Trying to create and loop through matrix of unbala

Question

I am trying to conduct an hierarchical bayesian analysis but am having a little trouble with R and WinBUGS code. I don't have balanced data and am struggling with the coding. I have temperature data collected daily with iButtons (temperature recording devices) in transects and am trying to generate a model that relates this to remote sensing data. Unfortunately, each transect has a different number of iButtons so creating a 3D matrix of button(i), in transect(j), repeatedly "sampled" on day(t) is a problem for me.

Ultimately, my model will be something like:

Level 1 Temp[ijk] ~ N(theta[ijk], tau) theta[ijk] = b0 + b1*x1 + . . . + bn*xn

Level 2 b0 = a00 + a01*y1 + . . . an*yn b1 = a10 + a11*y1 ...

Level 3 (maybe?) - random level 2 intercepts

Normally I would do something like this: Wide <- reshape(Data1, idvar = c("iButton","block"), timevar = "julian", direction = "wide")

J <- length(unique(Data$block))
I <- length(unique(Data$iButton))
Ti <- length(unique(Data$julian))

Temp <- array(NA, dim = c(I, Ti, J))

for(t in 1:Ti) {
sel.rows <- Wide$block == t
Temp[,,t] <- as.matrix(Wide)[sel.rows, 3:Ti]
}

Then I could have a 3D matrix that I could loop through in WinBUGS or OpenBUGS as such:

for(i in 1:J) {          # Loop over transects/blocks
  for(j in 1:I) {        # Loop over buttons
    for(t in 1:Ti) {     # Loop over days
    Temp[i,j,t] ~ dnorm(theta[i,j,t])    
    theta[i,j,t] <- alpha.lam[i] + blam1*radiation[i,j] + blam2*cwd[i,j] + blam3*swd[i,j]
}}}

Anyway, don't worry about the details of the code above, it's just thrown together as an example from other analyses. My main question is how to do this type of analysis when I don't have a balanced design with equal numbers of iButtons per transect? Any help would be greatly appreciated. I'm clearly new to R and WinBUGS and don't have much previous computer coding experience.

Thanks!

oh and here is what the data look like in long (stacked) format:

    > Data[1:15, 1:4]
   iButton julian block       aveT
1        1      1     1 -4.5000000
2        1      2     1 -5.7500000
3        1      3     1 -3.5833333
4        1      4     1 -4.6666667
5        1      5     1 -2.5833333
6        1      6     1 -3.0833333
7        1      7     1 -1.5833333
8        1      8     1 -8.3333333
9        1      9     1 -5.0000000
10       1     10     1 -2.4166667
11       1     11     1 -1.7500000
12       1     12     1 -3.2500000
13       1     13     1 -3.4166667
14       1     14     1 -2.0833333
15       1     15     1 -1.7500000

Answer 1

Create a vector or array of lengths and use subindexing. Using your example:

J <- length(unique(Data$block))
I <- tapply(Data$iButton, Data$block, function(x) length(unique(x))
Ti <- tapply(Data$julian, list(Data$iButton, Data$block), function(x) length(unique(x))


for(i in 1:J) {          # Loop over transects/blocks
  for(j in 1:I[i]) {        # Loop over buttons
    for(t in 1:Ti[i, j]) {     # Loop over days
    Temp[i,j,t] ~ dnorm(theta[i,j,t])    
    theta[i,j,t] <- alpha.lam[i] + blam1*radiation[i,j] + blam2*cwd[i,j] + blam3*swd[i,j]
}}}

I think it would work, but I haven't tested since there no data.

Answer 2

Can you try using a list instead?

This allows a variable length for each item in the list where each index would correspond to the transect.

So something like this:

theta <- list()

for(i in unique(Data$block)) {
  ibuttons <- unique(Data$iButton[Data$block==i])
  days <- unique(Data$julian[Data$block==i])
  theta[[i]] <- matrix(NA, length(ibuttons), length(days)) # Empty matrix with NA's
    for(j in 1:length(ibuttons)) {
      for(t in 1:length(days)) {
        theta[[i]][j,t] <- fn(i, ibuttons[j], days[t])
      }
    }
  }