[R-sig-ME] Repeated measures with a non-linear time effect

[Daniel Rubi]

Hi,
I have repeated measures from two groups (treatment and control), three subjects in each, over three time points.

Here's the data in an R data.frame:df <- data.frame(subject=rep(c("T1","T2","T3","C1","C2","C3"),3), group=rep(c(rep("T",3),rep("C",3)),3), time=c(rep(1,6),rep(2,6),rep(3,6)), measure=c(0,253,155,16,232,251,1035,1014,760,98,239,87,371,60,47,0,260,190), col=rep(c(rep("red",3),rep("blue",3)),3), stringsAsFactors=F)


The plot shows the time x group interaction:

R code for producing the plot:
plot(df$time,df$measure,col=df$col,xlab="time",ylab="measure")
legend("topleft",legend=c("treatment","control"),col=c("red","blue"),pch=1)


My question is what model to use to capture the time x group interaction.
I thought:library(lmerTest)fit <- lmer(measure~time+group+time*group+(time|subject),data=df)
might do it.
But the summary of this model doesn't really capture that:> summary(fit)Linear mixed model fit by REMLt-tests use Satterthwaite approximations to degrees of freedom ['lmerMod']Formula: measure ~ time + group + time * group + (time | subject) Data: df
REML criterion at convergence: 210

Scaled residuals: 
   Min     1Q Median     3Q    Max 
-1.228 -0.448 -0.163  0.275  1.923

Random effects:
 Groups   Name        Variance Std.Dev. Corr
 subject  (Intercept) 0.00e+00 0.00e+00     
          time        3.06e-16 1.75e-08  NaN
 Residual             1.05e+05 3.25e+02     
Number of obs: 18, groups:  subject, 6

Fixed effects:
            Estimate Std. Error     df t value Pr(>|t|)
(Intercept)   168.89     286.35  13.78    0.59     0.56
time           -8.17     132.55  13.78   -0.06     0.95
groupT        218.33     404.96  13.78    0.54     0.60
time:groupT    19.83     187.46  13.78    0.11     0.92

Correlation of Fixed Effects:
            (Intr) time   groupT
time        -0.926              
groupT      -0.707  0.655       
time:groupT  0.655 -0.707 -0.926


So my question is what model to use?

Thanks a lot,Dan

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