[R-sig-ME] df pseudoreplication in lme model

[Lauren Meyer]

Hello, I am trying to assess weather or not my df are pseudoreplicated in my
lme model.

my study was undertaken on five fish (labeled PC) each tested in two
replicates(REP), across each combination of three treatments HOM, C18 and
CU, each of which had two levels; HOM(SON, BLD),C18 SML, BIG), CU (YES, NO).
The variable we are assessing is the amount of toxin extracted (TOX1). Also,
some data is missing, and has already been removed. I am using an lme
model, as the study design is similar to a split plot design, with a
2X2X2 full factorial design. There are a total of 65 observations.


Here is the model I am using:
>model<- lme(TOX1~HOM*C18*CU, random=~1|PC/REP, data=Data4, method="ML")
Linear mixed-effects model fit by maximum likelihood

which results in 48 DF for everything. Furthermore, I removed the
three way interaction as well as all of the two way interactions as
they were deemed non-significant, producing the final model :

> model5<- lme(TOX1~HOM+C18+CU, random=~1|PC/REP, data=Data4, method="ML")

which has 52 DF

However, I am unsure if these Df are pseudoreplicated and would like some
help in how to determine if this is the case. I am happy to upload the
full dataset and/or any of the outputs if that would help.

Thank you