[R-sig-ME] Two random effects with identical conditional modes

[boomslang]

Hello all,

I have data with one categorial variable 'p'.  A binary outcome ('result') is the result of a process determined by exactly two DIFFERENT levels of p.  

I am interested in the contribution of each level of p to the outcome of 'result'.

The code below produces a small but similar version of the dataset:

    set.seed( 1)
    p <- letters[1:6]

    p1 <- sample( p, 30, replace = T)
    p2 <- sample( p, 30, replace = T)
    result <- runif( n = 30) > 0.7

    x <- data.frame( p1, p2, result)
    x <- subset( x, p1 != p2)
    print( x, row.names = F)


If I do

   glmer( result ~ 1 + (1|p1) + (1|p2), x, binomial)
   ranef( fm)

... I get different conditional modes for the levels in p1 and p2, but this is not what I want since the condional mode of 'a' in p1 should be the same as the conditional mode of 'a' in p2.

If I look at the random effects model matrix fm at Zt I see:


12 x 27 sparse Matrix of class "dgCMatrix"

 [1,] . . . . . . . . . 1 . . . . . . . . . . . 1 . . 1 . . #p1-a
 [2,] 1 . . . 1 . . . . . 1 1 . . . . . . . 1 . . 1 . . . . #p1-b
 [3,] . 1 . . . . . . . . . . 1 . 1 . . 1 . . . . . 1 . 1 .
 [4,] . . 1 . . . . 1 1 . . . . . . . . . . . 1 . . . . . .
 [5,] . . . . . . . . . . . . . 1 . 1 . . . . . . . . . . .
 [6,] . . . 1 . 1 1 . . . . . . . . . 1 . 1 . . . . . . . 1 #p1-f
 [7,] . . . . . . . 1 . . . . . . . 1 . . . . . . 1 1 . . . #p2-a
 [8,] . . . 1 . . . . . . . . . . . . . . . . . 1 . . 1 . . #p2-b
 [9,] 1 . 1 . . . . . . 1 . . . . . . 1 . 1 . 1 . . . . . .
[10,] . 1 . . . . . . . . . 1 1 1 . . . . . . . . . . . 1 1
[11,] . . . . 1 1 1 . 1 . 1 . . . 1 . . 1 . . . . . . . . .
[12,] . . . . . . . . . . . . . . . . . . . 1 . . . . . . . #p2-f


... while I need Zt to be more like this:

 [1,] . . . . . . . 1 . 1 . . . . . 1 . . . . . 1 1 1 1 . . # a
 [2,] 1 . . 1 1 . . . . . 1 1 . . . . . . . 1 . 1 1 . 1 . . # b
 [3,] 1 1 1 . . . . . . 1 . . 1 . 1 . 1 1 1 . 1 . . 1 . 1 . # c 
 [4,] . 1 1 . . . . 1 1 . . 1 1 1 . . . . . . 1 . . . . 1 1 # d 
 [5,] . . . . 1 1 1 . 1 . 1 . . 1 1 1 . 1 . . . . . . . . . # e
 [6,] . . . 1 . 1 1 . . . . . . . . . 1 . 1 1 . . . . . . 1 # f


i.e. a 6x27 with exactly two 1's in each column.

Is there a simple way/trick to obtain this?  Is the Pinheiro package perhaps better suited for my problem?


Any help is appreciated. Thanks in advance.


PS: The dataset is very large: it has about 2 million rows and 'p' has about 10000 levels. (This is the reason why I use random effects for p. Preferably I would use fixed effects.)