Dear all,
Consider a completely randomized block design (let's use data(Oats)
irrespoctive of the split-plot design it was arranged in). Look:
library(nlme)
fit <- lme(yield ~ nitro, Oats, random = ~1|Block, method="ML")
fit2 <- lm(yield ~ nitro + Block, Oats)
anova(fit, fit2)
gives this:
Model df AIC BIC logLik Test L.Ratio p-value
fit 1 4 624.3245 633.4312 -308.1623
fit2 2 8 611.9309 630.1442 -297.9654 1 vs 2 20.39366 4e-04
Clearly, considering block a random term is worse than considering it
a fixed term. Let's see if blocking should be included in the model at
all:
fit3 <- lm(yield ~nitro, Oats)
anova(fit2,fit3)
which gives a very small P value in favor of fit2, which suggests the
block term should be included. So, I go for the second model, with
block considered fixed.
Is this indeed how I should generally proceed when choosing the
optimum model for a situation that calls for mixed effects? Of course,
the example above is overly simplistic, yet such situations can occur
-- from a complex model with a couple of random terms one can finally
get to a simple fixed-effects model. Please comment.
Thanks in advance,
Stats Wolf
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