# Fixed effects numerator df

From: Holland, Jim <Jim.Holland_at_ARS.USDA.GOV>
Date: Mon, 8 Feb 2010 09:59:25 -0500

Here is what surely is a very stupid question. I have done an analysis
where one factor is a fixed effect called "hr", which has 3 levels in
the data set. The model and a bit of .asr and .pvs output is given
below, so you can see that the data summary indicates 3 levels for this
factor and the means for this factor have 3 levels. The ANOVA output is
troubling, however, because the F-test for hr has 3 NUMERATOR df instead
of the 2 I expect. The male and female terms each have 2 levels and 1
df, and the hr*male and hr*female interactions correctly have 2
numerator df. But the hr*male*female has 3 rather than 2, unexpectedly.

Otherwise the output looks fine. I thought that perhaps the several
random term variance components going to zero may contribute to the
problem, but dropping them leads to the same result.

So, I must be doing something very stupid, but cannot figure it out!

!Path 2

tuberize ~ hr female male hr.male hr.female hr.male.female,

!r trial trial.hr rep.hr.trial trial.male trial.female trial.male.female
trial.hr.male trial.hr.female trial.hr.male.female,

clone.male.female trial.clone.male.female hr.clone.male.female
trial.hr.clone.male.female

predict hr

Model term Size #miss #zero MinNon0 Mean MaxNon0

1 fam 4 0 0 1 2.5079 4

2 clone 504 0 0 1 252.8171 504

3 female 2 0 0 1 1.4993 2

4 male 2 0 0 1 1.5093 2

6 rep 3 0 0 1 2.0004 3

7 hr 3 0 0 1 1.9731 3

8 trial 2 0 0 1 1.4695 2

9 hr_trial 6 0 0 1 3.3815 6

10 code 24 0 0 1 12.0339 24

Etc...

12 LogL=-1502.61 S2= 0.30679 8140 df

Source Model terms Gamma Component Comp/SE % C

trial 2 2 0.274478E-06 0.842059E-07 0.00 0 B

trial.male 4 4 0.404772E-09 0.124178E-09 0.00 0 B

trial.female 4 4 0.404772E-09 0.124178E-09 0.00 0 B

trial.hr 6 6 0.313836 0.962804E-01 1.11 0 P

trial.male.female 8 8 0.404772E-09 0.124178E-09 0.00 0 B

trial.hr.male 12 12 0.210220E-01 0.644925E-02 0.54 0 P

trial.hr.female 12 12 0.422180E-02 0.129519E-02 0.16 0 P

rep.hr.trial 18 18 0.228102E-01 0.699783E-02 2.23 0 P

trial.hr.male.female 24 24 0.345968E-01 0.106138E-01 1.01 0 P

clone.male.female 2016 2016 0.296399 0.909309E-01 5.82 0 P

trial.clone.male.fem 4032 4032 0.157650E-09 0.483647E-10 0.00 0 B

hr.clone.male.female 6048 6048 0.838479 0.257233 13.61 0 P

trial.hr.clone.male.12096 12096 0.505442 0.155062 14.81 0 P

Variance 8152 8140 1.00000 0.306785 51.34 0 P

Analysis of Variance NumDF DenDF_con F_inc F_con M P_con

7 hr 3 3.1 106.69 106.69 a 0.002

3 female 1 7.1 14.83 14.87 A 0.006

4 male 1 5.2 9.12 9.13 A 0.029

13 hr.male 2 4.0 2.13 2.13 B 0.235

14 hr.female 2 4.7 14.97 14.97 B 0.008

16 hr.male.female 3 5.9 0.09 0.09 C 0.965

Results of predict statement:

hr Predicted_Value Standard_Error Ecode

20 1.4526 0.2314 E

14 2.0116 0.2314 E

8 3.3285 0.2315 E

SED: Overall Standard Error of Difference 0.3267

Jim Holland

USDA-ARS Plant Science Research Unit

Department of Crop Science

North Carolina State University

Phone: 919-513-4198

Fax: 919-515-7959

Received on Mon Feb 08 2010 - 09:59:25 EST

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