unidim: An Index of Scale Homogeneity and Unidimensionality

How to evaluate how well a psychological scale measures just one construct is a recurring problem in assessment. We introduce an index, u, of the unidimensionality and homogeneity of a scale. u is just the product of two other indices: τ (a measure of τ equivalence) and ρ_c (a measure of congeneric fit). By combining these two indices into one, we provide a simple index of the unidimensionality and homogeneity of a scale. We evaluate u through simulations and with real data sets. Simulations of u across one-factor scales ranging from three to 24 items with various levels of factor homogeneity show that τ and, therefore, u are sensitive to the degree of factor homogeneity. Additional tests with multifactorial scales representing 9, 18, 27, and 36 items with a hierarchical factor structure varying in a general factor loading show that ρ_c and, therefore, u are sensitive to the general factor saturation of a test. We also demonstrate the performance of u on 45 different publicly available personality and ability measures. Comparisons with traditional measures (i.e., ω_h, α, ω_t, comparative fit index, and explained common variance) show that u has greater sensitivity to unidimensional structure and less sensitivity to the number of items in a scale. u is easily calculated with open source statistical packages and is relatively robust to sample sizes ranging from 100 to 5,000.