Chapter 6 Model Identifiability

In some statistical models, different parameter values can give rise to identical probability distributions. When this happens, there will be a number of different parameter values associated with the maximum likelihood of any set of observed data. This is referred to as the model identifiability problem. (Everitt & Howell, 2005)

An example (Everitt & Howell, 2005)

Can you regress \(Y\) on \(X_1\), \(X_2\), and \(X_3=X_1+X_2\)?

Identifiability is important for

• model interpretations

• statistical inferences

References

Everitt, B., & Howell, D. C. (Eds.). (2005). Encyclopedia of statistics in behavioral science. John Wiley & Sons.