A Note on Using Eigenvalues in Dimensionality Assessment

The dimensionality of a set of items is important for scale development. In practice, tools that make use of eigenvalues are often used to assess dimensionality. Parallel analysis is featured here as it is becoming an increasingly popular method for assessing the number of dimensions, and computational tools have recently been made available which will likely increase its use by practitioners. The current paper argues that methods that use eigenvalues to ascertain the number of factors may perform poorly under certain conditions, particularly for increasing levels of variable complexity and/or inter-factor correlations in the latent structure. A simulation study and an example are offered to substantiate this assertion. Accessed 2,400 times on https://pareonline.net from September 06, 2017 to December 31, 2019. For downloads from January 1, 2020 forward, please click on the PlumX Metrics link to the right

Classification Performance of Answer-Copying Indices Under Different Types of IRT Models

Test fraud has recently received increased attention in the field of educational testing, and the use of comprehensive integrity analysis after test administration is recommended for investigating different types of potential test frauds. One type of test fraud involves answer copying between two examinees, and numerous statistical methods have been proposed in the literature to screen and identify unusual response similarity or irregular response patterns on multiple-choice tests. The current study examined the classification performance of answer-copying indices measured by the area under the receiver operating characteristic (ROC) curve under different item response theory (IRT) models (one- [1PL], two- [2PL], three-parameter [3PL] models, nominal response model [NRM]) using both simulated and real response vectors. The results indicated that although there is a slight increase in the performance for low amount of copying conditions (20%), when nominal response outcomes were used, these indices performed in a similar manner for 40% and 60% copying conditions when dichotomous response outcomes were utilized. The results also indicated that the performance with simulated response vectors was almost identically reproducible with real response vectors