Model modification and improvement

Modification indices are a way of improving your model by identifying parameters which, if included, would improve model fit (or constraints removed). However, remember that:

  • Use of modification indices should be informed by theory
  • MI may suggest paths which don’t make substantive sense

It’s very important to avoid adding paths in a completely data-driven way because this is almost certain to lead to over-fitting.

It’s also important to work one step at a time, because the table of modification indices may change as you add additional paths. For example, the second largest MI value may change once you add the path with the largest MI to the model.

The basic steps to follow are:

  1. Run a simple, theoretically-derived model
  2. Notice it fits badly
  3. Add any additional paths which make theoretical sense
  4. Check GOF; If it still fits badly then,
  5. Run MI and identify the largest value
  6. If this parameter makes theoretical sense, relax the constraint
  7. Re-run the model and return to step 4