[R-sig-ME] interaction term in null hypothesis

[Junqian Gordon Xu]

On 4/26/11 4:53 AM, peter dalgaard wrote:
> 
> On Apr 26, 2011, at 00:05 , Junqian Gordon Xu wrote:
> 
>> I have a quick question for a simple model as below:
>> 
>>> Fix + (1 | Rand) + (1 | Rand : Fix)
>> 
>> Which one is the null hypothesis:
>> 
>>> 1 + (1 | Rand)
>> 
>> or
>> 
>>> 1 + (1 | Rand) + (1 | Rand : Fix)
>> 
>> To me the interaction term (1 | Rand : Fix) does not make much
>> sense if no fixed effect term is present in the model, but I'm not
>> sure.
>> 
> 
> It does make sense, at least sometimes. For one thing, such
> interactions are often aliased to aspects of the experimental design;
> e.g., if you have randomized different treatment to left side and the
> right side of test subjects, then the random interaction is
> equivalent to the (random) difference between the two sides within
> the same subject. Also, you could conceivably have a kill-or-cure
> drug with positive effects for some and negative effects for others,
> with the question being whether the total effect is positive or
> negative.

It's helpful to put it into the context. Thanks.

Gordon