[R-sig-ME] the equation of a mixed model fitted using nlme

jos matejus matejus106 at googlemail.com
Wed Mar 18 10:50:23 CET 2015

Dear R mixed modellers

I am writing to the R mixed modelling community to request some help and
advice regarding reporting a mixed model in a publication. I have recently
received referees comments regarding a paper I submitted some time ago. The
referee has requested that I write one of the models used to analyse my
data 'statistically'. I think they mean that I should write out the
equation, and while I don’t think this is unreasonable I am having trouble
doing so. I know many of you have heard the excuse ‘I am not a
statistician’ but I’m afraid that this applies in my case, but I have tried
for a couple of days to figure this one out and harassed many colleagues
but without success. Therefore I am hoping I can prevail on the kindness of
the R mixed modelling community to help me with this problem.

The code used for the model was

vf1Exp<-  varExp(form=~I(days-7)|habitat*treat)

final.model <- lme(length.sq~ poly(I(days-7),2)*treat*habitat, data=mydata,
method="REML",random=~poly(I(days-7),2)|family, weights=vf1Exp)

length.sq = square root transformed length of fish

days = day following exposure (10, one day intervals starting from day 7
after exposure)

treat = two level treatment factor

habitat = two level habitat factor

family = 19 level factor

I have 10 fish per treatment combination (treat*habitat) at each time point
for each family.

The second order polynomial term for day was included to account for non
linear growth and the variance structure to account for an increase in
variance over time that was different depending on the treatment
combination. The 3-way interaction was significant.

How should I represent this model as an equation?

Thanks a million for your help.


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