Three Mahalanobis distances and their role in assessing unidimensionality

Source abstract

Unidimensionality is the hallmark psychometric feature of a well‐constructed measurement scale. However, in determining the degree to which a set of items form a unidimensional scale, aberrant item response patterns may distort our investigations. For example, aberrant response patterns may adversely impact interitem covariances which, in turn, can distort estimates of a scale's dimensionality and reliability. In this study, we investigate and compare the utility of three Mahalanobis distance (M‐distance) measures in identifying and downweighting aberrant item response patterns. Our findings indicated that a residual‐based M‐distance measure had the best properties. Specifically, response patterns having greater residual‐based M‐distances were responsible for observed violations of unidimensionality. When these response patterns were properly downweighted according to this M‐distance, the data fitted a one‐factor model better and scale reliability increased. The procedures are illustrated using three real data sets.