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

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))

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))

recap_random0<-lmer(breath~handling+stress + (1|rnr))

recap_random1<-lmer(breath~handling+stress + (1|rnr)+(0+stress|rnr))

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???

 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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