[R] random interactions in lme

Ignacio Colonna iacolonn at uiuc.edu
Tue Apr 26 18:36:39 CEST 2005


The code below gives almost identical results for a split-block analysis in
lme and SAS proc mixed, in terms of variance components and F statistics. It
just extends the example in Pinheiro & Bates (p.162) to a split block
design. 

I am including below the SAS code and the data in case you want to try it.
The only difference between both is in the df for the F denominator, which I
wasn't able to compute correctly in lme, but this may be my ignorance on how
to correctly specify the model. It is not a big issue though, as the F
values are identical, so you can compute the p-values if you know how to
obtain the correct DenDF. 

# a split block design
spbl.an1<-lme(yield~rowspace*ordered(tpop),random=list(rep=pdBlocked(list(pd
Ident(~1),
pdIdent(~rowspace-1),pdIdent(~ordered(tpop)-1)))),data=spblock)

* SAS code
proc mixed data=splitblock method=reml;
class rep rowspace tpop;
model yield=rowspace tpop rowspace*tpop;
random rep rep*rowspace rep*tpop;
run;


# data

rowspace	tpop	rep	plot	yield
9	60	1	133	19
9	120	1	101	19.5
9	180	1	117	22
9	240	1	132	19.4
9	300	1	116	23.9
18	60	1	134	15.8
18	120	1	102	26.2
18	180	1	118	21.9
18	240	1	131	20
18	300	1	115	23.3
9	60	2	216	20.6
9	120	2	233	22
9	180	2	201	23.4
9	240	2	217	28.2
9	300	2	232	25.9
18	60	2	215	19.7
18	120	2	234	30.3
18	180	2	202	22.4
18	240	2	218	27.9
18	300	2	231	28.5
9	60	3	309	20.8
9	120	3	308	21.6
9	180	3	324	24.6
9	240	3	340	25.3
9	300	3	325	35.3
18	60	3	310	17.2
18	120	3	307	23.6
18	180	3	323	24.9
18	240	3	339	30.7
18	300	3	326	33
9	60	4	435	15.6
9	120	4	403	20.4
9	180	4	430	24.4
9	240	4	414	21
9	300	4	419	23.2
18	60	4	436	17.7
18	120	4	404	23.6
18	180	4	429	21.7
18	240	4	413	24.4
18	300	4	420	26.2


Ignacio


-----Original Message-----
From: r-help-bounces at stat.math.ethz.ch
[mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Douglas Bates
Sent: Monday, April 25, 2005 6:40 PM
To: Jacob Michaelson
Cc: r-help at stat.math.ethz.ch
Subject: Re: [R] random interactions in lme

Jacob Michaelson wrote:
> 
> On Apr 24, 2005, at 8:52 AM, Douglas Bates wrote:
> 
>> Jacob Michaelson wrote:
>>
>>> Hi All,
>>> I'm taking an Experimental Design course this semester, and have 
>>> spent many long hours trying to coax the professor's SAS examples 
>>> into something that will work in R (I'd prefer that the things I 
>>> learn not be tied to a license).  It's been a long semester in that 
>>> regard.
>>> One thing that has really frustrated me is that lme has an extremely 
>>> counterintuitive way for specifying random terms.  I can usually 
>>> figure out how to express a single random term, but if there are 
>>> multiple terms or random interactions, the documentation available 
>>> just doesn't hold up.
>>> Here's an example: a split block (strip plot) design evaluated in SAS 
>>> with PROC MIXED (an excerpt of the model and random statements):
>>> model DryMatter = Compacting|Variety / outp = residuals ddfm = 
>>> satterthwaite;
>>> random Rep Rep*Compacting Rep*Variety;
>>> Now the fixed part of that model is easy enough in lme: 
>>> "DryMatter~Compacting*Variety"
>>> But I can't find anything that adequately explains how to simply add 
>>> the random terms to the model, ie "rep + rep:compacting + 
>>> rep:variety"; anything to do with random terms in lme seems to go off 
>>> about grouping factors, which just isn't intuitive for me.
>>
>>
>> The grouping factor is rep because the random effects are associated 
>> with the levels of rep.
>>
>> I don't always understand the SAS notation so you may need to help me 
>> out here.  Do you expect to get a single variance component estimate 
>> for Rep*Compacting and a single variance component for Rep*Variety?  
>> If so, you would specify the model in lmer by first creating factors 
>> for the interaction of Rep and Compacting and the interaction of Rep 
>> and Variety.
>>
>> dat$RepC <- with(dat, Rep:Compacting)[drop=TRUE]
>> dat$RepV <- with(dat, Rep:Variety)[drop=TRUE]
>> fm <- lmer(DryMatter ~ Compacting*Variety+(1|Rep)+(1|RepC)+(1|RepV), dat)
>>
>>
>>
> 
> Thanks for the prompt reply.  I tried what you suggested, here's what I 
> got:
> 
>  > turf.lme=lmer(dry_matter~compacting*variety+(1|rep)+(1|rc)+(1|rv), 
> turf.data)
> Error in lmer(dry_matter ~ compacting * variety + (1 | rep) + (1 | rc) +
:
>     entry 3 in matrix[9,2] has row 3 and column 2
> 
> Just to see what the problem was, I deleted the third random term, and 
> it didn't complain:
> 
>  > turf.lme=lmer(dry_matter~compacting*variety+(1|rep)+(1|rv), turf.data)
>  > anova(turf.lme)
> Analysis of Variance Table
>                    Df Sum Sq Mean Sq  Denom F value    Pr(>F)
> compacting          5 10.925   2.185 36.000  18.166  5.68e-09 ***
> variety             2  2.518   1.259 36.000  10.468 0.0002610 ***
> compacting:variety 10  6.042   0.604 36.000   5.023 0.0001461 ***
> 
> Now obviously this isn't a valid result since I need that third term; 
> but interestingly, it didn't matter which term I deleted, so long as 
> there were only two random terms.  Any ideas as to what the error 
> message is referring to?
> 
> Thanks for the help,
> 
> Jake Michaelson

Unfortunately, yes I do know what the error message is referring to - a 
condition that should not happen.  This is what Bill Venables would call 
an "infelicity" in the code and others with less tact than Bill might 
call a bug.

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