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…

Traditional estimators of reliability such as coefficients alpha, theta, omega, and rho (maximal reliability) are prone to give radical underestimates of reliability for the tests common when testing educational achievement. These tests are often structured by widely deviating item difficulties. This is a typical pattern where the traditional…

Test-takers, policymakers, teachers, and institutions are increasingly demanding that testing programs provide more detailed feedback regarding test performance. As a result, there has been a growing interest in the reporting of subscores that potentially provide such detailed feedback. Haberman developed a method based on classical test theory…

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…

As students are exposed to extreme temperatures with ever-increasing frequency, it is important to understand how such exposure affects student learning. In this paper we draw upon detailed student achievement data, combined with high-resolution weather records, to paint a clear portrait of the effect of temperature on student learning across a…

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…

The use of the aggregate scoring method for scoring concordance tests requires the weighting of test items to be derived from the performance of a group of experts who take the test under the same conditions as the examinees. However, the average score of experts constituting the reference panel remains a critical issue in the use of these tests.…

Though a substantial amount of research exists on imputing missing scores in educational assessments, there is little research on cases where responses or scores to an item are missing for all test takers. In this paper, we tackled the problem of imputing missing scores for tests for which the responses to an item are missing for all test takers.…

This study was conducted to further research into the impact of student-group item parameter drift (SIPD) --referred to as subpopulation item parameter drift in previous research-- on ability estimates and proficiency classification accuracy when occurring in the discrimination parameter of a 2-PL item response theory (IRT) model. Using Monte…

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…

In operational testing, item response theory (IRT) models for dichotomous responses are popular for measuring a single latent construct [theta], such as cognitive ability in a content domain. Estimates of [theta], also called IRT scores or [theta hat], can be computed using estimators based on the likelihood function, such as maximum likelihood…

Coefficient alpha reliability persists as the most common reliability coefficient reported in research. The assumptions for its use are, however, not well-understood. The current paper challenges the commonly used expressions of coefficient alpha and argues that while these expressions are correct when estimating reliability for summed scores,…

We develop a "latent variable forest" (LV Forest) algorithm for the estimation of latent variable scores with one or more latent variables. LV Forest estimates unbiased latent variable scores based on "confirmatory factor analysis" (CFA) models with ordinal and/or numerical response variables. Through parametric model…

The multistage testing (MST) design has been gaining attention and popularity in educational assessments. For testing programs that have small test-taker samples, it is challenging to calibrate new items to replenish the item pool. In the current research, we used the item pools from an operational MST program to illustrate how research studies…

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…