Multistage Testing


Multistage testing (MST) is a type of computerized adaptive testing (CAT).  This means it is an exam delivered on computers which dynamically personalize it for each examinee or student.  Typically, this is done with respect to the difficulty of the questions, by making the exam easier for lower-ability students and harder for high-ability students.  Doing […]

Maximum Likelihood Estimation

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Maximum Likelihood Estimation (MLE) is an approach to estimating parameters for a model.  It is one of the core aspects of Item Response Theory (IRT), especially to estimate item parameters (analyze questions) and estimate person parameters (scoring).  This article will provide an introduction to the concepts of MLE. Content History behind Maximum Likelihood Estimation Defining […]

Multidimensional Item Response Theory

camera lenses for multidimensional item response theory

Multidimensional item response theory (MIRT) has been developing from its Factor Analytic and unidimensional item response theory (IRT) roots. This development has led to an increased emphasis on precise modeling of item-examinee interaction and a decreased emphasis on data reduction and simplification. MIRT represents a broad family of probabilistic models designed to portray an examinee’s […]

The IRT Item Pseudo-guessing Parameter

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The item pseudo-guessing parameter is one of the three item parameters estimated under item response theory (IRT): discrimination a, difficulty b, and pseudo-guessing c. The parameter that is utilized only in the 3PL model is the pseudo-guessing parameter c.  It represents a lower asymptote for the probability of an examinee responding correctly to an item. […]

The IRT Item Discrimination Parameter

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The item discrimination parameter a is an index of item performance within the paradigm of item response theory (IRT).  There are three item parameters estimated with IRT: the discrimination a, the difficulty b, and the pseudo-guessing parameter c. The item parameter that is utilized in two IRT models, 2PL and 3PL, is the IRT item […]

The IRT Item Difficulty Parameter

man in the mountains for IRT b parameter post

The item difficulty parameter from item response theory (IRT) is both a shape parameter of the item response function (IRF) but also an important way to evaluate the performance of an item in a test.   Item Parameters and Models in IRT There are three item parameters estimated under dichotomous IRT: the item difficulty (b), […]

The One Parameter Logistic Model

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The One Parameter Logistic Model (OPLM or 1PL or IRT 1PL) is one of the three main dichotomous models in the Item Response Theory (IRT) framework. The OPLM combines mathematical properties of the Rasch model with the flexibility of the Two Parameter Logistic Model (2PL or IRT 2PL). In the OPLM, difficulty parameters, b, are […]

Ebel Method of Standard Setting

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The Ebel method of standard setting is a psychometric approach to establish a cut score for tests consisting of multiple-choice questions. It is usually used for high-stakes examinations in the fields of higher education, medical and health professions, and for selecting applicants. How is the Ebel method performed? The Ebel method requires a panel of […]

Item parameter drift

item parameter drift slide rule

Item parameter drift (IPD) refers to the phenomenon in which parameter values a given test item changes over multiple testing occasions within the item response theory (IRT) framework. This phenomenon is often relevant to student progress monitoring assessments where a set of items is used several times in one year, or across years, to track […]

Item fit analysis

Item Fit analysis red lines

Item fit analysis is a type of model-data fit evaluation that is specific to the performance of test items.  It is a very useful tool in interpreting and understanding test results, and in evaluating item performance. By implementing any psychometric model, we assume some sort of mathematical function is happening under the hood, and we […]