Examining Parameter Estimation when Treating Semi-Mixed Multidimensional Constructs as Unidimensional.

In this study, parameter estimation error was examined when three dimensional tests of a semi-mixed structure were estimated unidimensionally. Since previous studies have generally focused on two-dimensional mixed structured tests or three-dimensional approximately simple structured tests, this study adds to the literature by considering the impact of fitting a unidimensional model to multidimensional data using a test structure that has not previously been considered. Test structure, interdimensional correlation, difficulty of the test, and different underlying distributions of ability were considered. Test length was set at 30 items for all conditions. Although test length was fixed, the number of approximately simple and complex items varied. Under all conditions for both moderately difficult and difficult tests, the lowest error values for all discrimination parameters, with the exception of MDISC, were obtained, surprisingly, with a correlation of 0.00. The lowest RMSE values for the difficulty parameter were obtained for tests of medium difficulty when the underlying ability distribution was simulated as standard normal for all three dimensions. The estimation errors associated with the difficulty parameter were greatly impacted by differences in the underlying ability distributions. Ability estimation errors associated with the unidimensional estimate of ability decreased as the correlation between dimensions increased.