x"            "lettere:x"            "letterf:x"           
[25] "letterg:x"            "letterh:x"            "letteri:x"           
[28] "letterj:x"            "letterk:x"            "letterl:x"           
[31] "letterm:x"            "lettern:x"            "lettero:x"           
[34] "letterp:x"            "letterq:x"            "letterr:x"           
[37] "letters:x"            "lettert:x"            "letteru:x"           
[40] "letterv:x"            "letterw:x"            "letterx:x"           
[43] "lettery:x"            "letterz:x"            "letterb:I(x > 5)TRUE"
[46] "letterc:I(x > 5)TRUE" "letterd:I(x > 5)TRUE" "lettere:I(x > 5)TRUE"
[49] "letteri:I(x > 5)TRUE" "letterj:I(x > 5)TRUE" "letterl:I(x > 5)TRUE"
[52] "letterm:I(x > 5)TRUE" "letterp:I(x > 5)TRUE" "letterq:I(x > 5)TRUE"
[55] "letterr:I(x > 5)TRUE" "letteru:I(x > 5)TRUE" "letterv:I(x > 5)TRUE"
[58] "letterx:I(x > 5)TRUE" "lettery:I(x > 5)TRUE" "letterz:I(x > 5)TRUE"

From this I would like to have a formula

~ I(letter=="d") + I(letter=="e") + ...(etc)

I checked out formula() and all.vars() to no avail. Also, writing a function to parse this is a bit of a pain because of the different types of terms that can arise. For example, for x:letter when x is a numeric value and letter is a factor, or I(x>5):letter as another annoying case.

So am I not aware of some function to convert between formula and its character representation and back again?

Answer 1

When I ran the code, I got something a bit different, since set.seed() had not been specified. Instead of using the variable name "letter", I used "letter_" as a convenient splitting marker:

> fnew <- rownames(myfit$beta)[which(myfit$beta != 0)]

> fnew
 [1] "letter_c" "letter_d" "letter_e" "letter_f" "letter_h" "letter_k" "letter_l"
 [8] "letter_o" "letter_q" "letter_r" "letter_s" "letter_t" "letter_u" "letter_v"
[15] "letter_w"

Then made the split and packaged into a character matrix:

> fnewmtx <- cbind( lapply(sapply(fnew, strsplit, split="_"), "[[", 2),
+ lapply(sapply(fnew, strsplit, split="_"), "[[", 1))

fnewmtx [,1] [,2]
letter_c "c" "letter" letter_d "d" "letter" letter_e "e" "letter" letter_f "f" "letter" snipped the rest

And wrapped the paste function(s) output in as.formula() which is half of the answer to how to "convert between formula and its character representation and back." The other half is as.character()

form <- as.formula( paste("~", 
             paste( 
               paste(" I(", fnewmtx[,2], "_ ==", "'",fnewmtx[,1],"') ", sep="") , 
             sep="", collapse="+")
                 ) 
           )  # edit: needed to add back the underscore

And the output is now an appropriate class object:

> class(form)
[1] "formula"
> form
~I(letter_ == "c") + I(letter_ == "d") + I(letter_ == "e") + 
    I(letter_ == "f") + I(letter_ == "h") + I(letter_ == "k") + 
    I(letter_ == "l") + I(letter_ == "o") + I(letter_ == "q") + 
    I(letter_ == "r") + I(letter_ == "s") + I(letter_ == "t") + 
    I(letter_ == "u") + I(letter_ == "v") + I(letter_ == "w")

I find it interesting that the as.formula conversion made the single-quotes around the letters into double-quotes.

Edit: Now that the problem has an additional dimension or two, my suggestion is to skip the recreation of the formula. Note that the rownames of myfit$beta are exactly the same as the column names of X, so instead use the non-zero rownames as indices to select columns in the X matrix:

> str(X[ , which( colnames(X) %in% rownames(myfit$beta)[which(myfit$beta != 0)] )] )
Formal class 'dgCMatrix' [package "Matrix"] with 6 slots
  ..@ i       : int [1:429] 9 54 91 157 166 37 55 68 117 131 ...
  ..@ p       : int [1:61] 0 5 13 20 28 36 42 50 60 68 ...
  ..@ Dim     : int [1:2] 200 60
  ..@ Dimnames:List of 2
  .. ..$ : chr [1:200] "1" "2" "3" "4" ...
  .. ..$ : chr [1:60] "letter_b" "letter_c" "letter_e" "letter_f" ...
  ..@ x       : num [1:429] 1 1 1 1 1 1 1 1 1 1 ...
  ..@ factors : list()

> myfit2 <- glmnet(X[ , which( colnames(X) %in% rownames(myfit$beta)[which(myfit$beta != 0)] )] ,as.vector(y),lambda=.05)
> myfit2

Call:  glmnet(x = X[, which(colnames(X) %in% rownames(myfit$beta)[
                                           which(myfit$beta != 0)])], 
              y = as.vector(y), lambda = 0.05) 

     Df   %Dev Lambda
[1,] 60 0.9996   0.05

Answer 2

Christopher, what you are asking for appears, after some consideration and examination of sparse.model.matrix etc, to be somewhat involved. You haven't explain why you do not want to form the full sparse model matrix for X_test so it is difficult to advise a way forward other than the two options below.

If you have a large number of observations in X_test and hence do not want to produce the full sparse matrix for use in predict() for computational reasons, it might be more expedient to split X_test into two or more chunks of samples and form the sparse model matrices for each one in turn, discarding it after after use.

Failing that, you will need to study code from the Matrix package in detail. Start with sparse.model.matrix and note that it then calls Matrix:::model.spmatrix and locate calls to Matrix:::fac2Sparse in that function. You will probably need to co-opt code from these functions but use a modified fac2Sparse to achieve what you want to achieve.

Sorry I cannot provide an off-the-shelf script to do this, but that is a substantial coding task. If you go down that route, check out the Sparse Model Matrices vignette in the Matrix package and get the package sources (from CRAN) to see if the functions I mention are better documented in the source code (there are no Rd files for fac2Sparse for example). You can also ask the authors of Matrix (Martin Maechler and Doug Bates) for advice, although note that both of these chaps have had a particularly heavy teaching load this term.

Good luck!