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STATISTICAL MATCHING AND MICROSIMULATION MODELS 77 correlation between Z and X(A), which also affects the marginal distribution of Z in the merged file. The marginal distribution of Z in file B will not agree with the marginal distribution of Z in the merged file because the statistical match gives data different weight in the merged file than they had in file B. Thus, the sum of Z in file B will not necessarily equal the sum of Z in the merged file. This reweighting also affects joint distributions involving Z, namely, the correlations between Z and X. Even assuming a relatively smooth relationship between Z and X, the correlations between Z and X(B) still will not necessarily agree with the correlations between Z and X (A), again due to reweighting. Thus, both differences between X(A) and X(B) and the reweighting of information from the B file contribute to changes in the correlations between Z and X. ALTERNATIVES TO STATISTICAL MATCHING Variance -Covariance Analysis One alternative to statistical matching, mentioned in Rodgers (1984), is to make use of the available variance-covariance matrices augmented with the conditional independence assumption. Specifically, consider the variance-covariance matrix, denoted V, for (X, Y, Z): The only nonestimable components of the above matrix are V(Y,Z). However, as Rodgers (1984) points out: In particular, statistical matching's conditional independence assumption implies that which is now a function of estimable quantities (or, if one has an independent estimate of V(Y,Z|X), it could be substituted in the above expression). Simply computing these matrix inversions and multiplications permits one to estimate regression coefficients, discriminant functions, and any other statistic that is defined in terms of matrix operations in a much more efficient manner than by performing a statistical match. Iterative Proportional Fitting If one performs a statistical match in order to determine multivariate frequency counts for a variety of variables that do not coexist on any individual data file,
