overparameterized model

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 {y_jk}, where j (=1, 2) signifies the treatment and k is the number of the observation. Consider the model

where the {ε_jk} 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+τ_j) can be estimated. The value attributed to μ can be arbitrarily chosen. However, the problem can be solved either by rewriting the model
or by retaining the original model and adding a constraint such as τ₁+τ₂=0.

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