The forward search algorithm for detecting aberrant response patterns in factor analysis for binary data

In this article we implement a forward search algorithm for identifying atypical subjects/observations in factor analysis models for binary data. Forward plots of goodness-of-fit statistics, residuals, and parameter estimates help us identify aberrant observations and detect deviations from the hypothesized model. Methods to initialize, progress, and monitor the search are explored. Simulation envelopes are constructed to investigate whether changes in the statistics being monitored are solely due to random variation. One real and two simulated datasets are used to illustrate the performance of the suggested algorithm. The two simulated datasets explore the effectiveness of the method in the presence of a single outlier and a cluster of outliers. Matlab computer code for implementing the proposed methods is available online.