R: Interpolation of NAs by group

Use data.frame, rather than cbind to create your data. cbind returns a matrix, but you need a data frame for dplyr. Then use na.approx inside mutate. I've commented out group_by, as you haven't provided the grouping variable in your data, but the approach should work once you've added the grouping variable to the data frame.

df <- data.frame(time=c(1,2,3,4,5,6,7,1,2,3),
            Individuals=c(1,1,1,1,1,1,1,2,2,2),
            Value=c(NA, 2, 3, NA, 5, NA, 7, 8, NA, 10))

library(dplyr)
library(zoo)

df %>%
  group_by(Individuals) %>%
  mutate(ValueInterp = na.approx(Value, na.rm=FALSE))    

   time Individuals Value ValueInterp
1     1           1    NA          NA
2     2           1     2           2
3     3           1     3           3
4     4           1    NA           4
5     5           1     5           5
6     6           1    NA           6
7     7           1     7           7
8     1           2     8           8
9     2           2    NA           9
10    3           2    10          10

Update: To interpolate multiple columns, we can use mutate_at. Here's an example with two value columns. We use mutate_at to run na.approx on all columns that include "Value" in the column name. list(interp=na.approx) tells mutate_at to generate new column names by running na.approx and adding interp as a suffix to generate the new column names:

df <- data.frame(time=c(1,2,3,4,5,6,7,1,2,3),
                 Individuals=c(1,1,1,1,1,1,1,2,2,2),
                 Value1=c(NA, 2, 3, NA, 5, NA, 7, 8, NA, 10),
                 Value2=c(NA, 2, 3, NA, 5, NA, 7, 8, NA, 10)*2)

df %>%
  group_by(Individuals) %>%
  mutate_at(vars(matches("Value")), list(interp=na.approx), na.rm=FALSE)

    time Individuals Value1 Value2 Value1_interp Value2_interp
   <dbl>       <dbl>  <dbl>  <dbl>         <dbl>         <dbl>
 1     1           1     NA     NA            NA            NA
 2     2           1      2      4             2             4
 3     3           1      3      6             3             6
 4     4           1     NA     NA             4             8
 5     5           1      5     10             5            10
 6     6           1     NA     NA             6            12
 7     7           1      7     14             7            14
 8     1           2      8     16             8            16
 9     2           2     NA     NA             9            18
10     3           2     10     20            10            20

If you don't want to preserve the original, uninterpolated columns, you can do:

df %>%
  group_by(Individuals) %>%
  mutate_at(vars(matches("Value")), na.approx, na.rm=FALSE)

We can use data.table

library(data.table)
library(zoo)
setDT(df1)[, ValueInterp:= na.approx(Value, na.rm=TRUE), by = Individual]