lme - problems with model

lme(maill6 ~ water * temp  , random= ~1|rep, data = milk)

lme(maill6 ~ water + temp  , random= ~1|rep, data = milk)

Thanks a lot for the answer!

Now, I only have the last one left - How do I get round it?
I knew about the missing cells in the design, but didn´t know how lme
would react on them.

In this case, I can remove the water:temp term, but how can I be sure
that this is the right thing to do?

Is the lm run without the random term enough for removing water:temp
from the lme model, or do I have to do a PROC MIXED run with the
random term to make that decision in a case like this? 

Is it possible (for me)  to understand why MIXED accepts the design
but not lme? They ought to get the same sort of problems, or have I
missed something?

/CG

-------------------
 

CG Pettersson <cg.pettersson at evp.slu.se> writes:

   

Hello all!

I´m working with some training datasets in a SAS-based course,
     

trying
 

to do the same things in lme that I do in PROC MIXED. 

Why don´t lme do an analysis on this dataset when I use the model
water*temp?
The trouble comes from the water:temp term, as it works with
water+temp.
The data are, indeed, assymetric but lm accepts the water:temp
     

term
 

giving results in the F-test near what PROC MIXED produces. MIXED
accepts the model.

The water:temp term can be removed from the model according to the
F-test in SAS (and to the lm model without any random term). Doing
     

so
 

in both MIXED and lme gives reasonably similar results for both
systems.

What do the error message mean, and how can I get around this?
     

Because of missing cells in the design

   

xtabs(~water + temp, milk)
     

    temp
water 100 110 120 140
   1 3   3   3   0  
   2 3   0   3   3  
   3 3   3   0   3  

the model matrix for the fixed effects is rank deficient.  In lm the
rank deficiency is detected and appropriate adjustments made

   

coef(summary(lm(maill6 ~ water * temp, milk)))
     

                 Estimate Std. Error    t value     Pr(>|t|)
(Intercept)     2.17666667  0.1142339 19.0544730 2.218661e-13
water2          0.28333333  0.1615511  1.7538308 9.647013e-02
water3          0.05333333  0.1615511  0.3301329 7.451108e-01
temp110         0.14000000  0.1615511  0.8665987 3.975669e-01
temp120         0.31333333  0.1615511  1.9395305 6.827304e-02
temp140         0.23333333  0.1615511  1.4443312 1.658280e-01
water3:temp110 -0.18666667  0.2284678 -0.8170371 4.245898e-01
water2:temp120  0.09666667  0.2284678  0.4231085 6.772282e-01
water2:temp140  0.21666667  0.2284678  0.9483467 3.555125e-01

Notice that you would expect 6 degrees of freedom for the
   

interaction
 

term but only three coefficients are estimated.

In lme it is much more difficult to compensate for such rank
deficiencies because they could be systematic, like this, or they
could be due to relative precision parameters approaching zero
   

during
 

the iterations.  Because of this we just report the error (although
admittedly we could be a bit more explicit about the nature of the
problem - we are reporting the symptom that we detect, not the
probable cause).


   

The dataset:
     

milk
       

  water temp rep maill4 maill6 maill8 taste4 taste6 taste8
1      1  100   1   2.90   2.13   2.39   10.1   10.0    9.6
2      1  100   2   2.19   2.20   2.27   11.0    9.3   11.0
3      1  100   3   2.13   2.20   2.41   10.1    7.0    9.6
4      1  110   1   2.13   2.34   2.41   11.0   10.5    9.8
5      1  110   2   2.32   2.27   2.25   11.0   11.3   11.2
6      1  110   3   2.13   2.34   2.42    9.4   10.7    9.0
7      1  120   1   2.00   2.49   2.71   11.1   11.2   11.4
8      1  120   2   2.41   2.49   2.46   11.6   11.7    9.6
9      1  120   3   2.22   2.49   2.73   10.7   10.3   10.2
10     2  100   1   2.13   2.41   2.49   11.1   10.8   11.2
11     2  100   2   2.49   2.34   2.53   11.1   11.2    9.2
12     2  100   3   2.80   2.63   3.33    8.3    9.7    7.8
13     2  120   1   2.38   2.85   2.06   11.9   11.2   11.2
14     2  120   2   2.61   2.70   2.70   11.7   10.8   11.0
15     2  120   3   2.77   3.06   3.25   10.9    9.0    9.4
16     2  140   1   2.56   2.84   3.10   10.7   11.2    9.8
17     2  140   2   2.63   2.61   2.81   10.8   11.0   11.6
18     2  140   3   2.99   3.28   3.75    9.2    9.6    9.6
19     3  100   1   2.60   2.24   2.32   10.8    8.4   10.8
20     3  100   2   2.06   2.11   2.20   11.0   11.2   11.8
21     3  100   3   1.98   2.34   2.80   10.3   10.2   10.6
22     3  110   1   1.91   2.06   2.29   11.0   11.4    9.4
23     3  110   2   1.98   1.98   2.15   10.0   11.8   10.6
24     3  110   3   1.98   2.51   2.81    9.3    9.2   10.2
25     3  140   1   2.27   2.42   2.72   10.8   11.6   12.0
26     3  140   2   2.27   2.20   2.41   11.2   11.0   11.4
27     3  140   3   2.20   2.77   3.06   10.5   10.2   10.0

The failing model:
     

lme(maill6 ~ water * temp  , random= ~1|rep, data = milk)
       

Error in MEEM(object, conLin, control$niterEM) : 
       Singularity in backsolve at level 0, block 1

The smaller (working) model:
     

lme(maill6 ~ water + temp  , random= ~1|rep, data = milk)
       

Linear mixed-effects model fit by REML
 Data: milk 
 Log-restricted-likelihood: 4.922178
 Fixed: maill6 ~ water + temp 
(Intercept)      water2      water3     temp110     temp120    
temp140 
2.19466667  0.32800000 -0.04533333  0.07800000  0.32133333 
0.35066667 

Random effects:
Formula: ~1 | rep
       (Intercept)  Residual
StdDev:   0.1477760 0.1323057

Number of Observations: 27
Number of Groups: 3 
     



CG Pettersson, MSci, PhD Stud.
Swedish University of Agricultural Sciences
Dep. of Ecology and Crop Production. Box 7043
SE-750 07 Uppsala