LATTICE-ORDERED CONDITIONAL-INDEPENDENCE MODELS FOR MISSING DATA

Statistical inference for the parameters of a multivariate normal distribution N(p)(mu, SIGMA) based on a sample with missing observations is straightforward when the missing data pattern is monotone (= nested), reducing to the analysis of several normal linear regression models by step-wise conditioning. When the missing data pattern is non-monotone, however, such analysis is impossible. It is shown here that every missing data pattern naturally determines a set of lattice-ordered conditional independence restrictions which, when imposed upon the unknown covariance matrix-SIGMA, yields a factorization of the joint likelihood function as a product of (conditional) likelihood functions of normal linear regression models just as in the monotone case. From this factorization the maximum likelihood estimators of mu and SIGMA (under the conditional independence restrictions) can be explicitly derived.