Iterated model building using formulas

[mschubert]

Consider the following setup of A, B, and C, where you want to apply a formula (e.g. lm(...), rlm(...), etc. - lm() supports matrix row indexing, but most other do not). The proposed syntax would add support for iterated calculation of a model where this is not implicitly supported, and a common output format.

A = matrix(1:4, nrow=2, ncol=2, dimnames=list(c('a','b'),c('x','y')))
B = matrix(5:6, nrow=2, ncol=1, dimnames=list(c('b','a'),'z'))
C = matrix(4:5, nrow=2, ncol=2)
# (A)   x y    (B)   z    (C)     [,1] [,2]
#     a 1 3        b 5      [1,]    4    4
#     b 2 4        a 6      [2,]    5    5

With those, you should be able to write (using lm here as an example):

# multiple outcomes - this works as expected
lm(A ~ B) # calculates lm(A[,1] ~ B), lm(A[,2] ~ B), etc.
# multiple inputs - this doesn't work
lm(B ~ A) # calculates lm(B ~ A[,1]), lm(B ~ A[,2]) + the general case
# each should return effect size, p-value, and other metrics

Now, if I want a generalized syntax to specify matrix iterations in models that only need to work on vectors, which one would be the best option?

• implicitly assume all matrices are iterated, specify grouping with additional arguments
• specify grouping using interaction syntax

# example 1: iterate A and C through columns. don't iterate B
x1 = create_formula_index(A ~ B + C) # option 1
x1 = create_formula_index(A ~ B:0 + C:0) # option 2
#   A B C
#1 x z 1
#2 y z 1
#3 x z 2
#4 y z 2

# example2: iterate A and C together, don't iterate B
x2 = create_formula_index(A ~ B + C, group=c("A", "C"), atomic="B") # option 1
x2 = create_formula_index(A:1 ~ B:0 + C:1) # option 2
#   A B C
#1 x z x
#2 y z y

The advantage of option 1 is that this is what lm(...) does, but it can be a bit verbose if want groups and atomic variables. Option 2 is more verbose when iterating, less when not.

Which option should be preferred?

[mschubert]

replaced by narray::lambda https://github.com/mschubert/narray#mapping-functions-on-arrays