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.

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