[R] F-test degree of freedoms in lme4 ?

Wed Jan 11 17:53:25 CET 2006

I have a problem moving from multistratum aov analysis to lmer.

My dataset has observations of ampl at 4 levels of gapf and 2 levels of bl
on 6 subjects levels VP, with 2 replicates wg each, and is balanced.

Here is the summary of this set with aov:
>> summary(aov(ampl~gapf*bl+Error(VP/(bl*gapf)),hframe2))
>
>Error: VP
>          Df Sum Sq Mean Sq F value Pr(>F)
>Residuals  5    531     106               
>
>Error: VP:bl
>          Df Sum Sq Mean Sq F value Pr(>F)   
>bl         1   1700    1700    37.8 0.0017 **
>Residuals  5    225      45                  
>---
>Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
>
>Error: VP:gapf
>          Df Sum Sq Mean Sq F value  Pr(>F)    
>gapf       3    933     311    24.2 5.3e-06 ***
>Residuals 15    193      13                    
>---
>Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
>
>Error: VP:bl:gapf
>          Df Sum Sq Mean Sq F value Pr(>F)  
>gapf:bl    3   93.9    31.3    3.68  0.036 *
>Residuals 15  127.6     8.5                 
>---
>Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
>
>Error: Within
>          Df Sum Sq Mean Sq F value Pr(>F)
>Residuals 48    318       7               
>
This is mostly identical the analysis by BMDP 4V, except for the
Greenhouse-Geisser epsilons, which are not estimated this way.

I have to analyse a similar dataset, which is not balanced. So I need to
change the method. Following Pinheiro/Bates p.90f, I tried
> hf2.lme <- lme(ampl~gapf*bl,hframe2,random=list(VP=pdDiag(~gapf*bl),bl=pdDiag(~gapf)))
and some variations of this to get the same F tests generated. At least,
I got the F-test on error stratum VP:bl this way, but not the other two:
>> anova(hf2.lme)
>            numDF denDF F-value p-value
>(Intercept)     1    78  764.86  <.0001
>gapf            3    78   17.68  <.0001
>bl              1     5   37.81  0.0017
>gapf:bl         3    78    2.99  0.0362

Then I tried to move to lmer.
I tried to find something equivalent to the above lme call, with no
success at all.

In case, that the problem is in the data, here is the set:

VP ampl wg bl gapf
1 WJ 22 w s 144
2 CR 23 w s 144
3 MZ 25 w s 144
4 MP 34 w s 144
5 HJ 36 w s 144
6 SJ 26 w s 144
7 WJ 34 w s 80
8 CR 31 w s 80
9 MZ 33 w s 80
10 MP 36 w s 80
11 HJ 37 w s 80
12 SJ 32 w s 80
13 WJ 34 w s 48
14 CR 37 w s 48
15 MZ 38 w s 48
16 MP 38 w s 48
17 HJ 40 w s 48
18 SJ 32 w s 48
19 WJ 36 w s 16
20 CR 40 w s 16
21 MZ 39 w s 16
22 MP 40 w s 16
23 HJ 40 w s 16
24 SJ 38 w s 16
25 WJ 16 g s 144
26 CR 28 g s 144
27 MZ 18 g s 144
28 MP 33 g s 144
29 HJ 37 g s 144
30 SJ 28 g s 144
31 WJ 28 g s 80
32 CR 33 g s 80
33 MZ 24 g s 80
34 MP 34 g s 80
35 HJ 36 g s 80
36 SJ 30 g s 80
37 WJ 32 g s 48
38 CR 38 g s 48
39 MZ 34 g s 48
40 MP 37 g s 48
41 HJ 39 g s 48
42 SJ 30 g s 48
43 WJ 36 g s 16
44 CR 34 g s 16
45 MZ 36 g s 16
46 MP 40 g s 16
47 HJ 40 g s 16
48 SJ 36 g s 16
49 WJ 22 w b 144
50 CR 24 w b 144
51 MZ 20 w b 144
52 MP 26 w b 144
53 HJ 22 w b 144
54 SJ 16 w b 144
55 WJ 26 w b 80
56 CR 24 w b 80
57 MZ 26 w b 80
58 MP 27 w b 80
59 HJ 26 w b 80
60 SJ 18 w b 80
61 WJ 28 w b 48
62 CR 23 w b 48
63 MZ 28 w b 48
64 MP 29 w b 48
65 HJ 27 w b 48
66 SJ 24 w b 48
67 WJ 32 w b 16
68 CR 26 w b 16
69 MZ 30 w b 16
70 MP 28 w b 16
71 HJ 30 w b 16
72 SJ 22 w b 16
73 WJ 22 g b 144
74 CR 18 g b 144
75 MZ 18 g b 144
76 MP 26 g b 144
77 HJ 22 g b 144
78 SJ 18 g b 144
79 WJ 24 g b 80
80 CR 26 g b 80
81 MZ 30 g b 80
82 MP 26 g b 80
83 HJ 26 g b 80
84 SJ 24 g b 80
85 WJ 28 g b 48
86 CR 28 g b 48
87 MZ 27 g b 48
88 MP 30 g b 48
89 HJ 26 g b 48
90 SJ 16 g b 48
91 WJ 28 g b 16
92 CR 19 g b 16
93 MZ 24 g b 16
94 MP 32 g b 16
95 HJ 30 g b 16
96 SJ 22 g b 16
-- 
Dipl.-Math. Wilhelm Bernhard Kloke
Institut fuer Arbeitsphysiologie an der Universitaet Dortmund
Ardeystrasse 67, D-44139 Dortmund, Tel. 0231-1084-257