Multilevel Item Response Models Research Articles

Computerized Adaptive Testing With Item Cloning

To increase the number of items available for adaptive testing and reduce the cost of item writing, the use of techniques of item cloning has been proposed. An important consequence of item cloning is possible variability between the item parameters. To deal with this variability, a multilevel item response (IRT) model is presented which allows for differences between the distributions of item parameters of families of item clones. A marginal maximum likelihood and a Bayesian procedure for estimating the hyperparameters are presented. In addition, an item-selection procedure for computerized adaptive testing with item cloning is presented which has the following two stages: First, a family of item clones is selected to be optimal at the estimate of the person parameter. Second, an item is randomly selected from the family for administration. Results from simulation studies based on an item pool from the Law School Admission Test (LSAT) illustrate the accuracy of these item pool calibration and adaptive testing procedures. Index terms: computerized adaptive testing, item cloning, multilevel item response theory, marginal maximum likelihood, Bayesian item selection.

Item Analysis by the Hierarchical Generalized Linear Model

The hierarchical generalized linear model (HGLM) is presented as an explicit, two‐level formulation of a multilevel item response model. In this paper, it is shown that the HGLM is equivalent to the Rasch model and that, characteristic of the HGLM, person ability can be expressed in the form of random effects rather than parameters. The two‐level item analysis model is presented as a latent regression model with person‐characteristic variables. Furthermore, it is shown that the two‐level HGLM model can be extended to a three‐level latent regression model that permits investigation of the variation of students' performance across groups, such as is found in classrooms and schools, and of the interactive effect of person‐and group‐characteristic variables.

Bayesian estimation of a multilevel multidimensional item response model using auxiliary variables method: an exploration of the correlation between multiple latent variables and covariates in hierarchical data

Bayesian estimation of a multilevel multidimensional item response model using auxiliary variables method: an exploration of the correlation between multiple latent variables and covariates in hierarchical data