Hello.  This is not a technical question but rather an interpretational
one, so I apologise if it is not appropriate for this discussion group.
I am fitting a mixed model involving two predictor variables: x1 and x2.
x1 varies between groups but is constant within groups while x2 varies
both between and within groups.  I fit two nested models.

Model 1:  lme(y~x1*x2, random=~1|groups).  In this model, in which only
the intercepts randomly vary, both main fixed terms and their
interaction are highly significant.

Model 2: lme(y~x1*x2, random=~1+x1|groups).  In this model, in which
both the intercepts and the partial slope of x1 randomly vary, only x2
remains significant as a fixed term; both x1 and x1:x2 loose
significance (p>0.05).

 

Here is my interpretation, and I would like to know if it is correct:

The partial slope of x2 changes as a function of x1 (thus, a real
interaction).  However, because x1 only varies between groups,  the
variation in the partial slopes of x2 only occurs between groups.  Thus,
when I allow the partial slope of x2 to be random, these between-group
changes in its partial slope remove the effect of x1 (whose only effect
is to change these partial slopes between groups).

 

Does this make sense?  If not, how should one explain the differences in
the significance of the fixed terms in these two nested models?

 

Bill Shipley

Associate Editor, Ecology

North American Editor, Annals of Botany

Département de biologie, Université de Sherbrooke,

Sherbrooke (Québec) J1K 2R1 CANADA

Bill.Shipley@USherbrooke.ca

 <http://callisto.si.usherb.ca:8080/bshipley/>
http://callisto.si.usherb.ca:8080/bshipley/

 


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