How to fit multiple interaction models in a loop

Question

I have to fit n models with all the possible two way interaction term

In sort, I have 23 variables in my main effect model, and I want do add one by one interaction and check its significance Like this

model1 <- glm(y~x1+x2+...+x23)
model2 <- glm(y~x1+x2+...+x23+x1*x2)
summary(model2)
model3 <- glm(y~x1+x2+...+x23+x1*x3)
summary(model3)
#...
model73<- glm(y~x1+x2+...+x23+x22*x23)

Answer 1

To create the formulas, try

x_vec <- sprintf("x%d", 1:23)
base_formula <- reformulate(x_vec, response = "y")

all_formulas <- combn(x_vec, 2, \(x) {
  fmla <- paste("~ . + ", paste(x, collapse = "*"))
  update(base_formula, fmla)
}, simplify = FALSE)

all_formulas <- c(base_formula, unlist(all_formulas))
head(all_formulas)
#> [[1]]
#> y ~ x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 + x11 + 
#>     x12 + x13 + x14 + x15 + x16 + x17 + x18 + x19 + x20 + x21 + 
#>     x22 + x23
#> 
#> [[2]]
#> y ~ x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 + x11 + 
#>     x12 + x13 + x14 + x15 + x16 + x17 + x18 + x19 + x20 + x21 + 
#>     x22 + x23 + x1:x2
#> 
#> [[3]]
#> y ~ x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 + x11 + 
#>     x12 + x13 + x14 + x15 + x16 + x17 + x18 + x19 + x20 + x21 + 
#>     x22 + x23 + x1:x3
#> 
#> [[4]]
#> y ~ x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 + x11 + 
#>     x12 + x13 + x14 + x15 + x16 + x17 + x18 + x19 + x20 + x21 + 
#>     x22 + x23 + x1:x4
#> 
#> [[5]]
#> y ~ x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 + x11 + 
#>     x12 + x13 + x14 + x15 + x16 + x17 + x18 + x19 + x20 + x21 + 
#>     x22 + x23 + x1:x5
#> 
#> [[6]]
#> y ~ x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 + x11 + 
#>     x12 + x13 + x14 + x15 + x16 + x17 + x18 + x19 + x20 + x21 + 
#>     x22 + x23 + x1:x6

^{Created on 2022-12-08 with reprex v2.0.2}

Then fit the models with lapply. Something like this (untested, since there are no data).

model_list <- lapply(all_formulas, \(f) glm(f))
smry_list <- lapply(model_list, summary)
smry_list[[1]]