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

[peter dalgaard]

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.

> Regards
> Gordon
> 
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-- 
Peter Dalgaard
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com