Clarke, Paul S. and Smith, Peter W. F.
Results on point and interval estimation for log-linear models with non-ignorable non-response. Southampton, UK, Southampton Statistical Sciences Research Institute, 16pp.
(S3RI Methodology Working Papers, (M03/23) ).
It is common that log-linear models for multi-way contingency tables with one variable subject to non-ignorable non-response will yield non-response boundary solutions, where the probability of non-respondents being classified in certain cells of the table is estimated to be zero, resulting in infinite estimates for some of the log-linear parameters. This paper investigates the effect of such non-standard behaviour on the maximum likelihood estimator. Provided that the model parameters are identifiable from infinite samples, it is demonstrated that: 1) existence and uniqueness of the maximum likelihood estimates is assured under weak conditions; and 2) the maximum likelihood estimator is consistent and asymptotically normal. However, boundary solutions do result in a singular information matrix, which prevents calculating confidence intervals based on a normal approximation to the maximum likelihood estimator; it is shown that these singularities can be removed by a simple transformation of the log-linear parameters.
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