[R] Re: Mixed effects with nlme

[Manuel Ato Garcia]

Hi, R-users:

 Last week I send a request for help to this list. I have receive until now
two kindly responses from Spencer Graves and Renauld Lancelot. They both 
point interesting things to fit an adequate model to my data but
unfortunately 
it persists without a satisfactory solution. 

 I propose again the same problem but using with a different dataset
(Assay), taken from Pinheiro and Bates' book on page 163, that is relevant
with crossed 
random effects. I have fitted the same model (p. 165)

>fmAssay <- lme(logDens ~ sample * dilut, Assay, random=pdBlocked(list(,
         pdIdent(~1), pdIdent(~sample-1),pdIdent(~dilut-1))) )

and the results with "anova" function (p. 166) are
 
             numDF denDF  F-value p-value
(Intercept)      1    29 537.6294  <.0001
sample           5    29  11.2103  <.0001
dilut            4    29 420.5458  <.0001
sample:dilut    20    29   1.6072  0.1192

 The problem is that with this approach one obtains correct F-values, but 
using a common residual term for DenDF that is a combination of (Block +
Block:sample + Block:dilut). Then probability values are different to that
obtained when we used the classical AOV funtion to fit the same model,
because in this case each term is mapped with a error term (so "sample"
uses "Block:sample", "dilut" uses "Block:dilut", and "sample:dilut" uses
"Block:sample:dilut"):

>mod<-aov(logDens ~ sample*dilut + Error(Block+Block/sample+Block/dilut),
data=Assay)
>summary(mod)

Error: Block
          Df    Sum Sq   Mean Sq F value Pr(>F)
Residuals  1 0.0083115 0.0083115               

Error: Block:sample
          Df   Sum Sq  Mean Sq F value   Pr(>F)
sample     5 0.276153 0.055231  11.213 0.009522
Residuals  5 0.024627 0.004925                 

Error: Block:dilut
          Df Sum Sq Mean Sq F value    Pr(>F)
dilut      4 3.7491  0.9373  420.79 1.684e-05
Residuals  4 0.0089  0.0022                  

Error: Within
             Df   Sum Sq  Mean Sq F value Pr(>F)
sample:dilut 20 0.055525 0.002776  1.6069 0.1486
Residuals    20 0.034555 0.001728  


 Obviously, the interest on linear mixed effects is open with the
possibility of modeling with correlated and/or heterocedastic errors, and
this end cannot
be pursued with AOV function.

 Summarizing, the problem is that I have not found a way to obtain with
NLME the same results (DF, F-ratios and probabilities) that I get with AOV and
multistratum errors. Is this an inconvenience of program?, probably due
to the impossibility to use multiple nested arguments as 

 random(~1|Block/sample+dilut) or  random(~1|Block/sample*dilut)
 
SAS MIXED can also fit these data and obtain correct results by means of a
combination of "random" and "repeated" arguments:

 model = sample dilut sample*dilut;
 random = Block sample*Block dilut*Block;
 repeated /type=cs Sub=Block;


              Type 3 Tests of Fixed Effects

                      Num     Den
            Effect     DF      DF    F Value    Pr > F
            sample      5       5      11.21    0.0095
             dilut      4       4     420.79    <.0001
      sample*dilut     20      20       1.61    0.1486


May be possible obtain the same results with NLME function?

 I would appreciate any kind of help.

 Best regards,


			Manuel Ato
			University of Murcia
			Spain
			e-mail: matogar at um.es