Fill missing data using a linear model

Question

I have some data that looks a little like this

   ID year       var1      var2
1   1    1         NA 0.5632595
2   1    2  0.7546097 0.5609945
3   1    3 -0.4241935        NA
4   1    4  0.4056908 0.5890453
5   2    1 -0.8049815 0.3504281
6   2    2  0.8049250 0.4817798
7   2    3         NA        NA
8   2    4 -0.2969572 0.4985812
9   3    1  0.2909882 0.8504004
10  3    2  1.0957994 0.7365867
11  3    3 -0.2884501 0.1454566
12  3    4  0.4999331 0.7978971

tmp <- structure(list(ID = c(1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3), year = c(1L, 
2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L), var1 = c(NA, 0.754609745086276, 
-0.424193528509845, 0.4056908200679, -0.804981499494056, 0.804924965958355, 
NA, -0.2969572255706, 0.29098820839828, 1.09579940195461, -0.288450063674258, 
0.499933144375212), var2 = c(0.563259549904615, 0.560994466999546, 
NA, 0.589045349741355, 0.350428087171167, 0.481779781170189, 
NA, 0.498581154504791, 0.850400378694758, 0.73658673488535, 0.145456639816985, 
0.797897139331326)), .Names = c("ID", "year", "var1", "var2"), row.names = c(NA, 
-12L), class = "data.frame")

What I want to be able to do, is fit a linear model for each ID to each column, i.e.

tmp %>% group_by(ID) %>% lm(var1 ~ year, data = .)

tmp %>% group_by(ID) %>% lm(var2 ~ year, data = .)

I would then use the coefficients of these models to fill in the missing (NA) values within each column. So for ID 1 and Variable 1, I would have a model like this:

coefs_id1_var1 <- coef(lm(var1 ~ year, data = tmp[tmp$ID == 1, ]))
coefs_id1_var1[1] + coefs_id1_var1[2] * tmp[1, 2]
[1] -0.1341153 

so the missing value for ID 1 Variable 1 would be replaced by -0.134. My problem is that I have a LOT of variables for which I wish to do this for. I have considered an lapply and spliting on the ID, or possibly mutate_each however I haven't been able to get an efficient way of doing this. Any ideas?

My current solution is

fillWithLinMod <- function(var, df) {
  mod <- as.formula(paste0(var, " ~ year"))
  coefs <- coef(lm(mod, data = df))
  for (i in 1:nrow(df)) {
    if (is.na(df[i, var])) {
      df[i, var] <- coefs[1] + df[i, "year"] * coefs[2]
    }
  }
  df[, var][[1]]
}

(Note my df is a tibble which is why I have the subset at the end)

Then I can use the following

tmp$var1 <- do.call("c", lapply(split(tmp, tmp$ID), function(x) fillWithLinMod("var1", x)))

Answer 1

Here is a worker function that you can apply throughout your subsets. You pass in a data.frame and a character vector of variable names to be filled. It assumes there is a variable called 'year' as you have done in your function.

    fill_missing_with_lm <- function(dat, vars) {
      for(i in seq_along(vars)) {
        mod <- as.formula(paste0(vars[i], " ~ year"))
        mod <- lm(mod, dat)
        misses <- which(is.na(dat[[ vars[i] ]]))
        for(j in misses) {
          newdat <- data.frame(year = dat$year[j])
          dat[[ vars[i] ]][j] <- predict(mod, newdat)
        }
      }
      return(dat)
    }

Then you can apply it with this workflow (nested data.frame's) which i really like. I have found it generally helpful for handling data where you want do to something a little nuanced to subsets of rows of your data. The basic principle is the group_by() %>% nest. Then you use purrr::map() to apply your nuanced actions to each of the nested data.frames.

    library(dplyr)
    library(tidyr)
    library(purrr)
    filled <- tmp %>%
      group_by(ID) %>%
      nest %>%
      mutate(filled = map(data, fill_missing_with_lm, vars = c('var1', 'var2'))) %>%
      select(ID, filled) %>%
      unnest