 
Summary: LEMMA  Brief Summary of the Linear Model
Bar, Booth, Schifano and Wells (2009) de...ne the mixed e¤ect mixture linear model:
yijg = + i + g + ig + ijg
where:
yijg is the (normalized) response for gene g, individual j, in group i, where g = 1; : : : ; G;
j = 1; : : : ; nig; i = 1; 2;
is the overall mean;
i is the (...xed) e¤ect of treatment group i; constrained such that 1 + 2 = 0;
g is the (random) e¤ect of gene g; assumed to be distributed N(0; 2
);
ig is the (random) genetreatment interaction for treatment group i and gene g; constrained
such that 1g + 2g = 0; but where the di¤erence g 1g 2g is assumed to be distributed
N( ; 2
) for genes in the nonnull group, and identically 0 for genes in the null group.
ijg is the (random) genespeci...c error for gene g; assumed to be distributed N(0; 2
;g):
Further assume that 2
;g i.i.d. IG( ; ) and de...ne the latent indicator variables fbgg of nonnull
status, such that bg i.i.d. Bern(p1), where p1 is the prior probability of a gene being nonnull.
This model is referred to as the RR model  Random gene treatment interaction ( ig), Random
