this paper, included covariates may simultaneously be markers for several unmeasured covariates. The weight of a neonate is a marker for body surface area, which in turn is positively related to a component of fluid loss not measured. Although this component can be expected to be a major determinant of why neonates differ in measured fluid output, short term day to day variation in weight may be a marker for temporary fluid retention or diuresis. Thus, again omitted covariates are present, which have different relationships with influential unmeasured covariates within and between individuals. From a statistical point of view, omitted covariates create violations of assumptions with commonly used methods in regression analysis. There is a rich literature on model misspecification due to omitted covariates. Unless one has some additional information (such as observed instrumental variables; see Bowden and Turkington, 1984), some parameters in the regression model cannot be estimated because of the presence of omitted covariates. In this paper we focus on fitting the "marginal" model between the response variable and included covariates, using a model between the response variable and all covariates and a model between the omitted and included covariates. The fitted marginal model can be used for statistical inference (such as to test whether there are omitted covariates) and prediction of future response values. Although omitted covariates can be treated as random effects, there is an important difference between our approach and ordinary mixed effects modeling: it is usually implicitly assumed in mixed effects regression models that the distribution of the random effects does not depend on the fixed covariates. Palta and Yao (1991) and Palta and Qu (1995) demonstrated...