I am fitting a non-linear mixed effects growth model to size-at-age data.
Pinheiro & Bates? book on mixed effect models has been indispensable in the
process and there are only two questions I am unable to find answers to, both
concerning assessment of model assumptions:
1. One part of ?Assumption 2? (p. 174) is that ?random effects are normally
distributed?.
Does this particular assumption include random effects of parameters that
enter non-linearily in a model (which occurs in non-linear mixed effects
models)?
2. One part of ?Assumption 1? (p. 174) is that ?the within-group errors (...)
are independent of the random effects.?
This is the only assumption for which I?ve been unable to locate an assessment
method.
My solution was to plot residuals by random effect estimate (i.e. plots
similar to that in FIGURE 4.16, with ?Subject? substituted by a random
effect), i.e.
> plot(growth.nlme, Asym.i. ~ resid(.) )
> plot(growth.nlme, Rate.i. ~ resid(.) )
> plot(growth.nlme, WinterPoint.i. ~ resid(.) )
where Asym.i., Rate.i. and WinterPoint.i. are the random effect components of
growth model parameters Asym, Rate and WinterPoint.
(The plot requires Asym.i., Rate.i. and WinterPoint.i. to be found in the
dataset, so, after fitting growth.nlme, the random effects estimates were
extracted and added to the original dataset. growth.nlme was fitted again,
based on the extended dataset, which allowed to carry out the above >plot
commands.)
Given the plots, I would look for dependency between random effect estimate
and size of residuals. Is this a valid way to assess the assumption of
independency between within-group errors and random effects?
Any help would be appreciated.
Jørgen
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Jørgen Meisfjord
Dpt. Biology
University of Bergen
PB. 7800
5020 Bergen
Norway
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