[R-sig-ME] How to test significance of random effects (intercept and slope) biologically interpretable

[David Duffy]

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