1. Report of the Mplus Working Group on Issues regarding Unidimensionality
Psychometrics Working Group
Friday Harbor Laboratories
September 21-24, 2005
Members of the Mplus group included
Rosemary Abbott
Dagmar Amtmann
Mark Chatfield
Rich Jones
Carla Sharp
Doug Tommett
(did I forget anyone?)

2. This figure is a plot of scree (eigenvalues) from the factor analysis of 50 items from the 3MSE (CHS, year 5). A strong first factor explains more than 50% of the variance in the items. Nine eigenvalues are greater than 1. One is less than 0, signaling violations of the assumption of local independence.

3. This a histogram of the distribution of the 1,275 residual correlations among the 50 3MSE items, conditional on a single latent trait. The mean, by design, is 0. Many items have residual correlations in that are rather high. In the following slides, these item pairs are identified.

4. The group suggested that natural thing to do with these highly dependent (and perhaps logically dependent) items is to collapse them into item parcels.

5. This slide (and several to follow) summarizes results of an attempt to implement McDonald’s Hierarchical Factor Analysis approach to the assessment of unidimensionality. A ten-item factor model was imposed upon the data (year 5 data, 50 3MSE items, all participants with non-missing data on each item). The first factor was a general factor (loaded into all items). The second-tenth factors were modeled after the nine-item factor solution suggested by the exploratory factor analysis.
This table presents the items loading on the general factor, on an empirically-identified minor or sub-factor, and the number (2-9) identifying the sub-factor. A “+” in the final column identifies the items that have a higher loading on the general factor then the minor factor.