Interpolate NA values

Question

I have two set of samples that are time independent. I would like to merge them and calculate the missing values for the times where I do not have values of both. Simplified example:

A <- cbind(time=c(10, 20, 30, 40, 50, 60, 70, 80, 90, 100),
           Avalue=c(1, 2, 3, 2, 1, 2, 3, 2, 1, 2))
B <- cbind(time=c(15, 30, 45, 60), Bvalue=c(100, 200, 300, 400))
C <- merge(A,B, all=TRUE)

   time Avalue Bvalue
1    10      1     NA
2    15     NA    100
3    20      2     NA
4    30      3    200
5    40      2     NA
6    45     NA    300
7    50      1     NA
8    60      2    400
9    70      3     NA
10   80      2     NA
11   90      1     NA
12  100      2     NA

By assuming linear change between each sample, it is possible to calculate the missing NA values. Intuitively it is easy to see that the A value at time 15 and 45 should be 1.5. But a proper calculation for B for instance at time 20 would be

100 + (20 - 15) * (200 - 100) / (30 - 15)

which equals 133.33333. The first parenthesis being the time between estimate time and the last sample available. The second parenthesis being the difference between the nearest samples. The third parenthesis being the time between the nearest samples.

How can I use R to calculate the NA values?

Answer 1

Using the zoo package:

library(zoo)
Cz <- zoo(C)
index(Cz) <- Cz[,1]
Cz_approx <- na.approx(Cz)

Answer 2

The proper way to do this statistically and still get valid confidence intervals is to use Multiple Imputation. See Rubin's classic book, and there's an excellent R package for this (mi).