R help - Oct 2010 - specifying lme function with a priori hypothesis concerning between-group variation in slopes

I want to specify a 2-level mixed model using the lme function in order to
test an a priori hypothesis about the between-group values of the slopes but
don't know how to do this .  Here is the problem.

Consider first the case of a single group.  The model is: Y_i= a +bX_i +
error where I indexes the different values of X and Y in this group .   The
a priori hypothesis of the slope is: b=K.  This is easily tested with a
t-test (b-K=0).

Now imagine that there are j groups.  For each group j the model is: Y_ija_j +
b_jX_ij + error.  Both the intercepts (a) and the slopes (b) are
allowed to vary between groups.  The a priori (null) hypothesis of interest
involved the between-group values of the slopes and  is: b_j=Kj where Kj is
specified a priori for each group j based on theoretical considerations but
whose values differ between groups.

This is clearly a mixed-model problem.  I know how to specify the model in
lme but I don't know how to set up the inferential test that b_j=Kj for all
j groups versus the alternative hypothesis that b_j is not equal to Kj for
at least one group.  Any help in explaining how to do this using the mle
function in R is appreciated.

Thanks.

Bill Shipley
D?partement de biologie
Universit? de Sherbrooke
Sherbrooke (Qu?bec) J1K 2R1
(819) 821-8000, 62079
(819) 821-8049 (Fax)

NEW! Shipley, B. (2010). From plant traits to vegetation structure: Chance
and selection in the assembly of ecological communities.  Cambridge
University Press.
http://www.amazon.com/Plant-Traits-Vegetation-Structure-Communities/dp/05211
33556/ref=sr_1_3?ie=UTF8&s=books&qid=1260148938&sr=1-3