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overparameterized model


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A model having more parameters than can be estimated from the data. For example, suppose that the yields of two types of tomatoes are to be compared using the data {yjk}, where j (=1, 2) signifies the treatment and k is the number of the observation. Consider the model

yjk=μ+τj+εjk,

where the {εjk} are independent random errors, each with mean 0 and variance σ2. As it stands, this model is overparameterized, because for each value of j, only (μ+τj) can be estimated. The value attributed to μ can be arbitrarily chosen. However, the problem can be solved either by rewriting the model

yjk=μj+εjk,

or by retaining the original model and adding a constraint such as τ1+τ2=0.

Subjects: Probability and Statistics.


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