Fitting Log-Linear Models to Contingency Tables With Incomplete Observations
David A. van Dyk
Department of Statistics, The University of Chicago,
Chicago, IL 60637, U.S.A.
The study of contingency tables is prevalent throughout the biological
and physical sciences. A common difficultly occurs, however, when some
or all of the data can not be completely classified. This paper shows
how the ECM algorithm (Meng and Rubin, 1993) along with iterative
proportional fitting (Bishop, Feinberg, and Holland, 1975) can be used to
fit any hierarchical log-linear model to a table
with any combination of partially
and completely classified observations. Beyond this, we develop the
supplemented ECM (SECM) algorithm which can be used to calculate
asymptotic variance matrices of the maximum likelihood estimates fit
with a log-linear model. An infant survival example is given which
demonstrates both the precision of the SECM algorithm, and a powerful
internal checking system which detects errors in the implementation of
both ECM and SECM.
Key words: Contingency Table; Convergence Rate; EM
Algorithm; Fisher Information; Incomplete Data; IPF; Missing Data;
Observed Information; SEM Algorithm
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