[R] Balanced design, differences in results using anova and lmer/anova

[Lars Kunert]

Hi, I am trying to do an analysis of variance for an unbalanced design.
As a toy example, I use a dataset presented by K. Hinkelmann and O.
Kempthorne in "Design and Anaylysis of Experiments" (p353-356).
This example is very similar to my own dataset, with one difference: it
is balanced.
Thus it is possible to do an anaylsis using both: (1) anova, and (2) lmer.
Furthermore, I can compare my results with the results presented in the
book (the book uses SAS).

In short:
> using anova, I can reproduce the results presented in the book.
> using lmer, I fail to reproduce the results
However, for my "real" analysis, I need lmer - what do I do wrong?

The example uses as randomized complete block desigh (RCBD) with a
nested blocking structure
and subsampling.

response:
  height (of some trees)
covariates:
  HSF (type of the trees)
nested covariates:
  loc (location)
  block  (block is nested in location)

# the data (file: pine.txt) looks like this:

loc    block    HSF    height
1    1    1    210
1    1    1    221
1    1    2    252
1    1    2    260
1    1    3    197
1    1    3    190
1    2    1    222
1    2    1    214
1    2    2    265
1    2    2    271
1    2    3    201
1    2    3    210
1    3    1    220
1    3    1    225
1    3    2    271
1    3    2    277
1    3    3    205
1    3    3    204
1    4    1    224
1    4    1    231
1    4    2    270
1    4    2    283
1    4    3    211
1    4    3    216
2    1    1    178
2    1    1    175
2    1    2    191
2    1    2    193
2    1    3    182
2    1    3    179
2    2    1    180
2    2    1    184
2    2    2    198
2    2    2    201
2    2    3    183
2    2    3    190
2    3    1    189
2    3    1    183
2    3    2    200
2    3    2    195
2    3    3    197
2    3    3    205
2    4    1    184
2    4    1    192
2    4    2    197
2    4    2    204
2    4    3    192
2    4    3    190

#
# then I load the data
#
read.data = function()
{
	d = read.table( "pines.txt", header=TRUE )

	d$loc       = as.factor( d$loc   )
	d$block.tmp = as.factor( d$block )
	d$block     = ( d$loc:d$block.tmp )[drop=TRUE]  # lme4 does not support
implicit nesting

	d$HSF   = as.factor( d$HSF )

	return( d )
}

d = read.data()


#
# using anova.....
#
m.aov = aov( height ~ HSF*loc + Error(loc/block + HSF:loc/block), data=d )
summary( m.aov )

#
# I get:
#
Error: loc
    Df Sum Sq Mean Sq
loc  1  20336   20336

Error: loc:block
          Df  Sum Sq Mean Sq F value Pr(>F)
Residuals  6 1462.33  243.72

Error: loc:HSF
        Df  Sum Sq Mean Sq
HSF      2 12170.7  6085.3
HSF:loc  2  6511.2  3255.6

Error: loc:block:HSF
          Df  Sum Sq Mean Sq F value Pr(>F)
Residuals 12 301.167  25.097

Error: Within
          Df Sum Sq Mean Sq F value Pr(>F)
Residuals 24 529.00   22.04

#
# which is, what I expected, however, using lmer....
#
m.lmer = lmer( height ~ HSF*loc + HSF*(loc|block), data=d )
anova( m.lmer )

#
# I get:
#
Analysis of Variance Table
        Df  Sum Sq Mean Sq
HSF      2 12170.7  6085.3
loc      1  1924.6  1924.6
HSF:loc  2  6511.2  3255.6

#
# what is, at least not what I expected...
#
Thanks for your help, Lars