R - Linear linear regression with variables in different dataframes

Question

I have 4 large matrixes of the same size A, B, C and D. Each matrix has n samples (columns) and n observations (rows).

A <- structure(list(S1 = c(0L, 0L, 1L, 1L), S2 = c(0L, 1L, 0L, 0L), S3 = c(0L, 0L, 0L, 1L)), class = "data.frame", row.names = c("Ob1", "Ob2", "Ob3", "Ob4"))
#        S1  S2  S3
# Ob1     0   0   0
# Ob2     0   1   0
# Ob3     1   0   0
# Ob4     1   0   1

B <- structure(list(S1 = c(0L, 1L, 1L, 1L), S2 = c(0L, 8L, 0L, 0L), S3 = c(0L, 0L, 0L, 1L)), class = "data.frame", row.names = c("Ob1", "Ob2", "Ob3", "Ob4"))
#        S1  S2  S3
# Ob1     0   0   0
# Ob2     1   8   0
# Ob3     1   0   0
# Ob4     1   0   1

C <- structure(list(S1 = c(0L, 0L, 4L, 1L), S2 = c(2L, 1L, 0L, 2L), S3 = c(0L, 0L, 0L, 1L)), class = "data.frame", row.names = c("Ob1", "Ob2", "Ob3", "Ob4"))
#        S1  S2  S3
# Ob1     0   2   0
# Ob2     0   1   0
# Ob3     4   0   0
# Ob4     1   2   1

D <-  structure(list(S1 = c(0L, 0L, 4L, 1L), S2 = c(8L, 1L, 5L, 0L), S3 = c(0L, 0L, 0L, 1L)), class = "data.frame", row.names = c("Ob1", "Ob2", "Ob3", "Ob4"))
#        S1  S2 S3
# Ob1     0   8   0
# Ob2     0   1   0
# Ob3     4   5   0
# Ob4     1   0   1

Each matrix contains a different variable. I want to perform a linear regression of 4 variables for each sample and observation of the matrixes. I don't want a linear regression betweeen any combinaton of samples and observations, just pairwise regressions in the form of column 1 and row 1 in matrx A is going to be fitted with column 1 and row 1 in matrixes B, C and D; column 2 and row 2 with column 2 and row 2, and so on.

lm model:

lm(A ~ B * C + D)

I want:

lm(A$S1_Obs1 ~ B$S1_Obs1 * C$S1_Obs1 + D$S1_Obs1)
lm(A$S1_Obs2 ~ B$S1_Obs2 * C$S1_Obs2 + D$S1_Obs2)
lm(A$S1_Obs3 ~ B$S1_Obs3 * C$S1_Obs3 + D$S1_Obs3)

lm(A$S2_Obs1 ~ B$S2_Obs1 * C$S2_Obs1 + D$S2_Obs1)
lm(A$S2_Obs2 ~ B$S2_Obs2 * C$S2_Obs2 + D$S2_Obs2)
lm(A$S2_Obs3 ~ B$S2_Obs3 * C$S2_Obs3 + D$S2_Obs3)

...

Any help appreciated.

Answer 1

We may use asplit to split by row and then construct the linear model by looping each of the split elements in Map

out <- Map(function(a, b, c, d) lm(a ~ b * c + d),
      asplit(A, 1), asplit(B, 1), asplit(C, 1), asplit(D, 1))

Answer 2

Here is an approach using the purrr package that assigns names as well:

library(purrr)
seq_along(A) %>%
  map(~ lm(A[.] ~ B[.] * C[.] + D[.])) %>%
  set_names(map(seq_along(.),
                ~ arrayInd(.x, dim(A)) %>%
                    paste(collapse = "_")))

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