This paper presents the item and test information functions of the Rank two-parameter logistic models (Rank-2PLM) for items with two (pair) and three (triplet) statements in forced-choice questionnaires. The Rank-2PLM model for pairs is the MUPP-2PLM (Multi-Unidimensional Pairwise Preference) and, for triplets, is the Triplet-2PLM. Fisher's…

It is common to find mixed-format data results from the use of both multiple-choice (MC) and constructed-response (CR) questions on assessments. Dealing with these mixed response types involves understanding what the assessment is measuring, and the use of suitable measurement models to estimate latent abilities. Past research in educational…

In order to detect a wide range of aberrant behaviors, it can be useful to incorporate information beyond the dichotomous item scores. In this paper, we extend the l[subscript z] and l*[subscript z] person-fit statistics so that unusual behavior in item scores and unusual behavior in item distractors can be used as indicators of aberrance. Through…

Educational tests often have a cluster of items linked by a common stimulus ("testlet"). In such a design, the dependencies caused between items are called "testlet effects." In particular, the directional testlet effect (DTE) refers to a recursive influence whereby responses to earlier items can positively or negatively affect…

Introduction: Item response theory (IRT) has received much attention in validation of assessment instrument because it allows the estimation of students' ability from any set of the items. Item response theory allows the difficulty and discrimination levels of each item on the test to be estimated. In the framework of IRT, item characteristics are…

This paper examines one of three central diagnostic tools of the Concerns Based Adoption Model, the Stages of Concern Questionnaire (SoCQ). The SoCQ was developed with a focus on K12 education. It has been used widely since developed in 1973, in early childhood, higher education, medical, business, community, and military settings. The SoCQ…

This study utilizes an analysis of diminishing returns to examine the relationship between sample size and item parameter estimation precision when utilizing the Masters' Partial Credit Model for polytomous items. Item data from the standardization of the Batelle Developmental Inventory, 3rd Edition were used. Each item was scored with a…

Estimation of parameters for the many-facets Rasch model requires that conditional on the values of the facets, such as person ability, item difficulty, and rater severity, the observed responses within each facet are independent. This requirement has often been discussed for the Rasch models and 2PL and 3PL models, but it becomes more complex…

Composite scores are an exceptionally important psychometric tool for behavioral science research applications. A prototypical example occurs with self-report data, where researchers routinely use questionnaires with multiple items that tap into different features of a target construct. Item-level missing data are endemic to composite score…

The C-test is a type of gap-filling test designed to efficiently measure second language proficiency. The typical C-test consists of several short paragraphs with the second half of every second word deleted. The words with deleted parts are considered as items nested within the corresponding paragraph. Given this testlet structure, it is commonly…

In this digital ITEMS module, Dr. Brian Leventhal and Dr. Allison Ames provide an overview of "Monte Carlo simulation studies" (MCSS) in "item response theory" (IRT). MCSS are utilized for a variety of reasons, one of the most compelling being that they can be used when analytic solutions are impractical or nonexistent because…

Multiple choice results are inherently probabilistic outcomes, as correct responses reflect a combination of knowledge and guessing, while incorrect responses additionally reflect blunder, a confidently committed mistake. To objectively resolve knowledge from responses in an MC test structure, we evaluated probabilistic models that explicitly…

The development of assessments as part of the funded LOCUS project is described. The assessments measure students' conceptual understanding of statistics as outlined in the GAISE PreK-12 Framework. Results are reported from a large-scale administration to 3,430 students in grades 6 through 12 in the United States. Items were designed to assess…

One of the issues that hinder the students' learning progress is the inability to construct an epistemological explanation of a scientific phenomenon. Four-tier multiple-choice (hereinafter, 4TMC) instrument and Partial-Credit Model were employed to elaborate on the diagnosis process of the aforementioned problem. This study was to develop and…

A log-linear model (LLM) is a well-known statistical method to examine the relationship among categorical variables. This study investigated the performance of LLM in detecting differential item functioning (DIF) for polytomously scored items via simulations where various sample sizes, ability mean differences (impact), and DIF types were…