7.1 Relative Model-Data Fit at Test Level

Let $L\left(Y\right)$ be the likelihood of observing item response vectors of $N$ students.

Theoretically, a model with larger $L\left(Y\right)$ or smaller $-2\log L\left(Y\right)$ is perferred because it makes the data more likely to occur.

However, based on this rule, a model with more parameters is usually ‘’preferred’’, yielding overfitting issue.

What we can do is to add a penalty to penalize a model with too many parameters.