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Information loss for 2 × 2 tables with missing cell counts: binomial case
Author(s) -
Eisinga Rob
Publication year - 2008
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.2007.00384.x
Subject(s) - estimator , statistics , mathematics , inference , missing data , binomial distribution , negative binomial distribution , fisher information , binomial (polynomial) , count data , covariance , variance (accounting) , econometrics , conditional variance , maximum likelihood , computer science , poisson distribution , artificial intelligence , volatility (finance) , accounting , business , autoregressive conditional heteroskedasticity
We formulate likelihood‐based ecological inference for 2 × 2 tables with missing cell counts as an incomplete data problem and study Fisher information loss by comparing estimation from complete and incomplete data. In so doing, we consider maximum‐likelihood (ML) estimators of probabilities governed by two independent binomial distributions and obtain simplified expressions for their covariance. These expressions reflect well the additional uncertainty arising from the unobserved data compared to complete data tables. We also discuss an approximation to the expected conditional variance of the unobserved entries and ML parameter bias correction. An empirical example is used to demonstrate the results.