The goal of the present study was to address the analytical complexity of incorporating responses and response times through applying the Jeon and De Boeck mixture item response theory model in Mplus 8.7. Using both simulated and real data, we attempt to identify subgroups of responders that are rapid guessers or engage knowledge retrieval…

In confirmatory factor analysis quite similar models of measurement serve the detection of the difficulty factor and the factor due to the item-position effect. The item-position effect refers to the increasing dependency among the responses to successively presented items of a test whereas the difficulty factor is ascribed to the wide range of…

Rasch mixture models can be a useful tool when checking the assumption of measurement invariance for a single Rasch model. They provide advantages compared to manifest differential item functioning (DIF) tests when the DIF groups are only weakly correlated with the manifest covariates available. Unlike in single Rasch models, estimation of Rasch…

Cultural consensus theory (CCT) is a data aggregation technique with many applications in the social and behavioral sciences. We describe the intuition and theory behind a set of CCT models for continuous type data using maximum likelihood inference methodology. We describe how bias parameters can be incorporated into these models. We introduce…

This study examined the empirical differences between the tendency to omit items and reading ability by applying tree-based item response (IRTree) models to the Japanese data of the Programme for International Student Assessment (PISA) held in 2009. For this purpose, existing IRTree models were expanded to contain predictors and to handle…

The assessment of test data for the presence of differential item functioning (DIF) is a key component of instrument development and validation. Among the many methods that have been used successfully in such analyses is the mixture modeling approach. Using this approach to identify the presence of DIF has been touted as potentially superior for…

When missing values are present in item response data, there are a number of ways one might impute a correct or incorrect response to a multiple-choice item. There are significantly fewer methods for imputing the actual response option an examinee may have provided if he or she had not omitted the item either purposely or accidentally. This…

The many-faceted Rasch (MFR) model has been used to evaluate the quality of ratings on constructed response assessments; however, it can also be used to evaluate the quality of judgments from panel-based standard setting procedures. The current study illustrates the use of the MFR model for examining the quality of ratings obtained from a standard…

The article compares three different methods to estimate effects of task characteristics and to use these estimates for model-based proficiency scaling: prediction of item difficulties from the Rasch model, the linear logistic test model (LLTM), and an LLTM including random item effects (LLTM+e). The methods are applied to empirical data from a…

In this study, the authors extend the standard item response model with internal restrictions on item difficulty (MIRID) to fit polytomous items using cumulative logits and adjacent-category logits. Moreover, the new model incorporates discrimination parameters and is rooted in a multilevel framework. It is a nonlinear mixed model so that existing…

Building on the Kelley and Gulliksen versions of classical test theory, this article shows that a logistic model having only a single item parameter can account for varying item discrimination, as well as difficulty, by using item-test correlations to adjust incorrect-correct (0-1) item responses prior to an initial model fit. The fit occurs…

The linear logistic test model (LLTM) breaks down the item parameter of the Rasch model as a linear combination of some hypothesized elementary parameters. Although the original purpose of applying the LLTM was primarily to generate test items with specified item difficulty, there are still many other potential applications, which may be of use…

Relative difficulty of Separate (Form S) and Grouped (Form G) True-False tests may be expected to be dependent on the ability levels of examinees. At some levels Form S should be less difficult, at others equally difficult, and at still others, more difficult, than Form G. (Author/RL)

Two techniques for writing achievement test items to accompany instructional materials are contrasted: writing items from statements of instructional objectives, and writing items from semi-automated rules for transforming instructional statements. Both systems resulted in about the same number of faulty items. (Author/JKS)

The binomial error model includes form-to-form difficulty differences as error variance and leads to Ruder-Richardson formula 21 as an estimate of reliability. If the form-to-form component is removed from the estimate of error variance, the binomial model leads to KR 20 as the reliability estimate. (Author/BW)