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This paper outlines a multiple imputation method for handling missing data in designed longitudinal studies. A random coefficients model is developed to accommodate incomplete multivariate continuous longitudinal data. Multivariate repeated measures are jointly modeled; specifically, an i.i.d. normal model is assumed for time-independent variables and a hierarchical random coefficients model is...

1. Statement of the main results. Let X1,X2, . . . be independent random variables taking values in a measurable Abelian group ( , ) with respective distributions P1,P2, . . . . Moreover, if these random variables are identically distributed (the i.i.d. case), then we denote by P their common distribution. We suppose that {0} ∈ and the group operation “+” is measurable. In other words, a sum of...

In this paper, we study a random-coefficients model for a binary outcome. We allow for the possibility that some or even all of the explanatory variables are arbitrarily correlated with the random coefficients, thus permitting endogeneity. We assume the existence of observed instrumental variables Z that are jointly independent with the random coefficients, although we place no structure on the...

the notion of a $d$-poset was introduced in a connection withquantum mechanical models. in this paper, we introduce theconditional expectation of  random variables on thek^{o}pka's $d$-poset and prove the basic properties ofconditional expectation on this  structure.