[R] degrees of freedom in a LME model

[Federico Calboli]

Dear Prof. Bates,

Thank you for your reply. I did actually check the book at pages 89-92, but
I have to say I found it a bit "cryptic", if not downright confusing, for a
genetist like me. Any day of the week. 

To use the example in the book, I cannot see why MACHINE is inner to
WORKER. Or where the Pi = sum of df for the term estimatet at level i... 

To me it's just a two way anova with one random effect + one interaction.
My df correspond to those in the book, but I calculated them in the "bog
standard" way of 2 df for 3 machines, 5 df for 6 workers and 2 * 5 = 10 df
for the interaction...oh well...

I attach the datasest (I did a sample with replace = TRUE, should have
thought of this earlier...). I hope thing would be clearer. It is obvious
that if I consider day a "factor", as I have just one datapoint per day per
line within regime, I end up using all my degrees of freedom:

2 df for 3 regimes
6 df for line within regime
8 df for day (9 days, day as factor)
16 df for regime * day
48 df for line * day
total 80 df, with 0 df remaining for the error. A bit of a problem I
daresay, but I did not collect the data!

BUT I did calculate my anova considering day as a continuous variable,

2 df for 3 regimes
6 df for line within regime
1 df for day (day as a number)
2 df for regime * day
6 df for line * day
total 17 df, with 63 df remaining for the error. 

I still do not get why the interaction term Regime*Day is not tested on the
interaction Line-in-regime*Day... In my analysis LME is clumping Error and
Line-in-regime*Day together, judging by the df I was talking about in my
previuos email. To me it should be just another "bog standard"
situation...But if I were smart enough to be a statistician I would not be
here doing genetics ;)

Regards,
Federico Calboli



Day	Line	Regime	Matings
2	501	es	0.4
4	501	es	0.32989691
9	501	es	0.48484848
11	501	es	0.72727273
16	501	es	0.34042553
18	501	es	0.56470588
25	501	es	0.37509377
30	501	es	0.22222222
32	501	es	0.77777778
2	502	es	0.57142857
4	502	es	1.06666667
9	502	es	0.16
11	502	es	0.4
16	502	es	0.4
18	502	es	0.33333333
25	502	es	0.80808081
30	502	es	0.48
32	502	es	0.25531915
2	503	es	0
4	503	es	0.72727273
9	503	es	0.3
11	503	es	0.77777778
16	503	es	0.34042553
18	503	es	1.06666667
25	503	es	0.32989691
30	503	es	1.24444444
32	503	es	0.19153725
2	fb1	fb	0.72727273
4	fb1	fb	0.42105263
9	fb1	fb	0.32989691
11	fb1	fb	0.32323232
16	fb1	fb	0.37509377
18	fb1	fb	0.51612903
25	fb1	fb	0.4
30	fb1	fb	0.24742268
32	fb1	fb	0.24742268
2	fb2	fb	1.33333333
4	fb2	fb	0.25263158
9	fb2	fb	0.66666667
11	fb2	fb	1.06666667
16	fb2	fb	0.97959184
18	fb2	fb	0.42105263
25	fb2	fb	0.57142857
30	fb2	fb	1.15555556
32	fb2	fb	0.80808081
2	fb3	fb	0.18952106
4	fb3	fb	0.66666667
9	fb3	fb	1.22033898
11	fb3	fb	0.35955056
16	fb3	fb	1.68421053
18	fb3	fb	0.57461174
25	fb3	fb	0.93506493
30	fb3	fb	0.80808081
32	fb3	fb	0.57461174
2	mb1	mb	0.22222222
4	mb1	mb	0.3902439
9	mb1	mb	0.42105263
11	mb1	mb	0.48484848
16	mb1	mb	0.55555556
18	mb1	mb	1.68421053
25	mb1	mb	0.4
30	mb1	mb	0.16
32	mb1	mb	0.09523809
2	mb2	mb	0.77777778
4	mb2	mb	0.68817204
9	mb2	mb	0.25263158
11	mb2	mb	1.33333333
16	mb2	mb	0.5
18	mb2	mb	0.37509377
25	mb2	mb	0.16494845
30	mb2	mb	2.46153846
32	mb2	mb	0.47058824
2	mb3	mb	1.06666667
4	mb3	mb	0.5
9	mb3	mb	0.5
11	mb3	mb	0.38095238
16	mb3	mb	0.26373626
18	mb3	mb	0.87912088
25	mb3	mb	0.55555556
30	mb3	mb	0.74418605
32	mb3	mb	1.33333333

>
>I think your calculation is based on using only within-strata
>information whereas lme uses both within-strata and between-strata
>information for estimates of effects.
>
>The way that we calculate denominator degrees of freedom is described
>on pp. 90-91 of Pinheiro and Bates (2000).  For each term in the
>fixed-effects we determine the innermost level of the random effects
>at which is it changing.  Because Regime is constant for each Line it
>has the fewest degrees of freedom but Day is changing within Line so
>terms in Day have more degrees of freedom.  Is this what you intended?
>
>I must admit I am having difficulty understanding the structure of the
>experiment but it is still Monday morning for me so perhaps that is
>not surprising.


=========================

Federico C.F. Calboli

Department of Biology
University College London
Room 327
Darwin Building
Gower Street
London
WClE 6BT

Tel: (+44) 020 7679 4395 
Fax (+44) 020 7679 7096
f.calboli at ucl.ac.uk