How to create formulas programmatically in R based on pattern of omitted/included variables

I regularly have to create upwards of 10 sometimes more than 20 models for a single analysis. The underlying formulas for these models usually follow a clear pattern, but I often struggle to come up with a programmatic way to create them. If I need to add or change something in many models, not repeating myself for every model becomes all the more crucial.

Here is an example of what I mean.

Suppose we have this data:

mydata <- mtcars %>%
  mutate(standardized_mpg = scale(mpg)%>%as.numeric(),
         logged_mpg = log(mpg))

Now we want to create regression formulas for the three DVs mpg,standaridzed_mpg, and logged_mpg. For some arbitrary reason, we always want two IVs where the one of them is either gear or cyl and the other is either disp or hp. In other words, we want this:

mpg ~ gear + dips
mpg ~ cyl + dips
mpg ~ gear + hp
mpg ~ cyl + hp
logged_mpg ~ gear + dips
etc.
etc.
etc.
standardized_mpg ~ gear + dips
etc.
etc.
etc.

It's possible to achieve this with expand.grid():

specs_dv <- c("mpg", "standardized_mpg", "logged_mpg")
specs_iv1 <- c("gear", "cyl")
specs_iv2 <- c("disp", "hp")

f <-  expand.grid(
  specs_dv = specs_dv,
  " ~ ",
  specs_iv1 = specs_iv1,
  " + ",
  specs_iv2 = specs_iv2
) %>%
  arrange(specs_dv)

# Collapse each df row to char vector, then convert them to formulas
# At the end we will have a list-type object where every list item is a formula
f <- apply(f, 1, function(x) {
  as.formula(
    paste0(
      as.character(x), collapse = ""
    )
    )})

From here, I can use for loops and functions to create models and tables. I will not add them here as it's digresses from the main point.

Now, when the number of variables is fixed between models, the method above works nicely. However, more often, some models omit variables of other models. This is where I am stuck right now. Here is some sample data:

mydata <- ggplot2::economics %>%
  mutate(psavert_l1 = lag(psavert),
         standardized_psavert = scale(psavert)%>%as.numeric(),
         standardized_psavert_l1 = scale(psavert_l1)%>%as.numeric(),
         logged_psavert = log(psavert),
         logged_psavert_l1 = log(psavert_l1)
         )

And these are the formulas that I would like to generate:

uempmed ~ psavert + psavert_l1 + unemploy
uempmed ~ psavert + psavert_l1           
uempmed ~ psavert +              unemploy
uempmed ~           psavert_l1 + unemploy

uempmed ~ standardized_psavert + standardized_psavert_l1 + unemploy
uempmed ~ standardized_psavert + standardized_psavert_l1           
uempmed ~ standardized_psavert +                           unemploy
uempmed ~                        standardized_psavert_l1 + unemploy

uempmed ~ log_psavert + log_psavert_l1 + unemploy
uempmed ~ log_psavert + log_psavert_l1           
uempmed ~ log_psavert +                  unemploy
uempmed ~               log_psavert_l1 + unemploy

As you can see, this time I have two or three independent variables. The pattern here is to have one model with all three IVs and then three additional model where each time one of the IVs is omitted. Finally, I need this for three modified versions of two of the three variables.

Adding or removing variables like this is a very normal thing when modelling. Therefore, I was wondering if there is a faster way to create these formulas, like there is if the number of variables is fixed. What is your approach to handling this problem, especially if there are more variables more models to take care of? Writing everything by hand seems... just wrong.

After some more testing, I found a way that is reasonably programmatic.

My approach can be used if you have a formula and want to create many new formulas based on subtracting individual variables of that formula and some changes in variable names.

Note that I am using various tidyverse functions for this to work.

1. Create a df with one row that contains the formula, with formula elements as columns. Add a prefix if you need to modify the beginning of certain variables (like "logged_" or "standardized_").

f <- tibble(
  dv = "uempmed"
  tilde = "~",
  iv1 = "PREFIXpsavert",
  plus = "+",
  iv2 = "PREFIXpsavert_l1",
  plus2 = "+",
  iv3 = "unemploy"
)

2. Duplicate rows for as many times as the desired number of formulas. Here we need 3 sets of 4 formulas, so 12.

f <- f %>% slice(rep(1:n(), each = 12))

3. Replace the variables that should be left out in certain formulas with blank spaces

# This replaces the third IV with a blank space for every fourth model, counting from the second
# (Set "by" to the number of formulas per set of formulas. In this case it's three sets of four, so it's four.)
f[seq(2, nrow(f), by=4), c("iv3", "plus2")] <- " "

# This replace the second IV with a blank space for every fourth model, counting from the third
f[seq(3, nrow(f), by=4), c("iv2", "plus")] <- " "

# This replace the first IV with a blank space for every fourth model, counting from the fourth
f[seq(4, nrow(f), by=4), c("iv1", "plus")] <- " "

3. Collapse the data frame rows to character strings

f <- apply(f, 1, function(x) {
    paste0(
      as.character(x), collapse = ""
    )})

4. Change the prefix of variables for the first, second, third set of four models

f[1:4] <- str_replace_all(f[1:4], "PREFIX", "")
f[5:8] <- str_replace_all(f[5:8], "PREFIX", "standardized_")
f[9:12] <- str_replace_all(f[9:12], "PREFIX", "log_")

5. Finally, change the vector of strings to a list of formulas

f <- lapply(f, as.formula)

We end up with a list of formulas f that can be used with something like lm(formula = f[[1]], data = mydata).

Based on this structure, you could easily wrap everything in a function to make creating formulas even more programmatic. Of course, the actual models can also be created in a loop, like for example:

for(i in length(f)) {
  assign(
    x     = paste0("m", str_pad(i, width=2, pad=0)),
    value = lm(
      formula = f[[i]],
      data    = mydata
    )
  )}

Creating stargazer tables based on this is also possible, but it's too far from the original question, so I won't say more about it here. Hope this post helps people with a similar issue that I had!