R help - Feb 2010 - Adjusted means and generalized chain block designs

Dear Colleagues,

John Mandel ( Chain block designs with two-way elimination of heterogeneity.
Biometrics 10, 251-272 ,1954).
extended the class of chain block designs (Youden & Conner (1953)
to elimination of both row and column (blocks) effects.

These experimental designs can be useful in engineering
and other fields.

I am having difficulty obtaining his adjusted treatment means
in his example, shown below, by the use of lm(), or glm(), or ols().
However, I can obtain Mandel's analysis of variance.

# Mandel example, op. cit. page 263
# y are logs of treadwear, blocks are wheel positions,
# and rows are runs.
  blocks = factor( rep(1:4, 4) )    # blocks
  rows = factor(c( 1,1,1,1, 2,2,2,2, 3,3,3,3, 4,4,4,4)  )  #pos
  trt = factor( c(1:8, 7,8,2,1,3,4,6,5) )  # tires
  y = c(1.802, 1.862, 1.173, 1.762,
        1.935, 2.072, 1.703, 1.935,
        1.610, 1.568, 1.267, 1.522,
        1.816, 1.935, 1.418, 1.594)

  xtabs(y ~ rows + blocks)    # tabulate by row and column
 
# One of my attempts using lm() from the stats package:
  m1 = lm( y ~  trt + blocks + rows) 
 
Mandel obtrain the following adjusted means
mandel = c(1.728, 1.817, 1,588, 1.785,
                  1.512, 1. 678, 1.720, 1.658)

Can anyone shed light on how to obtain  in R
the correct treatment means,
adjusted for both row and column effects (blocks)
in these designs?

Cordially,
Giles Crane
gilescrane at verizon.net

To whom it may concern:

I compared several R package results,
and manual checked two generalized chain block
design experiments. The correct adjusted
treatment means can be computed
by using the effects library as follows:

    library(effects)

    aov1 = aov(y~blocks+rows+trt)
    means.aov = as.vector( allEffects(aov1)$trt$fit ) 

As a further check, I programmed an R function
to compute the adjusted treatment means
via John Mandel's manual method in his paper,
a somewhat lengthy and tricky task.

Finally, I will present  motivating examples
on behalf of my colleagues Cynthia Collins and 
Karin Mille, an index of Generalized Block Designs, and
GCB library in draft form, includingD-efficiency,
at the NIST UseR 2010 Conference
in July.

These designs are interesting combinatorially,
and quite applicable to physical measurements
which are made with high precision.

Best wishes,
Giles

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