Interpolation over different groups of values with not enough non-NA values

Question

I have a dataframe including all observation of distances (column DIST.y) and altitude (Z) and corrected altitude by moving average (ma_Z) encompassed within an interval fixed by the column LimAm and LimAv for a given point ID.x for a given distance Dist.x. My purpose do a regression of the DIST.y and the ma_Z for each group of ID.x. Here is the code I use:

df_sl %>% 
  do({
    mod = lm(ma_Z ~ DIST.y, data = .)
    data.frame(int = coef(mod)[1], slope = coef(mod)[2])
  })

This code works properly.

However, I would like to fill the NA in the column ma_Z by using an interpolation with the funtion zoo::na.approx() before doing the regression. Unfortunately, for some of the groups ID.x in the dataframe I have a error message saying there is not enough non-NA values for the code to works properly (in this example, the groups ID.x = "188473" and "188473").

I do not understand why I have this error message for the ID.x "188473" and "188474" having two non-NA values. While ID.x "9383" and "9384" does not trigger the error message but only have one non-NA value each.

df_sl <- structure(list(ID.x = c(1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 
2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 
5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 9383, 9383, 9384, 9384, 
188473, 188473, 188473, 188473, 188474, 188474, 188474, 188474
), DIST.x = c(0, 0, 0, 0, 0, 0, 0, 0, 11.515675154, 11.515675154, 
11.515675154, 11.515675154, 11.515675154, 11.515675154, 11.515675154, 
11.515675154, 21.823439218, 21.823439218, 21.823439218, 21.823439218, 
21.823439218, 21.823439218, 21.823439218, 21.823439218, 21.988363443, 
21.988363443, 21.988363443, 21.988363443, 21.988363443, 21.988363443, 
21.988363443, 21.988363443, 32.961571068, 32.961571068, 32.961571068, 
32.961571068, 32.961571068, 32.961571068, 32.961571068, 32.961571068, 
43.934778692, 43.934778692, 43.934778692, 43.934778692, 43.934778692, 
43.934778692, 43.934778692, 43.934778692, 0, 0, 13.891845289, 
13.891845289, 0, 0, 0, 0, 0, 0, 0, 0), ID.y = c(1, 2, 3, 4, 5, 
6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 
3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 
8, 9383, 9384, 9383, 9384, 188473, 188474, 188475, 188476, 188473, 
188474, 188475, 188476), LimAm = c(-375, -363.484324846, -353.176560782, 
-353.011636557, -342.038428932, -331.065221308, -330.991532192, 
-320.018324568, -375, -363.484324846, -353.176560782, -353.011636557, 
-342.038428932, -331.065221308, -330.991532192, -320.018324568, 
-375, -363.484324846, -353.176560782, -353.011636557, -342.038428932, 
-331.065221308, -330.991532192, -320.018324568, -375, -363.484324846, 
-353.176560782, -353.011636557, -342.038428932, -331.065221308, 
-330.991532192, -320.018324568, -375, -363.484324846, -353.176560782, 
-353.011636557, -342.038428932, -331.065221308, -330.991532192, 
-320.018324568, -375, -363.484324846, -353.176560782, -353.011636557, 
-342.038428932, -331.065221308, -330.991532192, -320.018324568, 
-375, -361.108154711, -375, -361.108154711, -375, -375, -375, 
-362.193750234, -375, -375, -375, -362.193750234), LimAv = c(375, 
386.515675154, 396.823439218, 396.988363443, 407.961571068, 418.934778692, 
419.008467808, 429.981675432, 375, 386.515675154, 396.823439218, 
396.988363443, 407.961571068, 418.934778692, 419.008467808, 429.981675432, 
375, 386.515675154, 396.823439218, 396.988363443, 407.961571068, 
418.934778692, 419.008467808, 429.981675432, 375, 386.515675154, 
396.823439218, 396.988363443, 407.961571068, 418.934778692, 419.008467808, 
429.981675432, 375, 386.515675154, 396.823439218, 396.988363443, 
407.961571068, 418.934778692, 419.008467808, 429.981675432, 375, 
386.515675154, 396.823439218, 396.988363443, 407.961571068, 418.934778692, 
419.008467808, 429.981675432, 375, 388.891845289, 375, 388.891845289, 
375, 375, 375, 387.806249766, 375, 375, 375, 387.806249766), 
    DIST.y = c(0, 11.515675154, 21.823439218, 21.988363443, 32.961571068, 
    43.934778692, 44.008467808, 54.981675432, 0, 11.515675154, 
    21.823439218, 21.988363443, 32.961571068, 43.934778692, 44.008467808, 
    54.981675432, 0, 11.515675154, 21.823439218, 21.988363443, 
    32.961571068, 43.934778692, 44.008467808, 54.981675432, 0, 
    11.515675154, 21.823439218, 21.988363443, 32.961571068, 43.934778692, 
    44.008467808, 54.981675432, 0, 11.515675154, 21.823439218, 
    21.988363443, 32.961571068, 43.934778692, 44.008467808, 54.981675432, 
    0, 11.515675154, 21.823439218, 21.988363443, 32.961571068, 
    43.934778692, 44.008467808, 54.981675432, 0, 13.891845289, 
    0, 13.891845289, 0, 0, 0, 12.806249766, 0, 0, 0, 12.806249766
    ), Z = c(193.07513428, 193.15454102, 192.17289734, 192.17289734, 
    190.82974243, 190.63618469, 190.63618469, 189.45043945, 193.07513428, 
    193.15454102, 192.17289734, 192.17289734, 190.82974243, 190.63618469, 
    190.63618469, 189.45043945, 193.07513428, 193.15454102, 192.17289734, 
    192.17289734, 190.82974243, 190.63618469, 190.63618469, 189.45043945, 
    193.07513428, 193.15454102, 192.17289734, 192.17289734, 190.82974243, 
    190.63618469, 190.63618469, 189.45043945, 193.07513428, 193.15454102, 
    192.17289734, 192.17289734, 190.82974243, 190.63618469, 190.63618469, 
    189.45043945, 193.07513428, 193.15454102, 192.17289734, 192.17289734, 
    190.82974243, 190.63618469, 190.63618469, 189.45043945, 353.19342041, 
    353.02838135, 353.19342041, 353.02838135, 344.16003418, 344.16003418, 
    344.16003418, 344.1892395, 344.16003418, 344.16003418, 344.16003418, 
    344.1892395), ma_Z = c(193.07513428, NA, 192.800857546667, 
    NA, 192.0825195325, NA, 191.0687522875, NA, 193.07513428, 
    NA, 192.800857546667, NA, 192.0825195325, NA, 191.0687522875, 
    NA, 193.07513428, NA, 192.800857546667, NA, 192.0825195325, 
    NA, 191.0687522875, NA, 193.07513428, NA, 192.800857546667, 
    NA, 192.0825195325, NA, 191.0687522875, NA, 193.07513428, 
    NA, 192.800857546667, NA, 192.0825195325, NA, 191.0687522875, 
    NA, 193.07513428, NA, 192.800857546667, NA, 192.0825195325, 
    NA, 191.0687522875, NA, 353.19342041, NA, 353.19342041, NA, 
    344.16003418, NA, 344.16003418, NA, 344.16003418, NA, 344.16003418, 
    NA)), class = c("grouped_df", "tbl_df", "tbl", "data.frame"
), row.names = c(NA, -60L), groups = structure(list(ID.x = c(1, 
2, 3, 4, 5, 6, 9383, 9384, 188473, 188474), .rows = structure(list(
    1:8, 9:16, 17:24, 25:32, 33:40, 41:48, 49:50, 51:52, 53:56, 
    57:60), ptype = integer(0), class = c("vctrs_list_of", "vctrs_vctr", 
"list"))), class = c("tbl_df", "tbl", "data.frame"), row.names = c(NA, 
-10L), .drop = TRUE))

df_sl %>% group_by(ID.x) %>% mutate(ma_Z = zoo::na.approx(ma_Z, DIST.y, na.rm = FALSE, rule = 2)) 

And the error that I get :

Error in `mutate()`:
ℹ In argument: `ma_Z = ifelse(...)`.
ℹ In group 9: `ID.x = 188473`.
Caused by error in `approx()`:
! need at least two non-NA values to interpolate

I still need the groups with NA values for the linear regression (it works even if there is only one non-NA values). Also the full dataset is composed of millions of observations. I cannot allow myself to check all of it.

I had the idea to use a ifelse() function to bypass the interpolation if the amount of non-NA is lower than 2. However the error is the same. If I rise the threshold for the condition (>2), there is no errors but it gives an unique value for all observations of each group (No interpolation then)...

df_sl %>% 
  group_by(ID.x) %>%
  mutate(ma_Z = ifelse(
    length(na.omit(ma_Z)) > 1, 
    zoo::na.approx(ma_Z, DIST.y, na.rm = FALSE, rule = 2),
    ma_Z)
  )

How could I fix the error for the whole dataset and obtain a proper interpolation in the ma_Z column?

Answer 1

Is this what you want?

> df_sl |> 
+   transform(ma_Z=ave(
+     ma_Z, ID.x, FUN=\(x) {
+       if (all(is.na(x))) {
+         rep_len(NA_real_, length(x))
+       }
+       else if (len <- length(x) < 3L) {
+         rep_len(na.omit(x), len)
+       } 
+       else {
+         approx(x, xout=seq_along(x), rule=2)$y 
+       }
+     })
+   )
     ID.x   DIST.x   ID.y     LimAm    LimAv   DIST.y        Z     ma_Z
1       1  0.00000      1 -375.0000 375.0000  0.00000 193.0751 193.0751
2       1  0.00000      2 -363.4843 386.5157 11.51568 193.1545 192.9380
3       1  0.00000      3 -353.1766 396.8234 21.82344 192.1729 192.8009
4       1  0.00000      4 -353.0116 396.9884 21.98836 192.1729 192.4417
5       1  0.00000      5 -342.0384 407.9616 32.96157 190.8297 192.0825
6       1  0.00000      6 -331.0652 418.9348 43.93478 190.6362 191.5756
7       1  0.00000      7 -330.9915 419.0085 44.00847 190.6362 191.0688
8       1  0.00000      8 -320.0183 429.9817 54.98168 189.4504 191.0688
9       2 11.51568      1 -375.0000 375.0000  0.00000 193.0751 193.0751
10      2 11.51568      2 -363.4843 386.5157 11.51568 193.1545 192.9380
11      2 11.51568      3 -353.1766 396.8234 21.82344 192.1729 192.8009
12      2 11.51568      4 -353.0116 396.9884 21.98836 192.1729 192.4417
13      2 11.51568      5 -342.0384 407.9616 32.96157 190.8297 192.0825
14      2 11.51568      6 -331.0652 418.9348 43.93478 190.6362 191.5756
15      2 11.51568      7 -330.9915 419.0085 44.00847 190.6362 191.0688
16      2 11.51568      8 -320.0183 429.9817 54.98168 189.4504 191.0688
17      3 21.82344      1 -375.0000 375.0000  0.00000 193.0751 193.0751
18      3 21.82344      2 -363.4843 386.5157 11.51568 193.1545 192.9380
19      3 21.82344      3 -353.1766 396.8234 21.82344 192.1729 192.8009
20      3 21.82344      4 -353.0116 396.9884 21.98836 192.1729 192.4417
21      3 21.82344      5 -342.0384 407.9616 32.96157 190.8297 192.0825
22      3 21.82344      6 -331.0652 418.9348 43.93478 190.6362 191.5756
23      3 21.82344      7 -330.9915 419.0085 44.00847 190.6362 191.0688
24      3 21.82344      8 -320.0183 429.9817 54.98168 189.4504 191.0688
25      4 21.98836      1 -375.0000 375.0000  0.00000 193.0751 193.0751
26      4 21.98836      2 -363.4843 386.5157 11.51568 193.1545 192.9380
27      4 21.98836      3 -353.1766 396.8234 21.82344 192.1729 192.8009
28      4 21.98836      4 -353.0116 396.9884 21.98836 192.1729 192.4417
29      4 21.98836      5 -342.0384 407.9616 32.96157 190.8297 192.0825
30      4 21.98836      6 -331.0652 418.9348 43.93478 190.6362 191.5756
31      4 21.98836      7 -330.9915 419.0085 44.00847 190.6362 191.0688
32      4 21.98836      8 -320.0183 429.9817 54.98168 189.4504 191.0688
33      5 32.96157      1 -375.0000 375.0000  0.00000 193.0751 193.0751
34      5 32.96157      2 -363.4843 386.5157 11.51568 193.1545 192.9380
35      5 32.96157      3 -353.1766 396.8234 21.82344 192.1729 192.8009
36      5 32.96157      4 -353.0116 396.9884 21.98836 192.1729 192.4417
37      5 32.96157      5 -342.0384 407.9616 32.96157 190.8297 192.0825
38      5 32.96157      6 -331.0652 418.9348 43.93478 190.6362 191.5756
39      5 32.96157      7 -330.9915 419.0085 44.00847 190.6362 191.0688
40      5 32.96157      8 -320.0183 429.9817 54.98168 189.4504 191.0688
41      6 43.93478      1 -375.0000 375.0000  0.00000 193.0751 193.0751
42      6 43.93478      2 -363.4843 386.5157 11.51568 193.1545 192.9380
43      6 43.93478      3 -353.1766 396.8234 21.82344 192.1729 192.8009
44      6 43.93478      4 -353.0116 396.9884 21.98836 192.1729 192.4417
45      6 43.93478      5 -342.0384 407.9616 32.96157 190.8297 192.0825
46      6 43.93478      6 -331.0652 418.9348 43.93478 190.6362 191.5756
47      6 43.93478      7 -330.9915 419.0085 44.00847 190.6362 191.0688
48      6 43.93478      8 -320.0183 429.9817 54.98168 189.4504 191.0688
49   9383  0.00000   9383 -375.0000 375.0000  0.00000 353.1934 353.1934
50   9383  0.00000   9384 -361.1082 388.8918 13.89185 353.0284 353.1934
51   9384 13.89185   9383 -375.0000 375.0000  0.00000 353.1934 353.1934
52   9384 13.89185   9384 -361.1082 388.8918 13.89185 353.0284 353.1934
53 188473  0.00000 188473 -375.0000 375.0000  0.00000 344.1600 344.1600
54 188473  0.00000 188474 -375.0000 375.0000  0.00000 344.1600 344.1600
55 188473  0.00000 188475 -375.0000 375.0000  0.00000 344.1600 344.1600
56 188473  0.00000 188476 -362.1938 387.8062 12.80625 344.1892 344.1600
57 188474  0.00000 188473 -375.0000 375.0000  0.00000 344.1600 344.1600
58 188474  0.00000 188474 -375.0000 375.0000  0.00000 344.1600 344.1600
59 188474  0.00000 188475 -375.0000 375.0000  0.00000 344.1600 344.1600
60 188474  0.00000 188476 -362.1938 387.8062 12.80625 344.1892 344.1600

Answer 2

The problem is that DIST.y does not vary enough for group 188473 . It is not clear what you want in that case but if you want to simply ignore DIST.y in that case use na.approx2 instead of na.approx where na.approx2 is the following. We have assumed if there are any duplicated elements in DIST.y then it does not vary enough:

na.approx2 <- function(object, x = index(object), ...) {
  if (anyDuplicated(x)) na.approx(object, x = index(object), ...)
  else na.approx(object, x, ...)
}