Parameter redundancy and the existence of maximum likelihood estimates in log-linear models
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Log-linear models are typically fitted to contingency table data to describe and identify the relationship between different categorical variables. However, the data may include observed zero cell entries. The presence of zero cell entries can have an adverse effect on the estimability of parameters, due to parameter redundancy. We describe a general approach for determining whether a given log-linear model is parameter redundant for a pattern of observed zeros inthe table, prior to fitting the model to the data. We derive the estimable parameters or functions of parameters and also explain how to reduce the unidentifiable model to an identifiable one. Parameter redundant models have a flat ridge in their likelihood function. We further explain when this ridge imposes some additional parameter constraints on the model, which can lead to obtaining unique maximum likelihood estimates for parameters that otherwise would not have been estimable. In contrast to other frameworks, the proposed novel approach informs on those constraints, elucidating the model that is actually being fitted.
Sharifi Far , S , Papathomas , M & King , R 2021 , ' Parameter redundancy and the existence of maximum likelihood estimates in log-linear models ' , Statistica Sinica , vol. 31 , no. 3 , pp. 1125-1143 . https://doi.org/10.5705/ss.202018.0100
Copyright © 2019 the Author(s). This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.5705/ss.202018.0100
DescriptionThe work of first author is supported by EPSRC PhD grants EP/J500549/1, EP/K503162/1 and EP/L505079/1.
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