Three Mahalanobis distances and their role in assessing unidimensionality.
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.
Yuan
Ke-Hai
KH
Department of Psychology, University of Notre Dame, USA. kyuan@nd.edu
Fung
Wing Kam
WK
Reise
Steven P
SP
D006801:Humans; D008962:Models, Theoretical; D011594:Psychometrics / Q000706:statistics & numerical data*; D015203:Reproducibility of Results