The forward search algorithm and confirmatory factor analysis

The forward search algorithm is a (graphical) method for data exploration and robust parameter estimation. The algorithm identifies those units in the sample that have disproportionately large impact on the subsequent statistical inference.

There are three possible ways to apply the algorithm when we are estimating the confirmatory factor model:

1. identify the units that are distant from the bulk of the data,
2. identify the units with disproportionately large impact on covariance matrix estimate,
3. identify the units with large impact on model parameters.

The structure and the performance of the algorithm will be demonstrated on a simple example.