Q-mode Factor Analysis: A Brief Tutorial Using MATLAB

MATLAB scripts and a tutorial introduce Q-mode factor analysis that examines similarity between sampled objects.

Two MATLAB scripts, QMODE4 and QMODE3D, are published here along with example data and a tutorial introducing Q-mode factor analysis to students of earth and environmental science. My motivation for this project derives from years of teaching statistical methods to graduate students in marine science who came to me with large data sets - sample data consisting of repeated variable measurements made on a large number of objects. When many variables were involved, reducing the "dimensionality" of the problem through the derivation of independent factors became the goal. Q-mode factor analysis - which examines the similarities between objects rather than correlations between variables - offered a way to explore patterns in their data with these factors. But throwing one's data into a program and pushing the GO button is not recommended! Insight and careful decision making is required along with an understanding of what factor analysis is and what it can and cannot do.

The example data provided here consist of the heavy mineral composition of marine sediment samples collected near the entrance to Chesapeake Bay. A total of twelve minerals were identified in each sample expressed as percent composition. After selecting a small number of factors, each sample is then represented as a mixture of hypothetical end-members defined by factor scores; spatial patterns are investigated based on sample location after the samples are "unmixed" into their component factors.