A Revised Modified Parallel Analysis for the Construction of Unidimensional Item Pools

Abstract

Modified parallel analysis (MPA) is a heuristic method for assessing "approximate unidimensionality" of item pools. It compares the second eigenvalue of the observed correlation matrix with the corresponding eigenvalue extracted from a "parallel" matrix generated by a unidimensional and locally independent model. Revised MPA (RMPA) generalizes MPA and alleviates some of its technical limitations. RMPA includes an important and useful feature for eliminating items that violate the test's unidimensionality. This is achieved by eliminating items, one at a time, to determine their contribution to the matrices' eigenvalues. A test for detecting items with large impact in the observed dataset and then eliminating them is proposed. The new method was tested in several simulations in which unidimensional item pools were "contaminated" by various proportions of items from a secondary pool. The results indicate that RMPA does an excellent job of detecting low (10%) and moderate (25%) levels of contamination, but fails in cases of maximal (50%) contamination.