Goodness-of-fit
Does the data agree with the model?
- Calculate the distance between data and model predictions.
- Apply Bayesian methods such as likelihood estimation: likelihood of observing the data if we assume the model; the results will be a set of fitting parameters.
- …
Why don’t we always use goodness-of-fit as a measure of the goodness of a model?
- We may experience overfitting.
- The model may not be intuitive.
This is why we would like to balance it with parsimony using some measures of generalizability.
K-means and overfitting
The overfitting problem is easily demonstrated using the K-means model.
Suppose we use $k=1$, i.e., considering only the data point and no neighbors, we will get a model that is 100% agreeing with the data. If we require only goodness of fit, we may as well choose this $k=1$ model. However, such a model is useless since it is the dataset itself without any other insights.
Planted:
by L Ma;
Dynamic Backlinks to
wiki/model-selection/goodness-of-fit:wiki/model-selection/goodness-of-fit Links to:L Ma (2020). 'Goodness-of-fit', Datumorphism, 11 April. Available at: https://datumorphism.leima.is/wiki/model-selection/goodness-of-fit/.