How to test significance of random effects (intercept and slope) biologically interpretable

I am aiming to assess the inter-individual variability of both random
intercept and slope in response to multiple changing variables.
In order to so, several studies have compared models two by two by changing
their structure. For example, to know whether there is a difference in the
plasticity of the responses between individuals, they compare a model with
both the interest variable*Identity individual as random effect and a model
with only "Identity individual" ad random effect. They then realize a
loglikelihood test and base their results only on the pvalues.

I am looking for an alternative as I have been strongly recommended to
base my results on effect size (and 95% IC) rather than on pvalues. This
has indeed several advantages as it gives the biological magnitude of an
effect, its uncertainty and it is comparable between studies.

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Thanks for your reply David.
In my area, animal behavior ecology,  the comparison of random slope
between studies is very advantageous. It has been underestimate so far but
many authors have pointed out its importance. This is why LRT has limits
because it only tells you whether a random effect is statistical
significant or not. It might be enough in your area but in my field I need
to give a biological meaning of my statistical results.
  There are a couple of alternative to LRT:
1) Iterative approach: based on the AIC score
2) Pseudo-bayesian approach: mcmcsamp
3) Bayesian approach: based on DIC score

 I am more familiar with the AIC approach and was tempted to use this one.
I know there are some drawbacks though, this is why I would like to discuss
with you those different methods and to choose the more appropriate one to
give a biological meaning of my results.

 Thanks,

 Tommy








2013/7/3 David Duffy <David.Duffy at qimr.edu.au>

On Tue, 2 Jul 2013, tommy gaillard wrote:

 I am aiming to assess the inter-individual variability of both random

intercept and slope in response to multiple changing variables.
In order to so, several studies have compared models two by two by
changing
their structure. For example, to know whether there is a difference in the
plasticity of the responses between individuals, they compare a model with
both the interest variable*Identity individual as random effect and a
model
with only "Identity individual" ad random effect. They then realize a
loglikelihood test and base their results only on the pvalues.

I am looking for an alternative as I have been strongly recommended to
base my results on effect size (and 95% IC) rather than on pvalues. This
has indeed several advantages as it gives the biological magnitude of an
effect, its uncertainty and it is comparable between studies.

Hopefully someone else will chime in, but I don't know if I would consider
an estimate of random slope effect as necessarily comparable between
*studies* - that will be really depend on the area.  If the dataset is not
too large, I'd probably find a graphical presentation of the fitted
regression line for each individual more biologically meaningful. Also, a
plot of the distribution of the individual slopes ("raw", or predicted from
your mixed model), as this may not be a single Gaussian.

My simple minded way of thinking is "can we summarize these data using a
model without interactions?", do a LRT and try and work out its
distribution under the null (a hard problem!), and if interaction is
nonignorable, then present what's going on as complicated.

Just 2c.

| David Duffy (MBBS PhD)                                         ,-_|\
| email: davidD at qimr.edu.au  ph: INT+61+7+3362-0217 fax: -0101  /     *
| Epidemiology Unit, Queensland Institute of Medical Research   \_,-._/
| 300 Herston Rd, Brisbane, Queensland 4029, Australia  GPG 4D0B994A v

--
*Tommy Gaillard
Etudiant stagiaire CNRS*
Universit? de Dijon
Master 2 Recherche
Tel: 06-71-81-94-66
Email: tommy.gaillard40 at gmail.com

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