Interval estimation for log‐linear models with one variable subject to non‐ignorable non‐response

Paul S. Clarke and Peter W. F. Smith

Journal of the Royal Statistical Society Series B, 2004, vol. 66, issue 2, 357-368

Abstract: Summary. Log‐linear models for multiway contingency tables where one variable is subject to non‐ignorable non‐response will often yield boundary solutions, with the probability of non‐respondents being classified in some cells of the table estimated as 0. The paper considers the effect of this non‐standard behaviour on two methods of interval estimation based on the distribution of the maximum likelihood estimator. The first method relies on the estimator being approximately normally distributed with variance equal to the inverse of the information matrix. It is shown that the information matrix is singular for boundary solutions, but intervals can be calculated after a simple transformation. For the second method, based on the bootstrap, asymptotic results suggest that the coverage properties may be poor for boundary solutions. Both methods are compared with profile likelihood intervals in a simulation study based on data from the British General Election Panel Study. The results of this study indicate that all three methods perform poorly for a parameter of the non‐response model, whereas they all perform well for a parameter of the margin model, irrespective of whether or not there is a boundary solution.

Date: 2004
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