[R] calculate adjacent log odds for a table

[Michael Friendly]

This is a question about array and data frame manipulation and 
calculation, in the
context of models for log odds in contingency tables.

I have a data frame representing a 3-way frequency table, of size 5 
(litter) x 2 (treatment) x 3 (deaths).
"Freq" is the frequency in each cell, and deaths is the response variable.

     Mice <-
     structure(list(litter = c(7L, 7L, 8L, 8L, 9L, 9L, 10L, 10L, 11L,
     11L, 7L, 7L, 8L, 8L, 9L, 9L, 10L, 10L, 11L, 11L, 7L, 7L, 8L,
     8L, 9L, 9L, 10L, 10L, 11L, 11L), treatment = structure(c(1L,
     2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L,
     2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L), .Label = c("A",
     "B"), class = "factor"), deaths = structure(c(1L, 1L, 1L, 1L,
     1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
     3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L), .Label = c("0", "1",
     "2+"), class = "factor"), Freq = c(58L, 75L, 49L, 58L, 33L, 45L,
     15L, 39L, 4L, 5L, 11L, 19L, 14L, 17L, 18L, 22L, 13L, 22L, 12L,
     15L, 5L, 7L, 10L, 8L, 15L, 10L, 15L, 18L, 17L, 8L)), .Names = 
c("litter",
     "treatment", "deaths", "Freq"), row.names = c(NA, 30L), class = 
"data.frame")


 From this, I want to calculate the log odds for adjacent categories of 
the last variable (deaths)
and have this value in a data frame with factors litter (5), treatment 
(2), and contrast (2), as detailed below.

The data can be seen in xtabs() form:

     mice.tab <- xtabs(Freq ~ litter + treatment + deaths, data=Mice)
     ftable(mice.tab)

                      deaths  0  1 2+
     litter treatment
     7      A                58 11  5
            B                75 19  7
     8      A                49 14 10
            B                58 17  8
     9      A                33 18 15
            B                45 22 10
     10     A                15 13 15
            B                39 22 18
     11     A                 4 12 17
            B                 5 15  8
     >


 From this, I want to calculate the (adjacent) log odds of 0 vs. 1 and 1 
vs.2+ deaths, which is easy in
array format,

     odds1 <- log(mice.tab[,,1]/mice.tab[,,2])  # contrast 0:1
     odds2 <- log(mice.tab[,,2]/mice.tab[,,3])  # contrast 1:2+

     odds1
           treatment
     litter          A          B
         7   1.6625477  1.3730491
         8   1.2527630  1.2272297
         9   0.6061358  0.7156200
         10  0.1431008  0.5725192
         11 -1.0986123 -1.0986123
     >

But, for analysis, I want to have these in a data frame, with factors 
litter, treatment and contrast
and a column, 'logodds' containing the entries in the odds1 and odds2 
tables, suitably strung out.

For this problem, the desired result is given by

 > result <- data.frame(expand.grid(litter=factor(7:11), 
treatment=c("A","B"), deaths=c("0:1", "1:2+")),
                        logodds=c(odds1, odds2))
 > result
    litter treatment deaths    logodds
1       7         A    0:1  1.6625477
2       8         A    0:1  1.2527630
3       9         A    0:1  0.6061358
4      10         A    0:1  0.1431008
5      11         A    0:1 -1.0986123
6       7         B    0:1  1.3730491
7       8         B    0:1  1.2272297
8       9         B    0:1  0.7156200
9      10         B    0:1  0.5725192
10     11         B    0:1 -1.0986123
11      7         A   1:2+  0.7884574
12      8         A   1:2+  0.3364722
13      9         A   1:2+  0.1823216
14     10         A   1:2+ -0.1431008
15     11         A   1:2+ -0.3483067
16      7         B   1:2+  0.9985288
17      8         B   1:2+  0.7537718
18      9         B   1:2+  0.7884574
19     10         B   1:2+  0.2006707
20     11         B   1:2+  0.6286087
 >


More generally, for an I x J x K table, where the last factor is the 
response, my desired result
is a data frame of IJ(K-1) rows, with adjacent log odds in a 'logodds' 
column, and ideally, I'd like
to have a general function to do this.

Note that if T is the 10 x 3 matrix of frequencies shown by ftable(), 
the calculation is essentially

log(T) %*% matrix(c(1, -1, 0,
                     0,  1, -1))
followed by reshaping and labeling.

Can anyone help with this?

-- 
Michael Friendly     Email: friendly AT yorku DOT ca
Professor, Psychology Dept. & Chair, Quantitative Methods
York University      Voice: 416 736-2100 x66249 Fax: 416 736-5814
4700 Keele Street    Web:http://www.datavis.ca
Toronto, ONT  M3J 1P3 CANADA