[R] How to write a two-way interaction as a random effect in a lmer model?

[Martin Henry H. Stevens]

Hi Eva,
A couple questions:
Are repeated measurements taken on rnr? Is rnr "subject"?
Is stress a continuous variable?

See below.
On Dec 11, 2006, at 11:04 AM, Fucikova, Eva wrote:

> Dear All,
>
>
>
> I am working with linear mixed-effects models using the lme4  
> package in
> R. I created a model with the lmer function including some main  
> effects,
> a two-way interaction and a random effect. Now I am searching how I
> could incorporate an interaction between the random effect and one of
> the fixed effects.
>
>
>
> I tried to express the interaction in:
>
> recap_random3<-lmer(breath~handling+stress+stress:handling+(1|rnr) 
> +(0|rn
> r:stress))
>

lmer will want rnr:stress to be a factor, but (0|factor) doesn't make  
sense. To test for random variation in slopes, you want (stress |  
rnr), (or (1|rnr) + (0+stress | rnr) for uncorrelated slopes).

> however R gives me the following error message
>
> :
>
> Error in eval(expr, envir, enclos) : fl[[2]] must be a factor of  
> length
> 1744
>
> In addition: Warning messages:
>
> 1: numerical expression has 1744 elements: only the first used in:
> rnr:stress
>
> 2: numerical expression has 1744 elements: only the first used in:
> rnr:stress
>
>
>
> If I fit this model in SPSS, this gives me output, but I don't know
> whether I can trust that.
>
>
>
>
>
> Therefore I went to look for an alternative:
>
> After looking at the help function in R for lmer I deduced these  
> models.
>
>
> Examples from R
>
> (fm1 <- lmer(Reaction ~ Days + (Days|Subject), sleepstudy))
> (fm2 <- lmer(Reaction ~ Days + (1|Subject) + (0+Days|Subject),
> sleepstudy))
> anova(fm1, fm2)
>
>
>
>
>
> My models would then look like this:
>
>
>
> recap_random0<-lmer(breath~handling+stress (1|rnr))
>
> recap_random1<-lmer(breath~handling+stress (1|rnr)+(0+stress|rnr))
>
Or rather with a plus sign
>
> recap_random0<-lmer(breath~handling+stress + (1|rnr))
>
> recap_random1<-lmer(breath~handling+stress + (1|rnr)+(0+stress|rnr))
or

>
> recap_random0<-lmer(breath~handling+stress (stress | rnr))


>
>
> However, I do not know how to interpret the results. Does the model  
> see
> stress|rnr as an interaction between stress and rnr, or did it take
> stress nested in rnr.
>
>
>
>> summary(recap_random1)
>
> Linear mixed-effects model fit by REML
>
> Formula: breath ~ handling + stress + stress:handling + (1 | rnr) +  
> (0 +
> stress | rnr)
>
>   AIC  BIC logLik MLdeviance REMLdeviance
>
>  9748 9781  -4868       9719         9736
>
> Random effects:
>
>  Groups   Name        Variance Std.Dev.
>
>  rnr      (Intercept) 55.6711  7.4613                       # BUT
>
>  rnr      stress      15.2805  3.9090                       # Does  
> this
> output line express the interaction???
>
If the model statement was correct, these would be variances  
associated with the intercepts and slopes of different levels of rnr.  
Thus, I would call that rnr by stress interaction.

Cheers,
Hank
>  Residual              7.4567  2.7307                    # If not, how
> should the interaction output look like?
>
> number of obs: 1744, groups: rnr, 217; rnr, 217
>
>
>
> Fixed effects:
>
>                  Estimate Std. Error t value
>
> (Intercept)     28.164471   0.716359   39.32
>
> handling         0.012477   0.012330    1.01
>
> stress           0.636979   0.416011    1.53
>
>
>
> Correlation of Fixed Effects:
>
>             (Intr) hndlng stress
>
> handling    -0.645
>
> stress      -0.517  0.667
>
>
>
>
>
> Could anybody please give me an advice how to solve this problem?  
> Which
> way is correct to express interaction in the random factors? How  
> should
> the output look like?
>
>
>
> Thank you in advance,
>
> Eva Fucikova
>
>
>
> ********************************************
>
> Msc. Eva Fucikova
> Netherlands Institute of Ecology (NIOO-KNAW)
> PO Box 40
> 6666 ZG Heteren
> The Netherlands
> tel.: +31 (0)26 4791248
> Email:E.Fucikova at nioo.knaw.nl
>
> *******************************************
>
>
>
>
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>
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Hank Stevens, Assistant Professor
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