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 LineRegime 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.
32 501 es 0.7778
2 502 es 0.57142857
4 502 es 1.0667
9 502 es 0.16
11 502 es 0.4
16 502 es 0.4
18 502 es 0.
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 0.7778
16 503 es 0.34042553
18 503 es 1.0667
25 503 es 0.32989691
30 503 es 1.2444
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.
4 fb2 fb 0.25263158
9 fb2 fb 0.6667
11 fb2 fb 1.0667
16 fb2 fb 0.97959184
18 fb2 fb 0.42105263
25 fb2 fb 0.57142857
30 fb2 fb 1.1556
32 fb2 fb 0.80808081
2 fb3 fb 0.18952106
4 fb3 fb 0.6667
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.
4 mb1 mb 0.3902439
9 mb1 mb 0.42105263
11 mb1 mb 0.48484848
16 mb1 mb 0.5556
18 mb1 mb 1.68421053
25 mb1 mb 0.4
30 mb1 mb 0.16
32 mb1 mb 0.09523809
2 mb2 mb 0.7778
4 mb2 mb 0.68817204
9 mb2 mb 0.25263158
11 mb2 mb 1.
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 1.0667
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 0.5556
30 mb3 mb 0.74418605
32 mb3 mb 1.
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
