
LINEAR MIXED EFFECT MODELS 155
Let X = x be the observations in (8.12). The association step yields the collec-
tion of sets R
x
(v) = {ρ : T (x) = φ(ρ) + v} indexed by v. Combine these with the
predictive random set above to get an enlarged x-dependent random set:
R
x
(S) =
[
v∈S
R
x
(v). (8.18)
Now, for a given assertion {ρ = r}, we compute the plausibility function,
pl
x|h
0
,ρ
0
(r) = P
S|h
0
,ρ
0
{R
x
(S) 3 r},
the probability that the random set R
x
(S) contains the asserted value r of ρ. A simple
calculation shows that
pl
x|h
0
,ρ
0
(r) = γ
S
T (x)−φ (r)
= 1 −F
h
0
,ρ
0
(|T (x)−φ (r) −µ
0
|),
where F
h
0
,ρ
0
is the distribution function defined above. The above display shows that
the