Factor Recovery in Binary Data Sets: A Simulation

The present study compares the performance of phi coefficients and tetrachorics along two dimensions of factor recovery in binary data. These dimensions are (a) accuracy of nontrivial factor identification, and (b) factor structure recovery given a priori knowledge of the correct number of factors to rotate. Nontrivial factor identification was poor for both indices, with phi's performing slightly better than tetrachorics. In contrast, factor structure recovery was quite good when the correct number of factors was rotated. Phi coefficients generally yielded better factor structure recovery than tetrachorics and were better at preventing items from intruding onto factors where they did not belong, while tetrachorics were better than phi's at preventing items from being omitted from factors where they should have been included. The solutions based on tetrachorics contained many Heywood cases. It is suggested that for most applications it is preferable to base factor analysis on phi coefficients.