The lattice conditional independence (LCI) model N() is defined to be the set of all normal distributions N(0, [Sigma]) on I such that for every pair L, M [set membership, variant] , xL and xM are conditionally independent given xL [intersection] M. Here is a ring of subsets (hence a distributive lattice) of the finite index set I such that [empty set][combining character] I [set membership, variant] , while for K [set membership, variant] , xK is the coordinate projection of x [set membership, variant] I onto K. These LCI models have especially tractable statistical properties and arise naturally in the analysis of non-monotone multivariate missing data patterns and non-nested dependent linear regression models [reverse not equivalent] seemingly unrelated regressions. The present paper treats the problem of testing one LCI model against another, i.e., testing N() vs N() when is a subring of . The likelihood ratio test statistic is derived, together with its central distribution, and several examples are presented.
