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Purpose:

Gives observation-level estimates of parameters from $2\times C$ tables with $C>2$. First decompose the $C$ outcome categories into a series of dichotomous choices. For example, in the $2\times 3$ running example in the book (see Table 2.2, page 31), Democrat/Republican/No Vote can be decomposed into Vote/No vote (which is analyzed as usual with ei) and Democrat/Republican, among those who vote (which ei2 can analyze given $V_i$, the Democratic fraction of the vote, and the output from ei). If desired, covariates in either ei or ei2 can be used to avoid possibly incorrect independence assumptions.

In this running example, this procedure will estimate $\lambda^b_i$ and $\lambda_i^w$ (and various related statistics) given $V_i$ (Democratic fraction of the vote) and given an estimate of $x_i$ (black fraction of voters) in this accounting identity: $V_i = \lambda^b_ix_i + \lambda^w_i(1-x_i)$. A first-stage estimate of $\beta_i^b$ from ei() is used to estimate $x_i$, since $x_i=\beta_i^bX_i/T_i$ (these first stage results should be studied with eiread and eigraph before proceeding). Multiple imputation is used to incorporate the extra uncertainty due to $x_i$ being estimated. The details of this procedure are discussed in Section 8.4.

The separately imputed data buffers are stored in the output global _ei2_mta. The simulations from each data buffer are combined in a single data buffer, dbuf2. Both can be read with eiread or graphed with eigraph. Because these programs work for both ei() and ei2(), reading estimates requires using the names ``betaB'' and ``betaW'' for the parameters (even though they might be more appropriately called ``lambdaB'' and ``lambdaW'' for this particular example). In dbuf2, x are the mean posterior estimates of $x_i$, and x2 is a ( $p\times\texttt{\_Esims}$) matrix of simulations of $x_i$ (see eiread and eigraph for further information). Diagnostic outputs in this data buffer, such as resamp, are those from the final imputed data set.