I have a model with a random-nested factor, I am comparing it with a model without the random factor (to test significance of random factor) as follows:
M2<-lme(score ~ disease* time* week, random=~1|treatment/Id, method = "REML", data = Dat1) M3<-gls(score ~ disease * time * week, method = "REML", data = Dat1)
Comparing the two I get:
df AIC M2 21 -2662.715 M3 19 -2612.308
This leads me to believe
M3 would be a better model (AIC closer to 0), meaning random could be taken out, or at least that
M3 are different.
I check with ANOVA:
Model df AIC BIC logLik Test L.Ratio p-value M2 1 21 -2662.715 -2550.233 1352.358 M3 2 19 -2612.308 -2510.538 1325.154 1 vs 2 54.40752 <.0001
and p is significant
I am not sure how to interpret this,
M3 are significantly different, but does this mean random effect is a significant factor, or does it mean
M3 is a better model and the therefore random effect is not significant?