Fit a different model for each row of a list-columns data frame

Question

What is the best way to fit different model formulae that vary by the row of a data frame with the list-columns data structure in tidyverse?

In R for Data Science, Hadley presents a terrific example of how to use the list-columns data structure and fit many models easily (http://r4ds.had.co.nz/many-models.html#gapminder). I am trying to find a way to fit many models with slightly different formulae. In the below example adapted from his original example, what is the best way to fit a different model for each continent?

library(gapminder)
library(dplyr)
library(tidyr)
library(purrr)
library(broom)

by_continent <- gapminder %>% 
  group_by(continent) %>% 
  nest()

by_continent <- by_continent %>% 
  mutate(model = map(data, ~lm(lifeExp ~ year, data = .)))

by_continent %>% 
  mutate(glance=map(model, glance)) %>% 
  unnest(glance, .drop=T)

## A tibble: 5 × 12
#  continent r.squared adj.r.squared     sigma statistic      p.value    df
#     <fctr>     <dbl>         <dbl>     <dbl>     <dbl>        <dbl> <int>
#1      Asia 0.4356350     0.4342026 8.9244419  304.1298 6.922751e-51     2
#2    Europe 0.4984659     0.4970649 3.8530964  355.8099 1.344184e-55     2
#3    Africa 0.2987543     0.2976269 7.6685811  264.9929 6.780085e-50     2
#4  Americas 0.4626467     0.4608435 6.8618439  256.5699 4.354220e-42     2
#5   Oceania 0.9540678     0.9519800 0.8317499  456.9671 3.299327e-16     2
## ... with 5 more variables: logLik <dbl>, AIC <dbl>, BIC <dbl>,
##   deviance <dbl>, df.residual <int>

I know I can do it by iterating through by_continent (not efficient as it estimates each model for every continent:

formulae <- list(
  Asia=~lm(lifeExp ~ year, data = .),
  Europe=~lm(lifeExp ~ year + pop, data = .),
  Africa=~lm(lifeExp ~ year + gdpPercap, data = .),
  Americas=~lm(lifeExp ~ year - 1, data = .),
  Oceania=~lm(lifeExp ~ year + pop + gdpPercap, data = .)
)

for (i in 1:nrow(by_continent)) {
  by_continent$model[[i]] <- map(by_continent$data, formulae[[i]])[[i]]
}

by_continent %>% 
  mutate(glance=map(model, glance)) %>% 
  unnest(glance, .drop=T)

## A tibble: 5 × 12
#  continent r.squared adj.r.squared     sigma  statistic       p.value    df
#     <fctr>     <dbl>         <dbl>     <dbl>      <dbl>         <dbl> <int>
#1      Asia 0.4356350     0.4342026 8.9244419   304.1298  6.922751e-51     2
#2    Europe 0.4984677     0.4956580 3.8584819   177.4093  3.186760e-54     3
#3    Africa 0.4160797     0.4141991 7.0033542   221.2506  2.836552e-73     3
#4  Americas 0.9812082     0.9811453 8.9703814 15612.1901 4.227928e-260     1
#5   Oceania 0.9733268     0.9693258 0.6647653   243.2719  6.662577e-16     4
## ... with 5 more variables: logLik <dbl>, AIC <dbl>, BIC <dbl>,
##   deviance <dbl>, df.residual <int>

But is it possible to do this without following back to loop in base R (and avoiding fitting models I don't need)?

What I tried is something like this:

by_continent <- by_continent %>% 
left_join(tibble::enframe(formulae, name="continent", value="formula"))

by_continent %>% 
   mutate(model=map2(data, formula, est_model))

But I don't seem to be able to come up with an est_model function that works. I tried this function (h/t: https://gist.github.com/multidis/8138757) that doesn't work:

  est_model <- function(data, formula, ...) {
  mc <- match.call()
  m <- match(c("formula","data"), names(mc), 0L)
  mf <- mc[c(1L, m)]
  mf[[1L]] <- as.name("model.frame")
  mf <- eval(mf, parent.frame())
  data.st <- data.frame(mf)

  return(data.st)
}

(Admittedly, this is a contrived example. My actual case is that I have substantial observations missing key independent variables in my data, so I want to fit one model with all variables on complete observations and another with only a subset of the variables on the rest observations.)

UPDATE

I came up with an est_model function that works (though probably not efficient):

est_model <- function(data, formula, ...) {
  map(list(data), formula, ...)[[1]]
}

by_continent <- by_continent %>% 
   mutate(model=map2(data, formula, est_model))

by_continent %>% 
  mutate(glance=map(model, glance)) %>% 
  unnest(glance, .drop=T)

## A tibble: 5 × 12
#  continent r.squared adj.r.squared     sigma  statistic       p.value    df
#      <chr>     <dbl>         <dbl>     <dbl>      <dbl>         <dbl> <int>
#1      Asia 0.4356350     0.4342026 8.9244419   304.1298  6.922751e-51     2
#2    Europe 0.4984677     0.4956580 3.8584819   177.4093  3.186760e-54     3
#3    Africa 0.4160797     0.4141991 7.0033542   221.2506  2.836552e-73     3
#4  Americas 0.9812082     0.9811453 8.9703814 15612.1901 4.227928e-260     1
#5   Oceania 0.9733268     0.9693258 0.6647653   243.2719  6.662577e-16     4
## ... with 5 more variables: logLik <dbl>, AIC <dbl>, BIC <dbl>, deviance <dbl>,
##   df.residual <int>

Answer 1

I find it is easier to make a list of model formula. each model was only fit once for the corresponding continent. I add a new column formula to the nested data to make sure that the formula and the continent are in the same order in case they are not.

formulae <- c(
    Asia= lifeExp ~ year,
    Europe= lifeExp ~ year + pop,
    Africa= lifeExp ~ year + gdpPercap,
    Americas= lifeExp ~ year - 1,
    Oceania= lifeExp ~ year + pop + gdpPercap
)

df <- gapminder %>%
    group_by(continent) %>%
    nest() %>%
    mutate(formula = formulae[as.character(continent)]) %>%
    mutate(model = map2(formula, data, ~ lm(.x, .y))) %>%
    mutate(glance=map(model, glance)) %>%
    unnest(glance, .drop=T)

# # A tibble: 5 × 12
#   continent r.squared adj.r.squared     sigma  statistic       p.value    df      logLik        AIC        BIC
#      <fctr>     <dbl>         <dbl>     <dbl>      <dbl>         <dbl> <int>       <dbl>      <dbl>      <dbl>
# 1      Asia 0.4356350     0.4342026 8.9244419   304.1298  6.922751e-51     2 -1427.65947 2861.31893 2873.26317
# 2    Europe 0.4984677     0.4956580 3.8584819   177.4093  3.186760e-54     3  -995.41016 1998.82033 2014.36475
# 3    Africa 0.4160797     0.4141991 7.0033542   221.2506  2.836552e-73     3 -2098.46089 4204.92179 4222.66639
# 4  Americas 0.9812082     0.9811453 8.9703814 15612.1901 4.227928e-260     1 -1083.35918 2170.71836 2178.12593
# 5   Oceania 0.9733268     0.9693258 0.6647653   243.2719  6.662577e-16     4   -22.06696   54.13392   60.02419
# # ... with 2 more variables: deviance <dbl>, df.residual <int>

Answer 2

I found purrr::modify_depth() that does what I want to do with est_model() in the original question. This is the solution I am now happy with:

library(gapminder)
library(tidyverse)
library(purrr)
library(broom)

fmlas <- tibble::tribble(
  ~continent, ~formula,
  "Asia", ~lm(lifeExp ~ year, data = .),
  "Europe", ~lm(lifeExp ~ year + pop, data = .),
  "Africa", ~lm(lifeExp ~ year + gdpPercap, data = .),
  "Americas", ~lm(lifeExp ~ year - 1, data = .),
  "Oceania", ~lm(lifeExp ~ year + pop + gdpPercap, data = .)
)

by_continent <- gapminder %>% 
  nest(-continent) %>%
  left_join(fmlas) %>%
  mutate(model=map2(data, formula, ~modify_depth(.x, 0, .y)))

by_continent %>% 
  mutate(glance=map(model, glance)) %>% 
  unnest(glance, .drop=T)